LLM-based Typed Hyperresolution for Commonsense Reasoning with Knowledge Bases
Authors: Armin Toroghi
Ali Pesaranghader
Tanmana Sadhu
Scott Sanner
Venue: ICLR 2025 Poster (2025)
Keywords: Large Language Models
Commonsense reasoning
Logical inference
Primary area: foundation or frontier models, including LLMs

Abstract: Large language models (LLM) are being increasingly applied to tasks requiring commonsense reasoning. Despite their outstanding potential, the reasoning process of LLMs is prone to errors and hallucinations that hinder their applicability, especially in high-stakes scenarios. Several works have attempted to enhance commonsense reasoning performance of LLMs by (i) using prompting styles that elicit more accurate reasoning, (ii) utilizing the LLM as a semantic parser for a symbolic reasoner, or (iii) enforcing the LLM to simulate a logical inference rule.  However, all these solutions have critical limitations: they are unable to leverage the internal commonsense knowledge of the LLM in tandem with an axiomatic knowledge base, they lack a mechanism to reliably repair erroneous inference steps, and their application is restricted to small knowledge bases that fit the context limit of the LLM. In this work, we present LLM-based Typed Hyperresolution (LLM-TH), a logical commonsense reasoning framework that leverages "theory resolution", a concept from classical logical inference which enables integrating LLMs into the "resolution" inference rule, thus mitigating reasoning errors and hallucinations and enabling verification of the reasoning procedure. LLM-TH is also equipped with a mechanism for repairing erroneous inference steps supported by theoretical guarantees. Using "Hyperresolution" and "Typed inference" schemes, we show that LLM-TH can efficiently reason over large knowledge bases consisting of tens of thousands of rules with arbitrary predicate arities. Our experiments on three diverse language-based reasoning tasks—preference reasoning, multi-domain deductive reasoning, and geographical question answering—showcase that LLM-TH, using merely a BART 406M parameter NLI entailment model, significantly reduces reasoning errors compared to baselines using Llama3-70B, Gemini1.5-Flash, GPT-3.5-Turbo, and Mixtral-46.7B.

Published as a conference paper at ICLR 2025
LLM-BASED TYPED HYPERRESOLUTION FOR COM- MONSENSE REASONING WITH KNOWLEDGE BASES
Armin Toroghi', Ali Pesaranghader', Tanmana Sadhu Scott Sanner University of Toronto, 'LG Electronics, Toronto AI Lab, VVector Institute of Al armin. toroghi @ma 1, utoronto. ca, fali.pesaranghader tanmana sadhu @1ge com
ABSTRACT
Large language models (LLM) being increasingly applied to tasks requiring commonsense reasoning. Despite their outstanding potential, the reasoning pro- cess of LLMs prone errors and hallucinations that hinder their applicabil- ity. especially in high-stakes scenarios. Several works have attempted to enhance commonsense reasoning performance of LLMs by (i) using prompting styles that elicit more accurate reasoning. (ii) utilizing the LLM as semantic parser for a symbolic reasoner, or (iii) enforcing the LLM to simulate a logical inference rule. However, all these solutions have critical limitations: they are unable to leverage the internal commonsense knowledge of the LLM in tandem with an axiomatic knowledge base, they lack mechanism reliably repair erroneous inference steps, and their application restricted to small knowledge bases that fit the con- text limit of the LLM. In this work, we present LLM--based Typed Hyperresolution (LLM-TH), a logical commonsense reasoning framework that leverages "theory resolution" ", concept from classical logical inference which enables integrat- ing LLMs into the "resolution" inference rule, thus mitigating reasoning errors and hallucinations and enabling verification of the reasoning procedure. LLM- TH is also equipped with a mechanism for repairing erroneous inference steps supported by theoretical guarantees. Using "Hyperresolution" " and "Typed infer- ence" schemes, we show that LLM-TH can efficiently reason over large knowl- edge bases consisting of tens of thousands of rules with arbitrary predicate arities. Our experiments on three diverse language-based reasoning tasks preffrenee reasoning, multi-domain deductive reasoning. and geographical question answer- ing showcase that LLM-TH, using merely BART 406M parameter NLI entail- ment model, significantly reduces reasoning errors compared to baselines using Llama3-70B, Geminil F--Flsh,, GPT-3.5-Turbo, and Mixtral-46.7B.
INTRODUCTION
The breakthrough in Large Language Models (LLMs) has significantly impacted AI research, paving the way for deploying Al-powered systems in various tasks and applications. This huge impact primarily due to the outstanding performance of LLMs in tasks that require substantial reasoning skills (Chang et al. 2024 Plaat et al. 2024). LLMs have also acquired commonsense understanding, critical element for interacting with the real world (Zhao et al. 2024 Valmeekam et al.) 2024). However, reasoning performance of LLMs is not infallible, LLMs commonly show reasoning errors and make hallucinations- geeerrainngggggggggeeeennn incorrect outputs that seem valid-which which hinders their reliable
deployment, particularly in high-risk tasks (Tonmoy al. 2024 /Zhan al. 2023b).
To overcome these challenges in LLM--bsedd reasoning, several approaches have been proposed in the literature that can be broadly categorized into three groups: (i) Using prompting styles that
can elicit more accurate reasoning from the LLM (Wei et al. 2022 Kojima al. 2022 Zhou
et al. 2022 or augmenting the prompt by retrieved information (Lewis et al. 2020b). b). (ii) using
the LLM translate natural language problem and knowledge bases (KB) for symbolic logical
solver OOlausson et al. 2023 Pan et al. (2023), and (iii) using the LLM to emulate logical inference
rule solve the reasoning problem (azemi et al. 2023 Lee & Hwang 2024).

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Figure 1: Workflow of LLM-TH shown with preference reasoning example. Top: Using LLM-based typed hyperresolution to compute proof scores for each recipe option to entail user query. Negated query is the first active clause, and each resolvent is assigned priority ple: (type entailment score, predicate entailment score, score,proof length score) and pushed to the prior- ity queue (only the foremost clause is shown for priority queue of recipe which becomes the next active clause). LLM makes two mistakes; assigming low score to "Souvlaki" entailing "Mediter- ranean" and high score to "cuttlefish" entailing "fish". Bottom: Both kinds of mistakes can be fixed after the insertion of repair axioms, resulting in the correct recommendation of Recipe 1.
These works have advanced the logical reasoning performance of LLMs; yet, they are hindered by number of important limitations: (a) Their application is limited to small KBs that can fit into the context limit of the LLM,, and are not scalable to practical KBs such as the widely-used Knowledge Graphs (KG) containing thousands of facts and axioms. (b) They are restricted to reason on complete KB containing all rules required to solve the problem. However, assuming access to such KB is typically unrealistic in practical use cases, thus calling for methodology to leverage the internal commonsense knowledge of the LLM the reasoning process. (c) All steps involved in the reasoning process are not transparent and thus, the correctness of the final answer cannot be determined by inspecting the reasoning process. (d) Upon observation of a reasoning error, they do provide any reliable framework to fix the error and ensure will not occur in the future.
In this work, we aim to address these limitations by making the following contributions:
We introduce LLM-based Typed Hyperersolution (LLM-TH), a framework for efficient complex logical commonsense reasoning with KBs containing predicates of arbitrary arti- ties, that facilitates the incorporation of the internal commonsense knowledge of LLMs in
the reasoning process. M. is founded on "theory resolution" " (Stickel 1985 Baum- |gartner 1992). concept from classical logical reasoning that allows for the incorporation of specialized theorem provers into the resolution inference rule. (Section 3.1
We equip LLM-TH with mechanism for incorporating the type information of the vari- ables and constants in the problem domain to prune the proof search space and terminate the exploration of reasoning paths that are unlikely to succeed at very early stages. Also, using hyperresolution, an extension of resolution that enables combining clauses to per- form several resolution steps simultaneously, make LLM-TH efficient and scalable
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'epecias sninal specks, anlmal, place
(4.9)
furb) mnddpe, flnn :aggodiorr
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Typed Resolution
it have types which are recip Ingrodient, respectively.
"lee aalling acthrtay (6) "-Aepodee Rab)) "meditrrraeen" (a) -paaii aone leattye)
Untyped Resolution (Incorrect)
Typed Resolation (Correct)
An example of typing mechanism of LLM-TH. The binary predicate "contains" is com- mon among clauses from different domains. Left: Application of resolution rule without considering types leads to resolving a literal about "recipes" with complementary literals from domains such as "animals" " Each incorrect resolution results in new branch that will be explored but lcads to fail- ure, making the process inefficient. Right: in typed resolution, only literals with consistent variable and constant types will be unified, therefore pruning the search space and enhancing effficieny..
Figure 2:
reasoning framework for logical commonsense reasoning with LLMs. We show that LLM- TH is easily scalable to KBs consisting of tens of thousands of rules. (Section 5.2.1
We show that by providing access to the exact axioms and facts used every reasoning step, LLM-TH results in a verifiable and faithful reasoning performance. Furthermore, we propose a reliable repair methodology for missed inferences and incorrect reasoning steps due to LLM hallucinations and missed inferences, and provide theoretical proof that it reliably fixes reasoning errors. (Section
We show that by using the theory hyperresolution framework, LLM-TH is able to leverage the internal commonsense knowledge of the LLM to compensate for KB incompleteness and perform accurate and reliable reasoning. (Section 5.2.22
We experiment with LLM-TH on three different tasks involving commonsense reasoning: preference reasoning, multi-domain deductive reasoning, and geographical QA, showcas- ing the superiority of LLM- TH in terms of answer and reasoning accuracy over Chain of Thought (Kojima et al. 2022: Wei et al. 2022) and retrieval augmented generation (RAG) (Lewis et al. 2020b baselines using orders of magnitude larger L.MMs. (Section
2 RELATED WORKS
Enhancing LLM Reasoning As LLMs scale, they exhibit emergent behaviors such as the ca- pability of solving problems that involve reasoning (Chang et al. 2024 Huang & Chang 2022) However, their reasoning performance often suffers from errors and hallucination
facts in their inferences (Tonmoy al. 2024 Zhang et al./ 2023b). Several works have shown that with certain prompting techniques such as Chain of Thought (CoT) (Wei et al., 2022 Kojima et al. 2022), Tree of thought (Yao et al. 2024), Selection-Inference (Creswell et al. 2022). Self-consistency (Wang) et al., (0022). Least-to-most prompting (Zhou et al., 2022). etc., more accurate reasoning can be elicited from LLMs. Retrieval Augmented Generation (RAG) (Lewis al., 2020b) has also been noted as an effective approach in reducing reasoning errors and hallucinations by including relevant content retrieved from KB in the prompt to condition LLM's reasoning on dependable information. These methods have made significant progress in advancing the reasoning behavior of LLMs. but even applying them does not guarantee an accurate reasoning behavior from the LLM. Furthermore, since the L.M is entirely in charge of doing the reasoning. there is control over the reasoning process and its correctness cannot be verified (Shanahan 2024 Pan et al. 2023). Moreover, the per- formance of these methods has been shown to degrade when being applied to long-horizon (Dzini et al. 2024) and out-of-domain (Saparov et al. 2024) reasoning tasks as well as problems involving negation (Anil et al. 2022) and contraposition ZZhang et al., 2024).
Formal Reasoning with LLMs To offer more control over the reasoning process, two groups of work have been proposed for formal reasoning with L.LMs: (i) Semantic parsing methods remove
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the LLM from reasoning and only use it to translate the problem into symbolic format and delegate
the reasoning task to a symbolic solver (Pan et al. 2023 Olausson et al. 2023). (ii) Works enforcing the LLM to emulate an established logical inference rule such as backchaining (Kazemi al. 2023
Lee & Hwang 2024). While these works make progress mitigating hallucinations, they rely on the existing KB rules and have mechanism use the rich commonsense knowledge of the LLM in their reasoning. Although recent works (Toroghi et al. (022a) used resolution inference rule for LLM-based reasoning, they are restricted unary predicates and small KBs.
Commonsense Reasoning with LLMs
We refer the reader to Appendix
3 METHODOLOGY
We first review the rreslttnnoolutioo rule for inference in first-order logic using a function and equality-free first-order logical (FOL) syntax in clausal normal form (Chang Lee 2014). We then proceed to introduce the concept of Theory resolution that leverages external sources of knowl- edge (such as LLMs) to augment the resolution process. Next, we introduce the concept of typed resolution that will be critical for improving the efficiency of inference in our work by prioritiz- ing inference with compatible types and reducing proof length. With all of these ingredients in place, we conclude with LLM Theory Hyperresolution algorithm (LLM-TH) along with crucial propositions that ensure the correctness of repair axioms used to override incorrect LLM inferences.
Resolution Rule and Hyperresolution Resolution is sound and complete inference rule which is widely used in logical reasoning. From two premise clauses containing complementary literals, resolution rule derives a resolvent clause by canceling (resolving) the complementary literals, e.g..
A(x) V B(x,v) -B(w, 2) V C(z)
A(x) V C(y)
(1)
under the unification 0 0= (x/u; y/z]. Repeated application of the resolution rule will either result in a contradiction, e.g., deriving both A(x) and -A(x) indicating an inconsistent clause set, or reaching a point where no further resolutions are possible.
