Partial Perspectives: How LLMs Handle Logically Inconsistent Knowledge in Reasoning Tasks
Authors: Zichao Li
Ines Arous
Jackie CK Cheung
Venue: COLM 2025 (2025)
Keywords: evaluation methodologies
reasoning
logical reasoning
calibration/uncertainty
TL;DR: We propose a new framework based on Markov logic network to evaluate LLM's reasoning over inconsistent knowledge and release accompanying datasets.

Abstract: Most natural language reasoning tasks in the research community assume consistent input knowledge. Nevertheless, real-world scenarios often involve inconsistent information, which might lead to divergent conclusions and are typically associated with varying levels of uncertainty. This raises a key research question: can large language models (LLMs) effectively handle uncertainty in their reasoning process to maximize knowledge consistency?
In this paper, we propose a framework for evaluating reasoning over inconsistent knowledge. Our approach models uncertainty via weights of logical rules, leveraging Markov logic networks (MLN), which integrate probabilistic reasoning with first-order logic. This enables us to quantify inconsistencies in knowledge bases, and hence rigorously evaluate LLM reasoning. We introduce two tasks using this framework: 1) QA, which involves answering questions by integrating inconsistent knowledge; and 2) knowledge rectification, where we aim to rectify language models' acquired knowledge to improve consistency. We curate a dataset of 3,000 MLN-formatted knowledge bases to implement these tasks. We evaluate state-of-the-art LLMs on these tasks and highlight their limitations in uncertainty-aware reasoning over inconsistent logical knowledge.

Published as a conference paper at COLM 2025
Partial Perspectives: How LLMs Handle Logically Inconsis- tent Knowledge in Reasoning Tasks
Zichao Li', Ines Arous?, Jackie C.K. Cheungl.3
McGill University, MILA Quebec AT Institute, York University, 'Canada CIFAR Al Chair
zichao. 11@mila la. quebec inesar@yorku.co ca crnkkiiicheung@mmgill..
Abstract
Most natural language reasoning tasks in the research community assume consistent input knowledge. Nevertheless, real-world scenarios often in- volve inconsistent information, which might lead divergent conclusions and are typically associated with varying levels of uncertainty. This raises a key research question: can large language models (LLMss) effectively handle uncertainty in their reasoning process to maximize knowledge consistency? this paper, we propose a framework for evaluating reasoning over in- consistent knowledge. Our approach models uncertainty via weights of logical rules, leveraging Markov logic networks (MLN), which integrate probabilistic reasoning with first-order logic. This enables to quantify inconsistencies in knowledge bases, and hence rigorously evaluate LLM reasoning. We introduce two tasks using this framework: 1) QA, which involves answering questions by integrating inconsistent knowledge; and 2) knowledge rectification, where we aim to rectify language models' ac- quired knowledge to improve consistency. We curate a dataset of 3,000 MLN-formatted knowledge bases to implement these tasks. We evalu- ate state-of-the-art LLMs on these tasks and highlight their limitations in uncertainty-aware reasoning over inconsistent logical knowledge. 1
1 Introduction
Natural language reasoning (Yu et al., 2024) forms cornerstone of modern Al systems, enabling a wide range of applications such as question answering (Geva et al., 2021), clinical support (Gao et al., 2023), and digital agents (Su et al., 2024). Recent advancements in large language models (LLMs) (Kojima et al., 2022; Achiam et al., 2023) have led to impressive tasks like commonsense reasoning (Bhagavatula et al., 2019)
benchmark performance and logical reasoning (Parmar et al., 2024). Notably, most of these reasoning tasks assume that the input data is consistent and reliable. In practice, however, we frequently encounter inconsistent evidence, claims, or narratives, such as diverging health reports during COVID- 19 (Nagler et al., 2020), varying interpretations of political and social issues (Pan et al., 2023), or evolving scientific discoveries that challenge prior findings (Kuhn, 1997).
Therefore, LLM-based applications need to process inconsistent information to derive well- reasoned conclusions. For example, an AI help desk responding to a network issue inquiry (see Figure 1) needs evaluate competing answers based on different technical rules. The system should estimate the likelihood of each possible cause and guide the user toward solution. Likewise, knowledge must adapt to new evidence that challenges existing beliefs (Konieczny & Pérezz 2005; Baral et al., 1992), such as revising taxonomies when genetic studies reveal unexpected relationships.