The efficiency of the repeated application of the resolution rule can be substantially improved by hyeperresolution (Robinson] 1965). an extension of resolution that enables combining multiple res- olution steps in one inference step. Concretely, it resolves positive literals with all possible matching negative clauses simultaneously, e.g.,
A(x) V v)... V Ba(x, v) A(x) V C(y)
V -B,(w, (x/w, /. y/=}.
(2)
LLM-based Theory Resolution Application of the resolution rule is originally restricted to clauses with complementary literals that share identical predicates. Theory resolution (Stickel) 1985] Baumgartnnr] 1992) relaxes this condition and broadens the applicability of the resolution rule by integrating special-purpose theories into resolution. Based on theory resolution, given two clauses e = A(x) V Bax, y) and C2 = -C(w, 2) V D(=), if theorem prover identifies B(x, y) and -Cww, 2) under unification 0 = (x/w, 3/2} to be unsatisfiable (i.e., Vz,y y) A -C(x, y) hT 1), the clauses can be resolved despite lacking complimentary literals with identical predicates:
A(x) v B(x,v) -C(w, D(z) ,0 Lt/w,y/2)
A(x) V D(v)
(3)
In this work, we use an L.M as the theory that identifies the unsatisfiable natural language predi- cates to perform reasoning via theory resolution. Translating natural language to symbolic form, as semantic parsing methods do, substantially restricted. For example, semantic parsing will map "packs some heat" and being "spicy" completely different symbolic predicates. Therefore, symbolic reasoner is unable to discern their entailment relationship unless given explicit axioms.
Using LLM-based theory resolution, reasoning process to find entailments between predicates and constants without requiring explicit axioms. We do this in extended version of FOL in which predicates, functions, and constants
integrate the LLM's commonsense knowledge into the
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no longer symbols, but natural language text. In this logical system, which we call natural language logic, the unsatisfiability condition in theory resolution reduces to natural language entail- ment. In other words, if an LLM identifies natural language predicate B to entail predicate D, i.e., B(x) FILM Dxx), and therefore, B(x)) A -D(x) Ful 1, then literals Bax)) and (xx) can be resolved. For instance, given clauses a "packs some heat"(x:) and c2 - "sppicy" (1:) V Q(x). in which ((z) is another literal with natural language predicate, since the LLM identifies the natural language entailment "packs some heat" Fum "spicy". theory resolution step can be performed as
"packs some heat"(x) -" ((x) Q(x)
Q(z)
(4)
LLM-based Typed Theory Resolution Although resolution is one of the most widely used infer- ence rules in logical reasoning with the key properties of being sound and complete, its application on real-world large-scale knowledge bases is computationally expensive. One of the key challenges that the space of possible resolutions- the combinations of literals and clauses that can potentially be unified and resolved can become enormous, and grows exponentially during the resolution pro- cess, leading to inefficiencies finding contradictions or valid derivations. This challenge is often addressed by choosing particular orderings that first explore resolution steps that are more likely to lead to valid proofs (Baumgartner 1992, Sanner & Mcllraith (006).
In addition to proposing ordering strategy which is explained in 3.1 we introduce the notion of typing into theory resolution which considerably prunes the space of possible resolutions. Many of the created resolvents during the resolution process, each opening new search branch, cre- ated by unifying variables and constants with inconsistent ontological types. For instance, a literal "small"(x) in clause about vehicles z can be resolved with literal -"small" animals y. However, the search branch created by this resolvent is very unlikely to result in a valid proof it uses semantically unlikely unification (vehicle-animall that is likely to lead to failed inference in subsequent steps. By associating variables and constants with their ontological types and considering type consistency in unification, we can significantly prune the space of allowable resolutions, by preventing the exploration of type inconsistent branches from the beginning.
which is about
Variable types can be introduced into an FOL sentence as unary predicates, e.g., "animal" (x:). Considering a universally quantified sentence in FOL as
Vr (xx) A T(v) A A(z,v) = R(r,y),
(5)
where H() and T()) are unary predicates indicating types of their corresponding variables. we equivalently write the above sentence in the ryped FOL
ArVy A(x,y) = R(z, y)(x H,y T. where, x H and y T indicate that x and y are of type H and T respectively. This clause can be equivalently written in the clausal form as
(6)
VrVy -A v) V R[z,,){x TT
Next, consider another clause in typed FOL as
VZvz -R(w, 2) V S(w, 2) M, x N. Using the unifier 0 = [w//2 2/ s/v.. we can perform ryped resolution between the clauses 7 and g
(8)
as
-A(z, V R(z, v) H,y : - -R(w, 2) V S(w, 2)(w M, N
A((, u) ((x,,)<> C, : D
where C' and D, the types of resolvent variables are C = HDM and D = TTNN using the following lemma which is proved in Appendix A Here, n indicates unary type intersection (conjunction). Lemma 1. Resolving two disjunctive clauses Ci and 02 that include complimentary literals 1(I ...,,.... [21 TI....,,, un. Tn and -1(y1,.., Un 11) HI,.., Vo. Hn, under the unifier 8 = (=1/ y1. ..., D2/ y2) creates a resolvent Cres with type variables x1 Ti r. HI...., In. Tr 17 TT,
Typed resolution can be directly extended to typed theory resolution in our natural language-based In. In. : T, and D(yi,.., yn 1891 :
logical system by resolving literals B(z 2.,)))..,,,))a 2x)]21
H1...., Hn if the LLM identifies the natural language predicate B to entail D. i.e., B(x), ..., 2x,) Frum D(y y,)) if their unified variables have consistent types. In the next section, elaborate on how type consistency is checked in our L.M-TH framework.
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Algorithm LLM-TH Algorithm
Input: K., g. max-proofs, max I. J
2: proofs 5 0
3: PQ 0 PQ is an initially empty priority queue.
4: PQ.push(~p) (1, 1)) // Negation of has priority (1. PQ is ordered by Equation 15
5: 5-0
6: while (PQ * 0) A (Iproofs) S maxxprrofs) A max_iters) do
7: c c P.-PQ-pop()
8:
c then
9:
proofs + proofs U ((Ac, (p'(c), (c), IIA. is the set of ancestors of c, found by backtracking up to -q
10: else
Be candidate clauses in K. with similar arity and different polarity 12: for Ctarget E B. do
Perform hyperresolution to compute resolvent Gee of c and Grareet using Equation 2
PQ push(Crss (Ges), (crss, (Cres) // cf. Equations 11 13 and 14
i 1+i+1
Output: proof'
3.1 LLM-TH ALGORITHM
We present LLM-TH, an algorithm for efficient logical commonsense reasoning that extends the- ory resolution LLM-based reasoning with predicates of arbitrary arity, hyperresolution and type inference. Its workflow is presented in Figures [and] Algorithm 1 and explained in Appendix
Problem Definition Let denote set of queries and represent a knowledge base (KB) com- prising a set of axioms and facts, a set of intended repair axioms I, and set of forbidden repair axioms F, all expressed in natural language logic and clausal form with arbitrary predicate arities. For each query q E Q. LLM-TH identifies set of proofs, denoted as proofs. Each proof prooff consists of a subset clauses in K,, and assigned a priority score p.
Algorithm To prove K entails the query via resolution, we need to show that repeatedly using the resolution rule on KA -q leads to a contradiction, and thus unsatisfiable. Following the backward chaining paradigm that offers efficiency benefits (Poole & Mackworth) 2010), we pick -y as the first
active clause to be resolved with a clause from K. At each step, given an active clause
Vld 4
where each 4; is literal of arbitrary arity, any clause Craggr E K. as Crorger considered a candidate clause to be theory resolved with c, yielding the resolvent Cress if at least one (4,, harges, ) pair can be formed where 1 and harger, have equal arities and different polarities. One can lift this polarity restriction for theory resolutions to allow implicit negation in the language of the predicate (e.g.." "nol spicy") in contrast to explicit logical negation (e.g., ""spicy")) As AC is often large and expands further with new resolvents being derived as resolution advances, efficiency is key desideratum, which LLM-TH achieves by prioritizing candidate clauses based on two criteria: (i) type consistency and (ii) predicate entailment between the active and candidate clauses.
i=1 lurger, is
Restricting the Space of Resolutions with Typing: The first mechanism used by LLM-TH to improve efficiency is the use of typed theory resolution to restrict the space of allowable resolutions. In typed theory resolution, the types of variables in the resolvent clause are determined by the conjunction of the types of variables in their parent clause, hence LLM-TH prioritizes clauses with variable types that align with the active clause to encourage valid types. For example, if two candidate clauses are considered to be resolved with an active clause of variable type "Animal". LLM-TH prioritizes candidate clause with a unifying variable type "Mammal" over one with type "Vehicle".
LLM-TH leverages the commonsense knowledge of the LLM to obtain the probability of entailment between the variable types. Formally, for the pair of literals with equal arities (1. hwrgee) denoting the set of argument types of I and hurger T {t,) and T" {t'} respectively, the plausibility of unifying each of their variables can be obtained by calculating the entailment probabilities between each I, and f. Since entailment is an asymmetric relation and its direction is unknown, need to

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calculate both FLLM ti and t FLLm to obtain the type consistency score. The average of type entailment scores for arguments determines pT (Cres), the overall type priority score for Cres-
0 (Cres)
Ei (max/p(t; Fulm (.),, p(t FLLM 4))).
(10)
[7:
Since the main objective is to find the most plausible proofs, i.c., the sequences of most plausible theory resolution steps, we define the first entry of our priority score for each Ges as the overall type consistency score of all resolution steps beginning from -q that led to its derivation. Let Pa.. be the set of parent clauses of Gres; the proof type consistency score of Cres is inductively defined as
( II (((d)
p² (Crres)
(11)
Pers
d'EPens
Resolution Ordering based on Predicate Entailment: Assigning the type consistency scores prunes the resolution search space ensuring that only clauses with compatible argument types will be con- sidered for resolution. To further enhance efficiency, L.MMTH prioritizes the remaining clauses based on their potential for being part of a plausible proof considering their predicate entailment. As explained, in our LLM-based theory resolution framework, LLM entailment is used to identify unsatisfiability of clauses. Therefore, the greater probability the LLM assigns to burrer entailing I the more plausible it becomes to resolve and harger. Therefore we define the plausibility of a theory resolution step between c and Guargrr by resolving literals I and larger generating Cress denoted by pontait
if (hurger F 1) E I. if -hharger | 1) F,
entaii Pero
0
(12)
P(laarger FLLm 1) otherwise.
These plausibility scores can help us prioritize the resolvent clauses based on their predicate entail- ment. For example, in the scenario depicted in Figure resolving "Sicilian" with "Mediterranean" results in a higher entailment score compared to resolving "Mussard-flavorer ranean". Hence, it is prudent prioritize the former resolvent, it is more likely to contribute to the final proof. As the definition of the overall proof type consistency score, we can compute the overall predicate entailment score inductively to obtain the second entry of our priority score as
with "Mediter-
p² (Cmrs) =
II p'((e))
(13)
e'EP...
Ultimately, among equally plausible proofs, we prioritize shorter ones that circumvent unnecessary steps. We define the proof length score, third priority score that accounts for this preference. The proof length score of Cres is derived inductively from the maximum length of its parent clauses as
(CCrs) + max pc(c)) d'EPrm
(14)
Each resolvent Cres is assigned the priority tuple (crea, (Cres) (Cres) and then pushed to the priority queue PQ, in which the order of clauses is specified as
c C2 = le (c) of (cz)) (('' ((2))) A (c) (c22)
(15)
V (())) A (c)) = (c)) ^ (p'(c)) < pc2(c))).
By applying this prioritization scheme, the type consistency priority score first applies a hard filter to avoid exploration of resolvents with invalid types, and the predicate entailment and length priorities together enable an efficient inference via LLM-based theory resolution. These efficiency enhance- ments enable LLM-TH be applied to large-scale KBs. Furthermore, is able to reason over incomplete KBs by benefiting from the commonsense knowledge of the LLM to fill in the missing axioms by identifying entailing predicates in the theory resolution process.
At the start of each iteration of LLM-TH, the clause with the highest rank in PQ becomes the active clause. When resolution step yields a contradiction, the proof and its respective priority score are added to the set of found proofs by backtracking the ancestor clauses. The algorithm terminates when either a certain number of proofs are found or the maximum number of iterations is exceeded. Notably, LLM-TH is not limited to proving single query; instead, it finds set of proofs and assigns a strength score to each. This feature enables it to evaluate the likelihood of each query being entailed, which is critical for tasks requiring ranking, such answering multiple-choice questions. Furthermore, LLM-TH can reason on incomllete KBs by using the LLM's 's commonsense knowledge to fill in the missing axioms by identifying entailed predicates via theory resolution.
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4 FIXING ERRONEOUS RESOLUTIONS IN LLM-TH TH
LLM-TH enables verification of the reasoning process by providing access to atomic resolution steps. Therefore, if an incorrect theory resolution step is identified, the source of failure can be provably repaired. In the example of Figure | the LLM's mistake in assigning a low probability for "Souvlaki" to entail "Mediterranean" " leads "cuttllefish" to entail being "fish" " leads to an incorrect resolution. To fix both errors, we (1) insert the missing axiom vy" "Suuvlaki" (y) = "Mediterranean "(y) to I and (2) insert the forbidden axiom "cuttlefish" VLM "fish" to F. The formal propositions below are proved in Appendix B
missed resolution. Also, incorrectly considering
Proposition 1. Consider proof P using axiom & that derives clause c. For missing LLM reasoning axiom i Repair Axiom ø' can be inserted into I such that Po' will be produced before P
Proposition 2. Consider proof Pg using axiom & that derives clause c. For any incorrect L.M reasoning axiom @, a Repair Axiom o' can be inserted into F such that p will receive priority O.
EXPERIMENTS
We empirically evaluate LLM-TH on three different tasks representing commonsense reasoning with KBs on different datasets and compare it against variations of four different baselines to com- pare them from different aspects by answering the following questions:
RQ1-Scalabilityy How does the reasoning performance of LLM-TH compare to baselines when reasoning with large, but complete knowledge bases?
RQ2-Reasoning with incomplete KBs: How effectively do LLM-TH and the baselines use the LLM's commonsense knowledge compensate for the incompleteness of the KB?
RQ3-Efficiency: How is the efficiency of LLM-TH influenced by typed hyperresolution?
5.1 TASKS AND DATASETS DESCRIPTION
Preference reasoning: An exemplar commonsense reasoning task is providing recommen- dations using natural language statements of user preferences and restrictions. For this task, we use Recipe-MPR (Zhang et al., 2023a), a dataset consisting of 500 queries, e.g., "/ want French food, but m budger" and five-way recipe options. This dataset covers broad range of commonsense reasoning skills such as temporal and analogical reasoning.
Multi-domain Deductive reasoning: Since established datasets for logical commonsense reasoning with LLMs, e.g., ProntoQA (Saparov & He 2022) and COPA-SSE (Brassard ct al. 2022). have small KBs with less than 20 facts and axioms per query, we find them insufficient for evaluating the reasoning capability on large KBs. Thus, following the approach in Saparov & He (2022). we create a deductive reasoning dataset using man- ually written commonsense axioms and ground facts sampled from Wikidata knowledge graph (Vrandečić & Krötzsch 2014). This dataset contains more than 32k rules about five different domains: Biological entities, foods, vehicles, drugs and diseases, and sports, and 1000 queries that answering them requires 2 to 7 reasoning steps. We release this dataset to encourage research on LLM-bassed commonsense reasoning on large-scale KBs.
Geographical QA: Using the same approach for generating the multi-domain deductive reasoning dataset, we create KB about geographical entities, e.g., cities, deserts, muse- ums, etc. containing more than 12k rules and 500 queries which we also release.
5.2 BASELINES AND EVALUATION
We use established methodologies for eliciting more faithful reasoning from the LLMs as our com- parison baselines: (a) zero-shot CoT (Kojima et al. 2022). ) (b) few-shot CoT (Wei et al. 2022), and (c) RAG (Lewis et al., 2020b) using dense retriever (Song et al. 2020) to find relevant rules from the KB and prompting the LLM with zero-shot CoT and (d) few-shot COT. (c) To enable compari- son to semantic parsing (Pan et al. 2023 Olausson et al. 2023), we provide them with ideal KB
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Table 1: Reasoning performance of methods across the three datasets on complete KBs.
Method
Preference Reasoning
Deductive Reasoming
Goographical
Accuracy
Macro
Miero
Accurncy
Macro
RS Micro
Accuracy
RS Macro
Micro
GPI-35 Tarbo
Zeno-Shot CoT
0. 0.8600.04
0.60
0.80
0.6920.02
0.45
0.48
0.71::003
0.60
0.77
Few-Shox
0.7700.22
0.63=0055
0.22:00022
RAG Zero Shot CoT
NA
NA
NA
0.68:0002
0.85
0.92
0.74100001
0.80
0.88
RAG Fow-Stot CoT
NA
NA
NA
0.69::0.02
0.65
0.84
0.83:10.02
0,75
0.84
Gemini-1.5.. 1.5.Flshh
Zero CoT
0.84=0.04
0.601:0011
0.7810:03
Sho-Shoe CoT
0.86-0.02
0.55
0.79
0.66+00.5
0.20
0.71
0.79+00.02
0.25
0.54
RAG Zero-S Shot CoT
NA
NA
NA
0.78::0.02
0.85
0.93
0.79
0.50
0.72
RAG Few-Shot CoT
NA
0.86++0.44
0.78+D0.0
0:25
Llama3 708
Shot CoT
0.87-0011
0.55
0.80
0.80++0.33
0.15
0.77
0.78+00.11
0.25
0.57
Fow-Stxx OCT
0.11-0.1
0.70
0.84
0.784 0.02
0.55
0.58
0.87:00022
0.45
0.45
RAG Zero-Shat CaT
NA
0.78-00011
0.87+0.000
0.65
RAG Fow-Shot CoT
NA
NA
NA
0.802:0002
0.75
0.80
0.91:10.02
0.65
0.71
Mistral 46.78
Zero Shat CoT
0.79=0.03
0.60
0.84
0.59
0.30
0.66
0.71+0.02
0.50
0.70
Few-Shot
0.74
0.67110.01
0.80.10.01
RAG Shro-Shot CaT
NA
NA
NA
0.65+00022
0.65
0.81
0.66++0.07
0.25
0.51
RAG Few Shot CoT
NA
NA
NA
0.46:10.03
0.30
0.43
0.70
0,50
0.65
VERA (TS SB)
0.86
NA
0.76
NA
0.68
NA
NA
Semantic Parsing
NA
NA
0.05
NA
LLM-TH (BART 406M)
0.84
0.90
0.94
1,00
L.00 1.00 1.00 1.00
1,00
including all axioms necessary to answer perfect semantic parse of the query (ef. Appendix C (e)
We also compare against (f) VERA (Liu et al., 2023). method for estimating commonsense plau- sibility of statements. VERA estimates a score in the range (0, 1), and we consider a score greater (smaller) than 0.5 as a True (False) prediction. Except VERA which uses T5 (Rafell et al. 2020).
we use different common LLMs for other baselines: (1) Gemini 1.5-flash. (2) Llama3 (70B), (3)
Mixtral (56.7B), and (4) GPT3.5 Turbo, while using BART large (Lewis et al. 2020a (406 M) and
RoBERTa large (Liu et al. 2019 (365 M) tuned on MNLI (Williams et al. 2018 dataset to obtain
entailment probabilities for LLM-TK TH. We use DyDatalo to perform hyperresolution for grounding on the KB facts and use Gemini 1.5-flash convert natural language axioms to clausal form.
We evaluate the reasoning performance based on both, (1) the correctness of the final answer, mea- sured by accuracy, and (2) the correctness of the reasoning process by evaluating proofs using the reasoning score (RS) (Kazemi et al.] 2023) metric which is manually calculated for 20 randomly chosen responses in which the final answer
correct. RS is typically assessed as binary deci- sion based on whether the predicted proof is entirely aligned with the ground truth proof (Kazemi al. 2023; Lee & Hwang 2024). which leads both a single erroneous step and wholly flawed reasoning being penalized equally. To achieve a more granular evaluation of the proofs, we calculate both the conventional macro RS and following the idea of Min et al. (2023), we propose metric which we call micro RS. Let P be a provided proof and pa valid ground truth proof. Using the indicator function T,, we define the micro RS for each query as R.S [PT Eper T(p P*).
Table 2:
Reasoning performance on incomplete KBs. Numbers in paren- thesis indicate the difference with the method's performance on complete KB (Table I with (f) showing a decrease (increase).
Heasening Staps Usvenage
Jwayped
Typas
Deductive Reasoning
Geographical QA
Method
Zero-Shot CoTl
Few-Shot CoT
Zero-Shot CoT
Few-Shot CoTl
GPT-3.5 Turbo
0.68 (0.031)
0.54.00.4 (0.151)
0.60=0002 (0.144)
0.64110.03 (0.19))
Dedudiv leaucting Goog
Batacet
Gemini- 1l5sFlshh
0.73 (0.05L)
0.7310.01 (0.13L)
0.68 (0.111)
0.6610:022 (0.111)
Figure 3: Influence of
1Jama3 708
0,77=0002 (1.01.)
0.77+0.01 (0.031)
0.660002 (0.211)
0.66+0.02 (0.25))
typing on the efficiency of the inference algo- rithm.
Mixuaa 46.7B
0.50.10.04 (0.144)
0. 0.402 (0.031)
0.53 (0.124)
0.58L0.03 (0.131)
1LM-TH (BART 406M)
0.97
0.95
LLM (RoBERT 356M)
0.96
0.92
"httss//hugginngface..
'httss//hugginnfacc. wacaaacccccco//aaaaeeeee

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Published as a conference paper at ICLR 2025
5.2.1 RQI: Reasoning Performance Complete KB Before proceed to the general case of reasoning with incomplete KBs, we first aim to study whether the typed hyperresolution method- ology of LLM-TH can scale to answer queries in an ideal and complete, yet large KB in comparison to the baselines. These results serve as an upper bound for incomplete KB reasoning performance and also allow to distinguish failure modes related to reasoning from failure modes related to KB incompleteness assessed in subsequent experiments. As the results in Table [ indicate, on the preference reasoning task with a small and implicit KB of the five available recipe options, although zero-shot and few-shot CoT with a large LLM such as Llama 3 (70B) yield superior accuracy. LLM- TH still shows a reasonable performance, exceeding zero-shot and few-shot CoT with Mixtral and is competitive with zero-shot CoT using GPT3.5 and Gemini despite using a substantially smaller LLM. For the reasoning scores, LLM-TH exhibits more correct and faithful reasoning process than all other methods. On this task, since the dataset does not contain an explicit KB, RAG-based base- lines reduce to zero-shot and few-shot COT. On larger KBs of deductive reasoning and geographical QA tasks, the limitations of existing -LM-based methods are revealed as none of them compare to the accuracy of LLM-TH. Furthermore, they all obtain imperfect reasoning scores, reflecting their hallucinations and reasoning errors. On these datasets, LLM-TH performs standard resolution which is a sound and complete inference rule, as reflected in the results. However, the existing semantic parsing methods that use off-the-shelf theorem provers (intended for mathematical theorem proving) are not scalable to these large instance-heav KBs, even with an ideal parser. While complete KBs are impractical in real-world use cases, results of this experiment highlight that existing baselines, as opposed to LLM-TH, exhibit reasoning failures on large scale KBs even when they are complete.
5.2.2 RQ2: Reasoning Performance on Incomplete KBs To enable reasoning over practical KBs, leveraging the commonsense reasoning ability of the LLM to compensate for KB incomplete- ness is essential. To assess this capability, our experiments on deductive reasoning and geographi- cal QA datasets that have explicit KBs, we simulate KB incompleteness by omitting one of the rules used in the proof of each query, to test whether the LLM can use its commonsense knowledge to deduce, e.g., "paying laxes" implies "earning revenue". ". Since few-shot and zero-shot CoT meth- ods rely solely on the internal L.MM knowledge, they are irrelevant to this RQ that examines the role of KB incompleteness. Hence, we compare L..M-TH against variations of RAG with zero-shot and few-shot CoT prompting. Results in Table show that using the theory hyperresolution framework, LLM-TH is able to achieve significantly higher accuracies compared to the RAG-based baselines that clearly struggle with incompleteness compared to RAG results for complete KBs in Table D
In order to provide further insight into the failure cases of RAG-based methods and the limitations of LLM-TH, we conduct a series of additional experiments with BAG-based methods using an ideal retriever, as well as robustness of different methods longer reasoning chains and different levels of KB incompleteness in Appendix D We provide comparative anecdotal examples in Appendix H
5.2.3 RQ3: Influence of Typing Efficiency To verify the efficiency enhancement offered by introducing type information to the hyperresolution framework of LLM-TH, we perform an ablation experiment on the complete KB, by comparing the average number of reasoning steps that LLM-TH takes to find the answers with its untyped variant that does not consider types in prioritization. In summary, the results of this experiment shown in Figure indicate that using the typed hyperreso- lution framework, a considerable improvement is obtained in the efficiency of the reasoning process by reducing the number of reasoming steps required to find the answers to almost half compare to the untyped variant. This efficiency benefit is crucial in interacting with vast real-world KBs.
6 CONCLUSION
We proposed LLM-TH for logical commonsense reasoning with large and incomplete KBs. Using theory resolution, LLM-TH integrates LLM commonsense knowledge into the resolution inference rule to enable reasoning over incomplete KBs with arbitrary predicates. LLM-TH shows strong performance: matches or outperforms baselines that use orders of magnitude larger LLMs; its use of an and repairability establish it as a solution for factual and correct reasoning on large-scale KBs. In summary, LLM-TH holds promise to significantly reduce hallucinations in M-M--baeed reasoning.
typed hyperresolution approach yields high efficiency gains; and its transparency
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Acknowledgments
This work supported by LG Electronics, Toronto Al Lab Grant Ref No. 2024-0565. We also thank Roxana Li for her valuable assistance evaluations.
By introducing LLM-TH, we tried enhance the transparency and increasing control over the reasoning process of LLM-based logical commonsense reasoning. However, draw- ing logically valid conclusions does not necessarily mean that all axioms, rules, and the internal commonsense knowledge of the LLM which are leveraged in the reasoning process follow ethical requirements. responsible and credible usage of LLM-TH, like any other reasoning framework, requires careful considerations and assessments of the knowledge base, the underlying LLM, and the user-defined axioms to ensure desired unbiased and ethical performance.
Ethics Statement:
Reproducibility Statement: We release all our code and data in the supplementary materials and the LLM- TH repository We also explain the experimental setup and dataset descriptions in Section 5 and include all prompts utilized for the LLM usage in Appendix G as well as in the supplementary materials.
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A PROOF OF LEMMA 1
Lemma 1. Resolving two disjunctive clauses O1 and C2 that include complimentary literals ((1 .... Kn)[a Ti Tn Tn and -1(31, mn Vn 11 11,,.. Un : Hn under the unifier 0 f2I/V1..... ................................ T2 22/V2] creates resolvent Cres with rype variables Ti H1 In, n 17 Tn.
Proof. Assume e₁ to be A(r In Vi(,,, In) Ti...., In Tn and cp to be -1(1 .... Vo V we can rewrite these clauses implication
B yo)ly/ I..... In Hn. Following 5
and 6
form FOL by adding type predicates
VE VEn A T((x.) A A AAI End = LII1....
(16)
2=1
Vy Vyn
H((y)) Aly.......
B(y Bn),
(17)
Converting these clauses to the disjunctive form yields
4. Van
(T(( V A(x1, (011,-..1))))
(18)
1=1
Vy
Vyn
H.(1)) V -lyh,,.... vn) V B(y1...., Vn).
(19)
i=1
Now, resolve (x11,... In) with -VV1....., Vn) under the unifier f21///2///1 (21//y...., y1..... 22/323
V T((x;) A(TI, II, Vi HH((s)) V -I(y),,..,,,))) Un) V B(y
V (T;(;; V (H, v A(T ...,,... F.,) V B B(I
(20)
which be rewritten
Vx
Ven
(1(x)) H.(x)) = A(E B(z
(21)
Therefore, the unary type predicates for each z; becomes the conjunction of the types from their parent clauses, which in our typed FOL notation, can be equivalently written as
Yzi,..., VI, A( En) V
Ti n H1 ...
T.. In Tn H
(22)
B PROOF OF REPAIRABILITY OF LLM-TH
Recall from Section 3.1 that we have two distinct sets of set of repair axioms:
Intended repair axioms I: these axioms used to provide missing information to the KB and are assigned priority score (cf. Equation 12 during inference since they are user- provided and known be true. proof with repair axiom will always receive higher priority over a proof using an equivalent L.LM inference (during theory resolution), since the equivalent LLM inference from entailment necessarily has priority score
Forbidden repair axioms F: these axioms are intended override erroneous LLM in- ferences (during theory resolution) and are assigned priority 0 (cf. Equation 12 during inference. Any proof that uses such forbidden axiom will automatically receive priority score due to Equation 13
We now formalize and prove these statements correctness. We begin by defining a proof p
P. U (Ø) the combined set of clauses P. and that derive clause
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Proposition 1. Consider proof p using axiom & that derives clause For missing LLM reasoning axiom o, Repair Axiom o' be inserted into I such that p will be produced before P
Proof. We can obtain the proof score of (P%) of clause by inductively unrolling Equation for p(()) over all ancestor clauses Pe that derive This yields a simple product form: of (Pa)
13
Po Heep. Petail Now, comparing two different derivations P and po of c, we can easily show
that pf (P > ps (P?) since ('(P'))
given that the explicit Repair
(²(P2))
Axiom has p = (following Equation 13 while the L.LM entailment score pfamail < 1. Hence,
the proof pe' containing the Repair Axiom o' will always be given precedence over p according to the total ordering of Equation 13 used prioritize proofs in the LLM-TH Algorithm T
Proposition 2. Consider proof Pg using axiom & that derives clause For any incorrect LLM reasoning axiom @, a Repair Axiom ø' can be inserted into such that P will receive priority 0.
Proof. In the presence of o', the priority score assigned the resolvent clause c, i.e. pemtail will be set to O following Equations 12 which then implies that the priority score of proof P must be according to 13), which is the product of priority scores of all constituent clauses of the proof. D
In general, priority 0 proofs contain a forbidden or zero probability entailment and should be avoided inference time.
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C COMPARISON TO EXISTING LLM-BASED FORMAL REASONING BASELINES
Existing formal reasoning methods with LLMss, i.e., semantic parsing methods and methods emulat- ing inference rules, suffer from two limitations that make them inapplicable to our studied datasets: (i) they cannot leverage the internal commonsense knowledge of the LLM and only rely on an ex- plicit and complete rule base, which Recipe-MPR lacks, (ii) They are limited to small KBs that fit the LLM context size, but our studied KBs are much larger.
Semantic parsing methods use the LLM to translate the KB and query to symbolic forms. Although these methods use the LLM solely for translating the NL problem into symbolic format, they in- clude all facts and axioms to the L.M in the context because they need the L.M to use consistent predicates and objects in its symbolic translation (otherwise, the symbolic reasoner will not be able to execute the symbolic problem). in recent work, Xu ct al. (2024) showed that even by including all facts and axioms in the context, these methods can have very high execution failure rates due to translation inconsistencies.
Since our large KBs exceed the LLM context limit, we cannot use the LLM in the same manner that semantic parsing baselines. Logic-LM (Pan et al., 2023) and LINC (Olausson et al. 2023). use for the translation process. Therefore, to ensure a fair comparison, we manually converted all of KB and queries to the symbolic format supported by Prover9 | the FOL theorem prover that both of these works used. We set the time limit of Prover9 to the maximum time it takes for LLM-TH to answer the same queries-as it does not support specifying the maximum number of inference steps. The major difference between LINC and Logic-LM is that the former performs multiple translations and uses majority voting on their results, but since we are using a perfect KB, they become equivalent. Similar to Logic-LM, we also experiment with two backup mechanisms for cases in which the symbolic solver fails: (i) randomly guessing the answer and (ii) using CoT.
When experimenting our deductive reasoning dataset (KB with about 32k rules), the Prover9 solver crashed and could not reason on problems with such large KB sizes. For the geographical QA dataset (KB with about 12k rules), the following results were obtained:
Method
Accuracy
Logic-LM/ LINC with Perfect Translation (no backup mechanism)
0.05
Logic-LM / LINC with Perfect Translation and random guess backup
0.61
Logic-LM LINC with Perfect Translation and CoT backup (GPT3.5)
0.73
Table 3: Accuracies obtained by semantic parsing baselines on the geographical reasoning data.
The underlying cause of Logic-LM's and LINC's imperfect symbolic reasoning component on these complete KBs is due to lack of design and optimization for large KBs with thousands of facts. To support this claim, it is important to note that the problems used by Logic-LM [2] and LINC [3] have much smaller KBs-ofice smaller than 30 facts-for which existing theorem provers like Prover9 sufficient as their experiments show. However, LLM-TH is equipped with efficiency enhancement and prioritization mechanisms such as typing and hyperresolution that significantly improve reasoning efficiency in these settings.
http://www.cs.um..cdhh m
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D ADDITIONAL EXPERIMENTS
In this section, provide set of additional experiments for more detailed evaluation of the LLM- TH and the studied baselines. Since the incomplete KB setting is more common in practical use cases, studying the behavior of different models in this setting more important than the complete KB case (which was studied in Section 5.2.1), all additional experiments that are introduced in this section focus on the incomplete KB case.
D.1 PERFORMANCE OF RAG-BASER BASELINES WITH IDEAL RETRIEVAL
In section 5.2.2 studied the performance of different RAG-based baselines on the incomplete KB cases on the deductive reasoning and geographical QA cases and showed that LLM-TH considerably outperforms these baselines. However, it not clear whether the inferior performance of RAG-based baselines is due to the failure of the retriever to retrieve the relevant facts and axioms, or that the LLMs are challenged with indicating the missing commonsense axioms from an incomplete KB and compensating for them. In this experiment, to have more fine-grained analysis of the performance of the RAG-based baselines, we repeat the experiments with these baselines, but this time we ensure that all the relevant facts and axioms in the ground truth proof are included in the set of retrieved rules to simulate an ideal retrieval setting.
Results of this experiment are presented in Table As expected, in all cases, the performance of different methods with ideal retrieval enhanced considerably, which indicates that the retriever failure is critical limitation in the performance of the RAG-based baselines. However, even though under the ideal retrieval condition, the gap between the performance the LLM-TH and that of the RAG-based baselines narrowed, e.g., Llama3 70B and Gemini 1.5-Flash achieve accuracies of 0.94 and 0.93 with ideal retrieval and few-shot prompting, the accuracies obtained by LLM-TH using considerably smaller LLMs is still superior. This experiment indicates the restrictions of directly applying LLMs to the task of logical reasoning on incomplete KBs, as they have limited ability to correctly identify the missing commonsense axioms to compensate for the KB incompleteness and provide logical proof, a task that LLM-TK can perform more aptly.
Table 4: Comparison of the performance of RAG-based baselines with an ideal retriever with the original retriever used. The substantial improvement in results when using an ideal retriever suggests a notable part of the incorrect answers are due to failure in the retrieval stage. However, even by using an ideal retriever, the RAG-based baselines cannot outperform LLM-TH, despite using substantially larger LLMs. These results indicate that existing LLM- methods are challenged with the task reasoning over incomplete KBs, whereas LLM-TH can better identify the missing axioms and compensate for them.
Recooning
Geugraphiza QA
Methed
Meal Retrisval
Real Retrieval
Ideal Retrieval
Retrieval
Ideal Retrieval
Retrieval
Retrival
Real Retrieval
GPT-355 Tu/oo
0.67
0.54
0.69
0.69
071
L.M Co--in BART (0M)
0.97
0.85
LLM: TH casine RoBERT 356M)
0.96
0.92
D.2 ROBUSTNESS OF DIFFERENT METHODS TO LONGER REASONING CHAINS
As explained Section 5. our deductive reasoning and geographical QA datasets include queries that answering them requires different number of reasoning steps. Concretely, the deductive reason- ing dataset contains queries whose reasoning lengths range from to 7, and the geographical QA dataset contains queries of length 2, 8. and 11. In this experiment, we want to study the robustness of LLM-TH and the RAG-based baselines against increase in the length of reasoning steps required answer queries.
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To this end, provide fine-grained analysis of the results provided in Table 2 accuracy obtained by each method for each group of queries that require equal number of reasoning steps. Results of this experiment for the deductive reasoning and geographical QA datasets provided in Figure Sesureeeeaasssseeitivvellll For clarity of representation, we provide results of zero-shot prompting and few-shot prompting with the RAG baselines in separate plots. These results show that LLM-TH maintains its superior performance over the baselines across queries with different numbers of reasoning steps in most cases. Overall, LLM-TH and most baselines show a proper robustness to an increase in the number of reasoning steps. For instance, in the deductive reasoning dataset, most methods (including LLM-TH) obtain lower accuracy for queries with a reasoning length of 3, compared to the queries with reasoning length of 4. This suggests that in reasoning over the incomplete KB, the difficulty incurred by an increase the proof length dominated by the difficulty of commonsense reasoning required to relate the query predicates to the correct predicates from the KB. For instance, finding the connection between the query predicate "Sold by businesses in" " to the KB axiom predicate "Consumed by people in" " (a query about foods with a proof length of 3) is more challenging for these methods than finding the connection between "Can be used interchangeably" and "Is prescribed for same condition" (a query about medications with proof length of 4).
by evaluating the
Deductive Reasoning
Deductive Reasoning
1.40
1.40
LITTH DanhiRoo
ENITH Buaning
1.20
1.20
1.00
FAS-Zes Midee
1.00
Accuracy
Accuracy
0.80
0.80
0.60
0.60
0.40
0.40
0.20
0.20
0.00
0.00
2
3
4 5
7
3
5
6
Number of Reasoning Steps
Number of Reasoning Steps
(a)
(b)
Figure 4: Study of robustness of different methods to an increase in the length reasoning chains required to answering queries from the deductive reasoning dataset. Plot (a) compares LLM-TH to RAG-based baselines with zero-shot prompting and plot (b) compares it to RAG-based basclines with few-shot prompting.
Geographical QA
Geographical QA
1.40
1.40
LAN DE Dert
1.20
Bape tecchi Lanas
1.00
Accuracy
Accuracy
0.80
0.60
0.40
0.40
0.20
0.20
0.00
0.00
Number of Reasoning Steps
Number of Reasoning Steps
(b)
Figure 5: Study of robustness of different methods to an increase in the length of reasoning chains required answering queries from the geographical QA dataset. Plot (a) compares LLM-TH to RAG-based baselines with zero-shot prompting and plot (b) compares it to RAG-based baselines with few-shot prompting.
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D.3 ROBUSTNESS OF DIFFERENT METHODS TO DIFFERENT LEVELS OF K.B INCOMPLETENESS
In our previous experiments on the incomplete KB case, we ablated one commonsense axiom en- sure no direct connection exists between the query and the KB axioms. However, practical KBs may suffer from various levels of incompleteness, therefore reasoning on them may require performing multiple steps of commonsense reasoning to find the connection between the query and KB rules.
In this experiment, we study the robustness LLM-TH and the RAG-based baselines against differ- ent levels of KB incompleteness. To this end, we ablate different number of commonsense axioms from the KB and perform experiments using each method. Considering the number of KB axioms used in the ground truth proof for each query, the number of rules we can ablate is different, There- fore, we group queries based on the maximum number of rules that can ablated, while still valid proof can be found for it by using KB facts and axioms.
Results of this experiment for the deductive reasoning and geographical QA datasets are provided in Figures 6 and respectively. As expected, with an increase in the number of ablated rules, the commonsense reasoning required to find the connection between the query predicate and the remaining commonsense axioms from the KB axioms becomes more challenging, resulting in drop in the performance of most methods. In particular, we observe that the performance of LLM- TH using standard III models (both BART and RoBERTa) drops drastically with increase in the number of required reasoning steps, whereas RAG-based baselines exhibit stronger robustness to the KB incompleteness.
This trend stems from the limitation of entailment models in performing multi-step reasoning which required to answer queries with an increased level of KB incompleteness. For instance, when only 1 commonsense axiom is ablated from the KB, finding the proof requires theory resolving the query predicate "Submitted tax forms in" " with the predicate "Earned revenue in" " from the KB which the entailment models are capable of. However, when 3 rules are ablated, the required theory resolution between "Submitted lax forms " with "Played in" " which requires multiple steps of reasoning (e.g., "since the person played in a professional sport club which is located in country, they have earned income and therefore should have paid taxes in that country which requires submitting tax forms".
This multi-step reasoning is beyond the capability of relatively small NLI models that are employed by LLM-TH. To overcome this limitation, also experiment LLM-TH by using larger LLM, Llama 3.1 (8B). Since Llama 3.1 does not directly provide entailment probabilities, we study two predicates: (i) provide Chain of thought prompting with few-shot examples, asking the I.LM to provide an entailment score between to 1, and (ii) we obtain the joint log probabilities of the sequence "predicatel entails predicate 2.". As shown in Figure 4 using the log probability method still does not provide a satisfactory performance, since this approach also does not offer the required multi-step reasoning. However, using the chain of thought prompting approach, allows the LLM to perform the multi-step reasoning and eventually propose final entailment score which results to robust performance of LLM-TH in even higher levels of KB incompleteness, outperforming RAG-based baselines that use even larger LLMs.
different methods to obtain entailment probabilities between
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Deductive Reasoning (Max Ablations: 1)
Deductive Reasoning (Max Ablations: 1)
1.75
1.50
1.50
Lakilis Lalmaa carder
Rad zono Sree
1.25
Accuracy
1.25
Akdi Aodindarro
Accuracy
1.00
1.00
0.75
0.75
0.50
0.25
0.00
0.00
0
Number of Ablated Rules
Number of Ablated Rules
(a)
(b)
Deductive Reasoning [Max Ablatioons: 2)
Deductive Reasoning (Max Ablations: 2)
1.50
Un le pueeto
1.50
LMM (5.80E0) 1Jamakoo
UNTTI Lrmneeunonn
LIKTI Mir-2mndee
1.25
Accuracy
Ban ttee frem
Accuracy
H6D1 we
1.00
1.00
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0
Number of Ablated Rules
Number of Ablated Rules
a
(b)
Deductive Reasoning (Max Ablations: 3)
Deductive Reasoning (Max Ablations: 3)
LUVTH Bart
1.50
1.50
Med-dendSer CFT55
1.25
1.25
Accuracy
Ron uou lowet
Accuracy
1.00
1.00
0.75
0.75
0.50
0.50
0.00
0.00
Number of Ablated Rules
Number of Ablated Rules
(b)
Figure 6: Study of robustness of different methods to different levels of KB incompleteness on the deductive reasoning dataset. Due to the limitation of NLI models in multi-step reasoning, per- formance of LLM-TH drops when multiple axioms are ablated from the KB. This restriction is addressed when Llama 3.1 (8B) with CoT prompting and few-shot examples is used to obtain the entailment scores, resulting in robust performance from LLM-TH.s
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Geographical QA (Max Ablations:
Geographical Ablations:
1.40
1.40
1.20
1.20
Miledie Samh
Made Teechee Camte
Accuracy
1.00
Rabi sdii Notell
Accuracy
1.00
Rab Wed Maana
0.80
0.80
0.60
0.60
0.40
0.40
0.20
0.20
0.00
0.00
0
2
1
Number of Ablated Rules
Number of Ablated Rules
(a)
(b)
Figure 7: Study of robustness of different methods to different levels of KB incompleteness on the geographical QA dataset. LLM-TH shows a more robust performance to ablation of commonsense axioms in this task, compared to deductive reasoning.
E EXPLANATION OF THE LLM-TH ALGORITHM
In this section, we provide detailed explanation of the LLM-TH algorithm, presented in Algorithm
The algorithm takes as inputs the knowledge base (IC), the query (g). a computational budget defined by the maximum number of iterations (max iters), the maximum number of found proofs shown by max pproffs, and two optional sets of repair axioms: (i) the set of intended resolutions denoted by I, and (ii) the set of forbidden resolutions shown by F.
As explained in Section rather it can find a number of proofs with different plausibilities, a capability that is necessary for answering multiple-choice questions. For example, in the preference reasoning example provided in Figure [ it finds a proof for each the candidate recipes with a plausibility score assigned to cach proof, which is used rank the recipe options.
3.1 LLM-TH is not limited to finding a single proof to the query, but
The algorithm initializes an empty set, proofs, to store discovered proofs, an iteration counter i, and an initially empty priority queue PQ. PQ stores resolvent clauses and orders them according to their priority scores, using Equation 15 In the backward chaining approach used in LLM-TH, the first clause stored in PQ is -Q with the priority of 1, The algorithm's 'ss main loop executes as long as the priority queue (PQ) is not empty, the maximum proof limit is not reached, and the iteration cap
exceeded. During each iteration, the clause e with the highest priority in PQ is dequeued and designated as the active clause. In the initial iteration, since PQ contains only -g. this clause becomes the first active clause.
If the active clause is _., the previous resolution step has resulted in contradiction. The proof can then be reconstructed by tracing the ancestors of starting from its parent set P. and continuing up to the initial clause -q. Once a proof is found, it is added to the set proofs. However, if c * 1. the algorithm proceeds by selecting clauses to resolve with e. first identifies 9c.. the set of candidate clauses in I. that are resolvable with A clause must meet two conditions to be resolvable with in theory resolution step following Equation 3 (i) it must share the same arity as c, and (ii) must have different polarity from After forming Bc. LLM-TH iterates through all clauses Garget 3 and resolves each with e via hyperresolution, as described in Equation 2, to obtain Ges- It then forms the priority tuple using Equations I1 [3 and 14 and adds Cres to PQ based on this priority.
The algorithm continues until either the maximum number proofs is found, PQ becomes empty, or the maximum allowed number of iterations is reached.
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F COMMONSENSE REASONING WITH LLMS
The general conception that humans have about the world and how it works, often referred to as commonsense knowledge, and the ability to reason about it, known as commonsense reasoning, are essential capabilities that average human beings possess. In order be able to interact with the real world and humans, Al agents are also required to obtain this knowledge (Baroni et al. 2017 Shen & Kejriwal 2023). Therefore, commonsense reasoning has been central problem in Al over the past decades (Moore 1982, Liu & Singh 2004 Davis & Marcus] 2015). With the advent of language models, and particularly, transformer based architectures, models were developed that exhibited decent performance on some commonsense reasoning tasks such as physical and social reason- ing (Bisk et al., 2020, Sap et al., 2019). Further improvements were obtained by scaled language models, i.e., LLMs, as they exhibited an outstanding capability of commonsense understanding and
reasoning across various evaluation benchmarks (Zhao et al. 2024 Krause Stolzenburg 2023
Guo et al. 2024).
These improvements paved the way for inspecting new aspects of commonsense reasoning. such as reasoning problems involving logical inference. vein of work referred to complex common-
sense reasoning IIsmayilzada et al. 2023: Singh et al. 2021: He et al. 202I). The introduction of this line of work shed light important limitations of LLMs in challenging commonsense reason- ing tasks. Although LLMs have shown outstanding reasoning performance on simple commonsense
reasoning benchmarks, they struggle with more challenging tasks, such commonsense reasoning in real-world use cases (Paul et al.).
These remaining challenges and the risk of reasoning errors restrict the deployability of LLMs in real-world applications, especially in high-stakes scenarios. Furthermore, LLMs lack the factual knowledge required reason in various applications, such information about recent events or personal data (Toroghi et al. 2024b). In these applications, factual KBs such as knowledge graphs have been widely exploited represent factual knowledge applications ranging from health- care (Rastogı & Zaki 2020) to recommendation (Toroghi et al. [0233] Raza et al., 2024]] Toroghi Sanner] 2024). Despite the extensive amount of existing work on commonsense reasoning with LLMs, to the best of our knowledge, no work has targeted the problem of combining commonsense reasoning with reasoning over factual KBs. This problem is particularly important since LLMs show factual hallucinations when they lack domain-specifis knowledge (Huang et al. [023)] Tonmoy et al., 2024). In this work, we aim to take complex logical commonsense reasoning task a step further, by proposing methodology that leverages both commonsense reasoning knowledge of the LLM, as well as the factual knowledge of the KB.
G PROMPTS USED FOR LANGUAGE MODELS
We provide the prompts that we used for the LLMs in the experiments of this paper. They are also included in repository along with the implementation code and data.
Prompt for Preference Reasoning Task (Zero-shot and Few-shot CoT)
Task: You will be giver a query that asks for recipe and five options that you have choose from. Think step by step, First state your zeason for your choice and then say: "Therefore, the selected zecipe is <recipe id>. Query: ([QURRY)) [Rxamples if few-shot:]
Prompt for Multi-domain Deductive Reasoning Task (Zero-shot and Few-shot CoT)
Task: You will be given query about some knowledge graph entities in the form of first order logic predicate that is (IpplliIIApppl., (Apple, Basket) which means one can hold an apple in a basket). Your task is to identify whether the answer to this query is "True" or "False" and also provide proof of the answer. First, state your proof mentioning the rules you used and then say: "therefore, the
either True or False (for example, "CanHolaIn
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answer is True" "Therefore, the is False". Think step by step.
Query: ([QUERY)) [Examples if fox-shot:]
Prompt for Multi-domain Deductive Reasoning (RAG with Zero-shot and Few-shot CoT)
Task: You will given query about some knowledge graph
entities in the form of a first order logic predicate that is either True or Palse (for example, "CanHoldin (Applle, Basket) which means one can hold an apple in basket) and Knowledge Base containing
set of rules that will help you identify the answer. Your task is to identify whether the answer to the query is "True" or "False" and also provide a proof of the query using the knowledge base. First state your proof mentioning the rules you used and then say: "Therefore, the answer is True" or "Therefore, the answer False", Think step by step. Query: ([QUERY))
xB: ((KB)) (Examples if few-shot:]
Prompt for Geographical QA Task (Zero-shot and Few-shot CoT)
Naak: You will be given a query about geographical entities in the form of first order logic predicate that is either True or ralse. Your task is to identify whether the answer to the query is "True" or "False" and also provide proof the query. First state your proof mentioning the rules you used and then say: "Therefore, the answer is True" or "Therefore, the answer is False". Think step by step.
Query: ({QUERY))
[Examples if few-shot:]
Prompt for Geographical QA Task (RAG with Zero-shot and Few-shot CoT)
Task: You will be given query about geographical entities in the form of first order Logic predicate that is either True of rules that will help you identify the anawer. Your task is to identify whether the answer to the query is "Trus" or "False" and also provide proof of the query using the knowledge base. First state your proof mentioning the rules you used and then say: "Therefore, the answer is True" or "Therefore, the answer False". Think step by step.
False, and
edde Hase containing
Query: ([QUERY))
xB: ((KB) [Examples if few-shot:]
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H ANECDOTAL EXAMPLES
To offer more insight into the responses and proofs provided by LLM-TH and the comparison base- lines, this section presents anecdotal examples illustrating each model's performance the eval- uated tasks. Since Llama3-70B shows the best overall performance for our comparison baselines in the experimental results provided in Section 5 we show the exemplar outputs from this LLM. Specifically, we showcase the outputs from the following models:
LLM-TRes
Zero-shot Chain of Thought prompting
Fhotshot Chain of Thought prompting
RAG Zero-shot Chain of Thought prompting
RAG Few-shot Chain of Thought prompting
We apply these models to the Deductive reasoning and Geographical QA tasks studied in RQ1 and RQ2 and provide anecdotal examples to elucidate their capabilities and limitations. In each anecdotal example, we present the query, the set of relevant facts and axioms from the KB, and the ground truth proof, followed by the response that each model provides. We also indicate correct proof steps with green color and highlight incorrect ones in red. It is noteworthy that since RQ2 requires access to the KB and studies the model's I's ability to compensate for KB incompleteness, the only relevant baselines are RAG-based models.
Examples of the experiments the complete KB are provided in section H.1 and examples of performance on the incomplete KB are detailed in section H.2
H.1 EXPERIMENTS ON THE COMPLETE KB
H.1.1 Deductive Reasoning
Query: Does Sulfadiazine disinfect Rhodospirillaceae?
Relevant Rules from the KB:
Facts:
(1) "Subclass "f ""Rhhddxpirillacccee"""" "echdddsprllaccc""""oooollrlllee bacteria"),
(2) "Gram Negative" ""hhoossprriiiilacce bacteria")
(3) "Treats Gram Negative "Sulfadiazine")
Axioms:
(4)
VA, B, C, "Subclass (A, A "Gram Negative"(B) A "Treats Gram Negative (C) "Unresistant To" ((A, C)JA: "Bacteria" B: "Taxon" C: "Antibiotic"
(5)
YA, B, "Unresistant (A"(A, -
"Can be Used to Treut" (A, B)JA: "Bacteria",
"B: Antibiotic"
(6)
A, B, "Can be Used Treat" (A, B) "Can be Used KAll"(A, B)JA: "Bacteria",
"B: Antibiotic"
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(7) VA, B, "Can be Used to (All"(A, B)
"Disinfects' (A,, B)JA: "Bacteria", "B: Antibiotic"
Ground Truth Proof:
Applying (I), (2), (3) (4) with the following substitution:
0 {A/" "AAooooooopiirllacceae,""""" BB/"Rhodospirillacee bacteria", """uuadddazzie") yields:
Unresistant To"( (""hhodospiirillaceee"" "Sulfadiazine"),
Applying "Unresistant To ( ("Rhodospirillaceee"" "Sulfadiazine") (5)
with 0 "AA""oooooppirrlaccaae""" / "Sulfadiaazii"" yields:
"Can be Used to Treat"
("Rhodospirilaaceae"" "
"Sulfadiazine")
3-Applying "Can be Used Treat" ("Rhodospirillaceee"" "Sulfadiazine") (6)
with 0 = "A/""loodspirrllaccea""" B/ "Sulfadiazzie"" yields:
"Can be Used to
"Sulfadiazine")
Applying "Can be Used Kill" ("Rhodoopirrillceeee" "Salfadiazine") (7)
with 0 [A|"Rhooospirillaccee," // "Sulfaddazzze"" ")
yields:
"Disinfects" ( ("Rhodospirilaceeee, "Sulfadiazine"),
Therefore, the answer the query True.
LLM-TH:
query: "Disinfects" (""nnectts""ttooooosspillaaa "Sulfadiazine"):
Negated query: Disinfects (( ("Rhodoopirillacceee"" ", "Sulfadiazine")
Note: In the following sequent calculus formulae, use "R" to refer to "Rhodospirillacae"" "S" to represent "Sulfadiazine", "GN" to show "Gram Negative", "TGN", to denote "Treats Gram Negative", and "SO" to show "Subclass Of due to space limitations.
Step 1-
Dissinfects' "("R,, "S") -"Can be Used to (A, "Disinfects" "(A,B)
-"Can be Used to Ki"l"("R","S""
Under unification 0 /A/ "Ah"hhoooopirrlllcceeee""" BB "Sulfaadizzine")
Step 2-
-CCan be Used to Kill"("R","" "S")
"Can be Used to VAI" be Used to Treat" (A,B)
"CCan be Used Treat"("R", "S")"
Under unification f (A/ "Rhooooppirillaccee""" BB/ """uufuddazzine)
Step 3-
-CCan be Used to Treat" ("R",""") "Can be Used to Treat"(A.B) V -Unresistant To (AA()
"Unresistant To "RR, "S")
Step 4-
-UUnresistant To"""R", "S") " "Unresistant To """AADDVV"""AABVV"""""""""""
""S""("R"BBVV "TGGN"("S"
Under unification 0 RAoopoooosprrriillceee""""" "cuuaaaaae"""""SSuuuutiiii"i""
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Step 5-
"SO"("R", "R bacteria") A "GN"("R bacteria") A "TGN"("S")
Proof score: Pquery (1,
#**
Zero-shot CoT:
To prove the answer the query, will use the following rules from the knowledge base: Rhodospirillaceae is type of Bacteria. (ISA(Rhodospirillacae,, Bacteria))
Sulfadiazine type of Antibiotic. (IsAAsulfadiazinn,, Antibiotic))
3. Antibiotics disinfect Bacteria. (Disinfccts Bacteria))
Using modus ponens on rules 1, 2, and 3, can infer that: Disinfectsssuliidaaziiee,, Rhodospirillaceee) Therefore, the answer is True.
Few-shot CoT:
L.Sulfdiazziee is an antibacterial drug.
Rhodospirillaceae is family of bacteria.
3. Sulfadiazine is not typically used as disinfectant, but rather as an antibiotic to treat bacterial infections.
Therefore, the answer is False.
RAG + Zero-shot CoT:
SubChassOOKRhodoppirlllaaa. Rhodospirillaceae bacteria) (KB)
Granngaaiveeehooossppillllaa bacteria) (KB)
3. A A:bacteria, B:Taxon, Csantibiotic, SubClassOf(A, B) && GramNegativve(B) && TreatsGram- Negative(C) > UnResistantTooAA, C) (KB)
UnnRsistaa/DooRhooddpiillllee sulfadiazine) (inferred from 1, 2, and 3, with A Rhodospir- illaceae, B Rhodospirillaceae bacteria, and C sulfadiazine)
A:bacteria Brantibiotic, UnResistantToCA. B) CanBeUseedTTreaafAAA B) (KB)
6. CanBBeUSccrrTTeee/RRoooprrlllle sulfadiazine) (inferred from 4 and 5)
A:bacteria Brantibiotic, CamBeUseeToTTraa(.. B) > CamBeUseeTTKKilIA, B) (KB)
8. CamBeCssedooK////Rdddspppllaaaee sulfadiazine) (inferred from and 7)
9. A A:bacteria B:antibiotic, CanBeUsedTTKKilIAA B) - Disinfects(A, B) (KB)
10. DishnfcctsRhhooossillllccaa. sulfadiazine) (inferred from and 9)
Therefore, the answer True.
RAG + Few-shot CoT:
1. Rhodospirillaceee is gram negative bacteria,
sulfadiazine treats gram negative bacteria,
3. and sulfadiazine can be used to treat gram negative bacteria, therefore sulfadiazine can be used to treat Rhodospirillaceae.
Therefore, the answer is True.
Discussion:
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These anecdotal examples demonstrate that on complete knowledge base (KB), LLM-TH can successfully prove the query by resolving complementary clauses, without requiring the LLM to generate any additional axioms.
analysis of the proofs generated by the baseline methods reveals limitations in LLM reasoning. particularly in zero-shot and few-shot settings. For instance, the zero-shot CoT baseline asserts that "Antibiotics disinfect bacteria"; however, this statement overly broad, as not all antibiotics can disinfect all types of bacteria. While the final answer in this case is correct, there is a flaw in of the reasoning steps. Also, the few-shot CoT baseline produces an incorrect final answer due to an error in reasoning. In contrast, the RAG-based baselines, utilizing both prompting styles, correctly prove the query by leveraging retrieved facts from the KB.
H.1.2 Geographical QA
Query: Can drive between Biyabanak and Ryam Frolovskiy?
Relevant Rules from the KB:
Facts:
(1) "Located in (""Byybanakk", "Iran") "),
(2) "Located in R"yyam Frolovskiy", "Russia"),
(3) "Share Land Borders" ( ("Iran", "Azerbaijan")
(4) "Share Land Borders" ( ("Azerbaijan", "Russia")
Axioms:
(5)
VA, B, "Share Land Borders" "(A,
"Land Connected"(AA. B)]A: country, B country
(6)
YA, B, C, "Land Connected" (A, A "Land Connected"(B,
"Land Connected" C)JA: location, B location, C location
(7)
YA, B, B,C,D, D, "Located in "A"(A A "Located in (B, D) "Land Connected" (C, D) "Can Drive Between (A, B)JA: location, B llocatiion C :locatiin, D location
Ground Truth Proof:
1- Applying (3) (5) with the following substitution:
0 [A/"Ir"n", BB/ "A""eerbaijaan" "} yields:
(8) "Land Connected"' (""raac, "Azerbaijan") ").
2- Applying (3) (5) with the following substitution:
0 [A/ "Azerbaijan" ", B/ "} yields:
(9) "Land Connected" ("Azerbaijan", "Russia").
3- Applying (8), (9) to (6) with the following substitution:
0 [I/"Iran" ""Azzeraijan" C/"Russia") CC/"ann,"","""""iii
yields:
(10) "Land Connected" "IIran", "Russia")
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4- Applying (I), (2), (10) to (7) with the following substitution:
0 (A/"Biyabanak" /R"Ryam Frolovskiy", "rolovski""C//""rrra "I/"Iran", D/ "RRsssis"")
yields:
(11) "Can Drive Between (( ("Biyabanak", "Ryam Frolovskiy").
Therefore, the answer to the query is True.
LLM-TH::
Proof for query "Can Drive Between" "etween""""iyaburui """Biyabnnak" "Ryam Frolovskiy")
Negated query: -CCan Drive Between' ("Biyabanak", "Ryam Frolovskiy")
Note: In the following sequent calculus formulae, we use "Bi" to refer to "Biyabanak"; "RF" to represent "Ryam Frolovskiy", "Az" to refer to 'Azerbaijan", "CDB" to show
"Can Drive Between", "I.I" to show "Located In", "L.C" to show "Land Connected", and "SLB" show ""haare Land Borders" due space limitations.
Step 1-
""CD""""i" "RF")
-"U("" CCDYVAENN-TTAAON-TEIIVVVYYYCCCCC
Under unification 0 = (A/ "Biyaaaaaan,"" C/ "Ryam Frolovskiy");
Step 2-
""LI" B"I""""".CCVV"""""""" D) -V"""(C"( "LI"("Bi", "Iran" ") A "LI"("RF", "Russia") - ""LC"("Iran" "Russia" ")
Under unification "C/"Iran", D/ "/"Russia")
Step 3-
"LC"("Iran" "Russia") "LC"4ACY---LCCABBV
""I_""("Iran" ,B) V-"IC""B (R,"sssia"))
Under unification (A/"Iran" CC/ "/"RRssiaa")
Step 4-
""LC"("Iran" BB) "LC"("Iran" .BB "SLB"""S""""HAAE
""SLB" ,B)
Step 5-
"LC"(B, "Russia")
"LC"(B, "Russia" V "SLB"((B "Russia")
-"SL.B((B, "Russia")
Step 6-
""SaB"""Iran"" ", B) (B, "Russia")
"SLB" ""Irnn" "Az") (""ra""""A=""" "SLB"("Az", "Russia")
Under unification "B/"
Proof score: Pqucry 1,)
Zero-shot CoT:
To answer this query. I will use the following rules from the knowledge base: CanDriveBetween(x, y) = Connected(x, y)
2. Binbacke Ryam Frolovskiy)
False (this is fact in the knowledge base)
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Using rule 1, I can infer that CunDriveBetweenniiyybaaddd Ryam Frolovskiy) implies Con- Bbybaak Ryam Frolovskiy).
However, according to rule 2, Comnecie(Biyybaank, Ryam Frolovskiy) is False. Therefore, the answer False.
Few-shot CoT:
I.Biyabanak is a desert in Iran,
and Ryam Frolovskiy an island in the Caspian Sea, which is not connected to Iran by land.
Therefore, the answer is False.
RAG Zero-shot CoT:
LocatedIn(Biyybankk, Iran) (Given in KB)
ParaO Iran) (Rule: A A:place or location B:place or location, LocatedIn(A, B) PartOf(A, )
ShareLandBordeex((ran,,, Azerbaijan) (Given in KB)
4. LandConneetedd(ran, Azerbaijan) Rule: A A:country B:country, ShareLandBorders(A. B) LandConnccted(A, B))
LocatedIn(Ryam Frolovskiy, Azerbaijan) (Assuming this is true, since it's not given in KB)
6. PartOr(Ryam Frolovskiy, Azerbaijan) Rule: V A:place location B:place location, Locate- dIn(A, B) = PartOf(A, B)
7. CanDriveBecweennBiyaaaa. Ryam Frolovskiy) Rule: V B, C, D. LocatedIn(A, C) && LocatedIn(B. D) && LandConnected(C, D) = CanDriveBetweennAA B)]Aclocation, B:location, Clocatioo, D:location)
Therefore, the answer is True.
RAG + Few-shot CoT:
Since Biyabanak a desert in Iran,
2. and Ryam Frolovskiy is place in Russia,
3.and Iran and Russia are land connected (although not explicitly stated in the provided KB, but it can be inferred from the general knowledge that Iran and Russia share a border), then it is possible to drive between Biyabanak and Ryam Frolovskiy.
Using the rule: V A, B, C, D, LocatedIn(A, ?C) && LocatedIn(B, ?D) && LandComnected(?C, ?D) CanDriieBetween(A. B) With A Biyabanak, B Ryam Frolovskiy, C= Iran, D Russia
Therefore, the answer is True.
Discussion:
Similar to the deductive reasoning experiment, LLM-TH produces the correct proof complete knowledge base (KB) without requiring the LLM to surface commonsense axioms from it. This example also highlights the limitations of the LLM-based baselines. For instance, the zero-shot CoT baseline incorrectly claims that Biyabanak and Ryam Frolovskiy are not connected, leading to an incorrect final answer. Similarly, the few-shot CoT baseline provides an inaccurate statement about Ryam Frolovskiy, describing it as an island in the Caspian sea when it is, in fact, forest in Russia.
The RAG-based baselines further reveal challenges in the retrieval stage. For example, the relevant fact about the location of Ryam Frolovskiy is not retrieved, prompting the LLM to make assumptions in the zero-shot setting. Although the final answer in this case is correct, the reasoning steps contain errors and deviate from the correct proof. In the few-shot prompting setting, while the final answer also correct, it is based inaccurate statement (in fact, Iran and Russia do not share land border).
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H.2
EXPERIMENTS THE INCOMPLETE KB
H.2.1
Deductive Reasoning
Query: Does Sulfadiazine resolve an infection caused by Rhodospinillaceee?
Relevant Rules from the KB:
Facts:
(1) "Subelass of "aap:pspppirilacc""""""tttariiir bacteria
(2) "Gram N ("hhoddsppirillaacee bacteria")
33) "Treats Gram Negative" ( "uufaudaazin"") ""euatve"("ulluuuuiiin""""
Axioms:
(4)
VA, B,C, "Subclass (A, A "Gram Negative"(BB) A "Treats Gram Negative (CC) "Unresistant To (AA, ()): "Bacteria", " "Taxon" " "Antibiotic"
(5)
VA, B, "Unresistant To To"(A,)) "Can be Used to Treat" Treat"(A. (A, B)J: "Bacteria",
"B: Antibiotic"
(6)
YA, B, "Can be Used to Treat"(A. B) - "Can be Used to Kill" B) "Bacteria",
"B: Antibiotic"
(7) VA, B, "Can be Used to (ill"(A,
"Disinfects" ((affectss(A,B))) B)]:: "Bacteria", "B: Antibiotic"
Ground Truth Proof:
1- Applying (I), (2), (3) (4) with the following substitution:
0 = = "Rhooooopiirillceeee" B "B"prrillllllae""""""""aoooooii" "Khodospirrillacee bacteria", C/ (""Sufaddizzine) yields:
" "Unresistant To" ("Rhodospirillaceee" ""neessttn""""tlooooorrllllllle
"Sulfadiazine"),
2- Applying "Unresistant To "( ("Rhodospirillaceaa"" "Sulfadiazine") to (5)
with "Ahopooosspiiillcceee;; B/ "Sulfadiazine") yields:
"Can be Used to Treat" ("Rhodospiriilaceaae" "Sulfadiazine")
3- 3-Applying "Can be Used Treat" T ""Rhodospirillcceae"" "Sulfadiazine") (6)
with = [[A/ "Aa"iooooxpprrllacceee"""" B/ "Sulfadiazine") yields:
"Can be Used to Kill" ("Rhodosppirillaceee""" "Sulfadiazine")
4- Applying "Can be Used Kill" (""hodospirrilaccee"" "Sulfadiazine") to (7)
with = (Al"Rhadospirillaccee"" "B""lfaddizzine yields:
5- "Disinfects" ""Dsiinfcts" "Rhhodospiiillcceee" "Sulfadiazine")
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6- Using the commonsense axiom (absent from the KB) that:
YA, B, "Disinfects" (A, B)
"Resolves Infection Caused By" B)]A: "Bacteria", "B: Antibiotic"
Therefore, the answer to the query is True.
LLM-TH:
Proof for query "Resolves Infection Caused By" ""(""oooospirillacceee "Sulfadiazine""
Negated query: - "essovvss Infection Caused """hloddoppiirillcceee"""" "Sulfadiazine") Note: the following sequent calculus formulae, we use "R" to refer to "Rhodospirillaeee", "S" to represent "Sulfadiazine" "GN" to show "Gram Negative", "TGN", to denote
"Treats Gram Negative", "SO" to show "Subclass Of due to space limitations.
Step
"Resolves Infection Caused By" "Disinfects(A.B"" V -CCa be Used to Kill(A,
- CCan be Used to Kill"("R". ("R"."S")
Under unification = ( "hhoooopiiiiirllaaeee"" B "Saulfaddiazine"
In this step. by theory resolving Pessinfects"AABi the LLM successfully surfaced the commonsense axiom:
"Resolves Infection Caused By"("R", "S") with
YA, B, "Disinfects"AA.
"Resolves Infection Caused By" B)JA: "Bacteria", "B: Antibiotic".
Step 2-
-"Can be Used to Kill"("R", "S") "Can be Used to V be Used to Treat" (A,B)
Can be Used Treat( "R"a "R",""") "S")"
Under unification f {A/ "hh"ssoosppirlllcccee""" ,B "Sulfadiazine")
Step 3-
-"Can be Used Treat" "S")
"Can be Used to Treat" V -" Unresssstnt To To"(A, "Unresistant To R", "S")"
Step 4-
-UUrresistant To To"("R"," "S")
"Unresistant To V """""VVV"""""ABBV"""""""""""" ""SO"("R".B) VBVV="G""BBVV""OTN"""
Under unification (A/""hoodoppirrllaccee""" hatp:pppprrrlacccceee"""scaaaaaa CC""Sulfadiazznee
Step 5-
BV "N"GNN"""" ""T"""("S" "SO"""R", "R bacteria
"GN"("R bacteria") A "TGN"("S")
1
Therefore, the query proven to be True with the Proof score: Pquery = (1, 0.981,5)
RAG + Zero-shot CoT:
SuuCCassOFKKhooosppilllcceee Rhodospirillaceae bacteria) (from KB)
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2. GranNegaiveelloodsppilllcaa bacteria) (from KB)
YA, B, C, SubClassOf(A, B) A GramNegative(BB UnResistanddT (A,, C)) (from KB)
TreatsGramNegative((()
SubCllasOOfkhaaooppilllaaae, Rhodospirillaceae bacteria)
PartOf(Rhodsspiiillacca., Rhodospirillaceae bacteria) (from
KBB
using
the
rule
VA, B, SubClassOf(A,, B) = PartOf(A, A) animal, B: Taxon)
PartOfiRhhodospirillacaaa, Rhodospirillaceee bacteria) Araaaa/aaaaaitieeeeoeeeellllleee bacteria)
PRresiitantTT((Rhooosiiirrirl =
sulfadiazine) (from 2,
and the assumption that sulfadiazine treats Graat-Negative bacteria)
6. AA, B, UnResistantTooA, B)
CanBeUseedToTreat( A, A.bacteria, Brantibiotic (from KB)
7.
TinReesttnnoo(RRooooppllllllc sulfadiazine)
Caanebplccdo.reeeeeooooorprreeee sulfadiazine) (from 5 and 6)
8. VA, B, CanBeUseeTTTTreatAA. B) KB)
CanBeUseaTTKKilIA, B))A: bacteria, B: antibiotic (from
Can (eaat sulfadiazine)
CanbeeJleccTkkillklodoopppllaae sulfadiazine) (from 7 and 8)
AA, B, CanBeesseeTKKillIA B) = Disinfects(A, B) bacteria, B: antibiotic (from KB)
11.
CuBBBUssdDDllll@@hadoppplllllle sulfadiazine)
(SinffettsRhoodoopiilllccaaaa sulfadiazine) (from and 10) Therefore, the answer is True.
RAG + Few-shot CoT:
Rhodospirillaceae is gram-negative bacteria,
and sulfadiazine treats gram gram-negative bacterias. Therefore, the answer is True.
Discussion:
This example demonstrates how LLM-TH can perform commonsense reasoning incomplete KB. Since no complementary literal for "Resolves Infection Caused By " is found, LLM-TH invokes the LLM to perform a theory resolution step. In this step. it correctly selects "Disinfects" as the clause with the highest priority for theory resolution, enabling it to provide the correct proof. In this example, all baselines are also able to produce the correct proof. However, the RAG+zero- shot CoT baseline exhibits minor errors, such as selecting incorrect KB rules step 4 and neglecting KB facts in step 5, instead basing its reasoning assumption.
H.2.2 Geographical QA
Query: Can take road trip between Ryam Frolovskiy and Biyabanak?
Relevant Rules from the KB:
Facts:
(1) "Located in "n (""Byabannak", "Iran"), "),
(2) "Located in ( Ryam Frolovskiy", "Russia") "),
(3) "Share Land Borders" ( ("Iran", "Azerbaijan")
(4) "Share Land Borders" " (aadeers"("Azeroaaa ("Azerbaijan", "Russia")
Axioms:
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(5)
VA, B, "Share Land Borders" Morders"(A,1) (A, = "Land Connected"(A. B)]A country, country
(6)
YA, B, C, "Land Connected" (A, (A, "Land Connected"(B, C)
"Land Connected" (A, C) location, location, C location
YA, D "Located in (), A "Located in (B, "Land Connected" (C, D) "Can Drive Between (Aa B) location, B location, C location, : location
Ground Truth Proof:
1- Applying (3) to (5) with the following substitution:
0 {A/"Iran" B/ "Azzerbaijja"" "} yields:
88) "Land Connected"" "Azerbaijan")
2- Applying (3) to (5) with the following substitution:
0 {A/ "Azebbaiaan" B/" "/"Russia") ") yields:
99) "Land Connected"' ("aetteddd""AAeeeiii "'Aerbbaian", "Russia")
3- Applying (8), (9) to (6) with the following substitution:
8 {A/"Iran) BB "Azerbbaijna"" C// " yields:
(10) "Land Connected"""Iraaant "Russia").
4- Applying (1), (2), (10) to (7) with the following substitution:
8 "A/"Bayabanak" B Frolovskiy". "Calovski"".C'""aaanii "C/""ran", "aoim",,D""ustiiii "R"Russia") "} yields:
(11) "Can Drive Between " "Byyabanak", "Ryam Frolovskiy")
5- Using the commonsense axiom (absent from the KB) that:
YA, B, "Can Drive Between" "(A,
"Can Take Road Trip Between" B) A: "location", "B: location" "
Therefore, the answer to the query is True.
LLM-TH:
Proof for query "Can Drive Between "(" "("Biyabanak", "Ryam Frolovskiy")
Negated query: "CCan Drive Between "( """yaabbanak", "Ryam Frolovskiy")
Note: In the following sequent calculus formulae, we use "Bi" to refer to "Biyabanak", "RF" represent "Ryam Frolovskiy", "Az" refer to 'Azerbaijan" "CTRTP" show "Can Take Road Trip Between", "CDB" to show "Can Drive Between". "Lf" to show "Located In". "LC show "Land Connected". and "SLB" to show "'Share Land Borders" "n due to space limi- tations.
Step
(CTRTB"("BIT (RF"" "CDD"ABBV--LVAAVVVVVEVEVVV"V"""" ""L[("ii"
Under unification =AA "Ayyaiyabanak", C/ "Ryam Frolovskiy"),
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In this step, by theory resolving -"Can Take Road Trip Between ("""",, "RF") with
"Can Drive Between (A, the LLM successfully surfaced the commonsense axiom:
YA, B, "Can Drive Between ((A, B)
"Can Take Road Trip Between"
Between"(AA (A, "location", "B: location".
Step 2-
"I'"(""",CVV-"""""" -""CC"""(C """"a"""""" "LI"("FF", "Russia")
-"LC"("lvan" "Russia") ")
Under unification "C/"Iran", "eriun",,/"Ruaaaee """Russia"" ")
Step 3-
"LC"("Iran" "Russia")
"LLC"( ("Iran",Bi V "Russia")
Under unification 0 "A/"Iran"CC/" C/"Russiaa")
Step 4-
""LC"("Irn" .B)
""C"("Iran" ,BB) - ""LL"""""""""reaa (ran",B)
""LL"""Irrn"
Step 5-
"LC"(B, "Russia") "LC"(B, "Russia" V "SLB"(B, "Russia")
-"SLB"(B, "Russia")
Step 6-
-"SLB"("Irrn" B) -SLB"(B "Russia")
"SLB" "Az") A. "SLB"("Az", "Russia")
Under unification 0 (B/"AZ")
Therefore, the query proven be True with the proof score: Pquery (1, (1.9. 6)
RAG + Zero-shot CoT:
From the knowledge base, we have: PartOf( Biyabanak, Iran) (from the given KB)
2- PartOf(Ryam Frolovskiy, Belarus) (not mentioned in the KB, but assuming it's true for the sake of the query)
Using the rule:
"vA, B, C, ParOffAA B) A PartOf(B, C) - PartOf(A, C)]A: location, B: location, C: location". can infer: Burabaiiiyyaankk, Asia) (since Iran is part of Asia)
4- and PartOfi Ryam Frolovskiy, Europe) (since Belarus part of Europe)
5- Using the rule: VA, B, C, LandConnected(A, B) A LandComnected C) LandConnected/A, Coouuryu B:couttry, C:country, we can infer: Not LandConnected Belarus) (since Iran is in Asia and Belarus is in Europe, and they are not land-connected)
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6- Using the rule:"VAA B, C. D, LocatedIn(A, C) A LocatedIn(B, D) A LandComectedI D) CanDriveBetweennA. B) location, B: location, C: country, country", we cannot infer Betweive Biyabanak, Ryam Frolovskiy) since Iran and Belarus are not land-connected. Therefore, the answer False.
RAG + Few-shot CoT:
To determine if you can take road trip between Biyabanak and Ryam Frolovskiy, we need to check if Biyabanak and Ryam Frolovskiy are located in countries that are land connected.
From the KB, we know that Biyabanak is part of Iran,
3- and Ryam Frolovskiy
not mentioned in the KB, but since it is not mentioned, we will assume it is in Russia (based on the name).
From the KB, we also know that Iran and Russia are land connected (rule 1).
5- Using the rule "VA, B, C.D,,eocaed C) LocatedIn(B, D) A LandConnectedi C, D) CanDriveBetveennAA, B)[A: location, B: location, C. country, D: country", we can infer that you can take road trip between Biyabanak and Ryam Frolovskiy. Therefore, the answer is True.
Discussion:
This example further illustrates the successful application of LLM- based theory resolution by LLM- TH, where theory resolution step leverages the LLM's commonsense knowledge to address KB incompleteness. Specifically, in Step 1, the LLM surfaces a commonsense axiom to theory resolve -Can Drive Between" with -Ca Take Road Trip Between".
This example also highlights the limitations of the RAG-based baselines. Due to a failure in retriev- ing facts about Ryam Frolovskiy, the RAG+Zeno-shot CoT baseline makes an incorrect assumption about its location. Furthermore, subsequent reasoning steps are flawed, resulting in a wrong an- swer. Although the RAG+Few-shot CoT baseline provides the correct final answer, its reasoning process is not entirely reliable. Notably, because the L.M lacks access to fact about the location of Ryam Frolovskiy, it makes an assumption about its location- -wiihh case. However, also incorrectly references rule in the KB that states Iran and Russia are land connected, even though no such rule exists in the KB.
which happens be correct this
These examples underscore the limited reliability of existing LLM-based baselines when combining commonsense reasoning with factual information.
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Reviews:
[{"review_id": "BKkLp1XwfI", "reviewer": "Reviewer_ngRa", "summary": "The paper introduces LLM-based Typed Hyperresolution (LLM-TH), a novel framework for enhancing commonsense reasoning by LLMs through logical inference with large, potentially incomplete KBs. The key ideas involve combining theory resolution, where the LLM fills in gaps in the KB by identifying commonsense entailments, with typed hyperresolution, which improves efficiency by limiting reasoning steps to type-consistent paths. This approach addresses the limitations of traditional LLM reasoning methods, which struggle with errors, hallucinations, and scalability to large KBs. \n\nThe main contributions are summarised at the end of the introduction section.", "questions": "How does the performance of LLM-TH change when paired with different LLMs that may vary in their levels of commonsense knowledge or domain-specific expertise? \n\nHow does LLM-TH handle cases where type assignments within the KB are ambiguous or inconsistent?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper successfully integrates LLMs with classical logical reasoning methods, leveraging the commonsense knowledge of LLMs to enhance reasoning over incomplete KBs.\n\nThe introduction of typed hyperresolution significantly improves the scalability of the reasoning process, making it feasible to handle large-scale KBs.\n\nThe framework provides transparency in the reasoning process and offers a reliable method to fix errors, which is crucial for high-stakes applications.\n\nThe paper presents a thorough empirical evaluation across multiple tasks and datasets, demonstrating the effectiveness of LLM-TH compared to existing baselines.", "weaknesses": "While the framework enhances reasoning accuracy, it remains heavily dependent on the LLM’s commonsense knowledge for entailment inference. This reliance could present challenges if the LLM lacks domain-specific knowledge or displays biases.\n\nAlthough typing improves search efficiency, ensuring type consistency across large datasets may introduce notable computational overhead, particularly in knowledge bases with complex hierarchical type structures.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Yehdu8v43X", "reviewer": "Reviewer_hYKL", "summary": "The paper introduces an LM-based hyper-resolution system LLM-TH that utilizes the language models' common sense to:\n1. augment incomplete KBs: The LM scores entail between literals and add rules that can help to complete the proofs.\n2. deduce type matching for typed resolution: The LM scores the consistency between two types to allow unification between literals with different types.\n\nThe LM entailment and type-match scores are used to implement a priority queue that allows proofs to be completed faster by finding clauses with a higher chance of being resolved. Moreover, the results require only a small LM to perform the NLI task. The paper uses a BART-large model trained on MNLI.\n\nThe method is evaluated on 3 knowledge-based reasoning tasks: Preference Reasoning (over recipes and user requests), Deductive Reasoning (a new task over five domains), and Geographical QA (a new task of geographical reasoning over a KB of geographical facts). The method shows strong performance (compared to larger LLM baselines) on all 3 tasks. Manual inspection shows that the method finds correct proofs, i.e., it is right for the right reasons.\n\nThe ability to perform inference with incomplete KBs is shown by removing facts from the KB that are required in the final proof. The LLM-TH system is able to recover (near perfectly) from the incomplete KB.\n\n---\n\n**Update after rebuttal:** The authors sufficiently address my concerns and questions. The new version of the paper clarifies several points of confusion. I am increasing my score from 5 to 8. I have not thoroughly reviewed all the new edits to the paper, just those concerning my questions.", "questions": "1. Algorithm 1: I feel there are several typos and unclear variable roles here\n    - What is the point of max_iters? The inner loop completes one entire proof search.\n    - The counter i never changes\n    - Line 9: Why is max_proofs increasing?\n    - Line 10: What is the point of saving the empty clause to proofs?\n    - Line 12: Is it invalid to resolve $c$ to a clause with less arity than $c$?\n    - Line 13: Is the loop over $\\beta_c$?\n2. How many LM inferences are performed in each resolution iteration is unclear. Please provide an explicit algorithm for implementing LM-based resolution\n3. Proof of Proposition 1: It is not obvious how incorrect LLM belief (invalid linkage of literals based on entailment) can be corrected with an axiom. This confusion again stems from the unclear implementation of the LM hyper-resolution. For the given example, if the LM incorrectly infers that $\\text{cuttlefish}(x) \\implies \\text{fish}(x)$, then how does adding $\\text{cuttlefish}(x) \\nRightarrow \\text{fish}(x)$ correct the reasoning? Is the predicted LM inference checked against all KB facts at every iteration?\n4. Please provide examples of query types in the DEductive Reasoning and Geographical QA datasets\n5. Sec 5.2.2: When reasoning with incomplete KBs, does LM-TH add back the removed edge?\n6. Sec 5.2.2: When creating the setting with incomplete KBs, does removing a single edge remove all valid proofs? Asked another way, is the KB truly incomplete or it just the \"gold\" proof invalidated?\n7. Sec 5.2.3: The dataset description states that some proofs in the Deductive Reasoning dataset require up to 7 steps. How are the average search steps in Fig 3 about 3.5 with typed resolution? Can you provide a breakdown of this comparison as a function of a number of steps in the \"gold\" proof?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- The method is verifiable and faithful by definition. The execution of proofs can be traced back deterministically\n- Faulty system reasoning can be modified by inserting corrected (repair) axioms into the knowledge base\n    - This ability is demonstrated theoretically (caveat in the later review section) via an example but not tested at scale\n- The method scales to large KBs since it does not require the entire KB to fit in the LM context\n- Experiments demonstrate that the method can handle incomplete KBs to some extent by compensating for missing facts with LM entailment inference", "weaknesses": "1. The reasoning for why any symbolic baselines cannot be implemented is not convincing\n    - One reason provided is that past methods require complete knowledge bases. Is that not the setting on Table 1?\n2. The complete algorithm of the method is not correctly presented\n    - Clarification questions about Algo 1 are in the next section\n3. The lack of the complete algorithm and the lack of any timing analysis makes it difficult to judge the feasibility of the system\n    - How many LM inferences are required in each resolution step? Theoretical or empirical measurement is necessary\n    - I do not believe that high latency (up to some reasonable degree) is grounds for rejecting the paper. However, this paper needs this analysis for completeness\n4. It is unclear how the repair axioms for LM entailment scoring are used in reasoning", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EWGQCCZJSb", "reviewer": "Reviewer_8yhZ", "summary": "This paper introduces LLM-based Typed Hyperresolution (LLM-TH), a novel framework for commonsense reasoning that combines large language models with traditional logical inference methods. The problem that the authors try to address is that current LLMs have limitations in commonsense reasoning tasks due to hallucinations and the inability to handle large knowledge bases. LLM-TH uses theory resolution to integrate LLMs into logical reasoning and implements a typing mechanism to reduce errors and improve efficiency. Meanwhile, LLM-TH also employs hyper-resolution to handle large knowledge bases and a mechanism to repair incorrect inference steps. In experiments, the authors used BART with 406M parameter model, LLM-TH outperformed larger models, such as Llama3-70B, Gemini1.5-Flash, GPT-3.5-Turbo, and MIstral 46.7B on three reasoning tasks: preference reasoning, multi-domain deductive reasoning, and geographical questions answering. However, the writing of this paper doesn't follow a good structure and the readers are hard to follow what are the authors trying to do in each section.", "questions": "No", "limitations": "", "rating": 1, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "1. This paper combines the two approaches to traditional logical reasoning: traditional logical reasoning and LLM's ability to understand commonsense, which is quite novel.\n2. The results on three benchmarks show that the model can solve the problem very effectively.\n3. The method also provides a theoretical framework for error repair.", "weaknesses": "1. The baseline compared in this paper is quite weak, with only some large LLMs like GPT-3.5 and Llama3-70B. You should add more commonsense models, like COMET and Vera.\n2. The writing of the paper needs significant improvement. Currently, it is quite hard to follow the paper and understand its content. The authors write the paper with very dense descriptions without clearly a clear logical flow. For example, the authors don't mention each component of the method and their purpose, making the whole method part quite hard to understand, while there are too many equations in the LLM-TH model on page 4 and page 5, which is too dense. (too many details, no brief introduction). \n3. The paper needs more case studies about why the LLM-TH can perform much better than solely LLMs. The authors need more motivations to justify why we need to use those symbolic methods to solve commonsense reasoning, which is not symbolic at all.\n\n**The experiments in this paper are very weak, with only two experiments on complete and incomplete graphs. There is literally no analysis of why their methods can work so well, given the authors introduced so many components in their framework (the repair mechanism, hyperresolution, and type inference). No ablation study, no case study or error analysis**", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YonrmiBR5t", "reviewer": "Reviewer_97vV", "summary": "The paper introduces LLM-based Typed Hyperresolution (LLM-TH), a novel framework designed to enhance logical commonsense reasoning in large language models (LLMs). LLM-TH addresses key limitations of existing methods by integrating the internal commonsense knowledge of LLMs with axiomatic knowledge bases, providing a mechanism to repair erroneous inference steps, and enabling reasoning over large knowledge bases with tens of thousands of rules. The framework is built on the concept of \"theory resolution,\" which allows the incorporation of specialized theorem provers into the resolution inference rule, and utilizes *hyperresolution* to efficiently combine clauses for scalable reasoning.\n\nExperiments on Preference reasoning, Multi-domain Deductive reasoning, and Geographical QA, which all requires commonsense reasoning over rules/KBs, prove the effectivenss of the method, outperforming standard RAG/CoT.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The main contribution is using the entailment ability of language models as substitute for semantic parsing to identifies the unsatisfiable natural language predicates to perform reasoning via theory resolution. The motivation is sound and natural.\n\n2. Sound writing and problem formulation.", "weaknesses": "- Simple commonsense reasoning is supposed to be considered as solved by scaling language models. For example, GPT-4o or its predecessors all know the commonsense/entailment knowledge in the examples you provided, “Souvlaki”(y) =⇒ “Meditteranean”(y) and \"cuttlefish is not fish\" with simple prompts, which kind of make the FIXING ERRONEOUS RESOLUTIONS module useless. \n\nE.g., \n> Prompt: Is this true? ∀y“Souvlaki”(y) =⇒ “Meditteranean”(y)\n> Response: The statement ∀y (“Souvlaki”(y) =⇒ “Mediterranean”(y)) can be interpreted as \"For all y, if y is Souvlaki, then y is Mediterranean.\" In general, this statement is true because Souvlaki is a popular Greek dish, and Greece is part of the Mediterranean region. Therefore, if something is identified as Souvlaki, it is reasonable to classify it as Mediterranean cuisine.\n\n- Second, since commonsense is quite simple for LLMs, the major part of performing commonsense reasoning based on axioms is the efficient and effective retrieval of constraints/rules in the KB, while this part is supposed to be well-studied before. Moreover, I am interested in the performance of transforming all clauses, axioms, queries into natural language and ask LLMs to solve the task based on it's own parametric knowledge. I don't think the performance would be significantly lower. \n\n- Missing discussions on commonsense reasoning. Most of \"commonsense knowledge\" are simple and do not requires complex reasoning, and state-of-the-art LLMs can already capture them after instruction tuning on manually curated commonsense resources. What your work is more closely related to is complex commonsense reasoning, which requires multiple reasoning steps and possibly grounded in logical forms. Checkout works like WinoLogic, COM2 (complex commonsense reasoning over KB), CRoW (commonsense in real world).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)