However, rigorous definition of reasoning over inconsistent knowledge is nontrivial to pin down. A key challenge lies in defining a clear ground truth; that is, which com- peting conclusion the model should prioritize. The common NLP practice of relying human annotations as a gold standard does not suffice here, since human judgments can
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be influenced by cognitive biases, such as confirmation bias (Nickerson, 1998) and belief perseverance (Anderson et al., 1980) due to limited cognitive resource (Simon, 1955). Pre- vious work (Xie et al., 2024; Qian et al., 2023) addresses this challenge using heuristics, such as prioritizing the most recent or user-provided information. However, heuristics are inherently rigid and fail to adapt to nuanced, marrtinty--ware scenarios common in real-world decision-making. For example, a rule may have lower priority than another a priori, yet its implications should carry more weight if numerous facts align with it.
To tackle this challenge, we draw on previ- ous work in symbolic AI that handles un- certainty in logical reasoning. Specifically, we propose novel framework based on the formulation of Markov logic networks (MLN) (Richardson & Domingos, 2006), in order to rigorously evaluate reasoning over inconsistent knowledge. MLN combines first-order logic rules with probabilistic rea- soning such that we can assign weights to potentially inconsistent statements as a measure of uncertainty and precisely quantify a knowledge base's is consistency.
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Rule
Rule 2:
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Maltcout network acthetyfere comprembed dewics can ouseeto
cweftadded during bunyhouss.
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Figure 1: Contradicting conclusions derived using different rules.
Using this framework, we propose two tasks, consistency-enforeed question-answering (QA) and knowledge rectification. The goal of QA is to answer questions through integrating potentially inconsistent knowledge. For example, in the scenario illustrated in Figure 1, each rule will be assigned weight, and the system determines the most coherent response based on both the rule weights and the extent to which factual evidence aligns with them. In knowledge rectification, the model identifies and rectifies specified number of facts for each knowledge base to maintain consistency. While the QA task aligns more closely with real-world use cases, the rectification task is more challenging, requiring reasoning across high-dimensional space of possible resolutions and evaluating trade-offs for optimal consistency.
Both tasks are based collections of knowledge bases, each of which provides factual and logical knowledge with varying levels uncertainty. To implement these task setups, we curate new dataset iKnow consisting of 3,000 knowledge bases, each of which contains fac- tual statements and logical rules expressed in natural language. We conduct comprehensive evaluation of state-of-the-art open-sourced and proprietary LLMs. Our contributions are threefold: (1) We are the first to systematically study how LLMs reason with logically incon- sistent knowledge using Markov logic network formulation. (2) We propose two new tasks, comsistency-enforee
QA and knowledge rectification, and release accompanying datasets. (3) We show in our experiments that current LLMs often fail to comprehensively resolve inconsistent knowledge. Instead, they tend to selectively pick subset of the knowledge base, drawing conclusions based solely on that subset while ignoring the rest.
2 Related Work
2.1 Knowledge Conflicts
There has been growing body of work studying knowledge inconsistencies in LLMs. Xu et al. (2024) taxonomize and categorize these inconsistencies into context-memory con- flicts (Longpre et al., 2021), inter-context conflicts (Xie et al., 2024; Qian et al., 2023), and intra-memory conflicts (Qi et al.). They highlight conflicts arising from different sources of information, including parametric knowledge and external information in prompts. These studies reveal LLMs' susceptibility to confirmation bias; for instance, Xie et al. (2024) report that LLMs tend to favor external information that aligns with their parametric knowledge. Another closely related area of research is fact-checking, which aims to identify discrep- ancies between claims and supporting evidence drawn from textual (Thorne et al., 2018; Wadden et al., 2020) or tabular sources (Chen et al., 2019).
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Previous work focused primarily factual knowledge conflicts, such as the number of Olympic medals a country has won. Additionally, these studies often adopt a simplistic, binary view of conflict, which usually stems from misinformation or outdated facts, over- looking the inconsistencies caused by knowledge uncertainty. By contrast, our proposed framework extends beyond the binary case, offering more general approach to reasoning over inconsistent knowledge, including contradictions and factual-logical discrepancies, by modeling varying degrees of uncertainty. In other words, requires LLMs to weigh competing hypotheses in uncertain logical contexts.
2.2 Logical Reasoning with Natural Language
There has been increasing interest in using LLMs for logical reasoning. Natural language provides a flexible interface for injecting rule-based knowledge to guide or control neural models, which is fundamental challenge when using neural AI systems, Recent studies have explored various types of logical reasoning in neural language models, such as ab- ductive reasoning (Bhagavatula et al., 2019), defeasible inference (Rudinger et al., 2020), deductive reasoning (Clark et al., 2021), and theorem proving (Tafford et al., 2021). However, existing research often assumes the provided logical knowledge consistent, overlooking reasoning in the presence of contradictions. More recently, there has been growing interest on resolving logical conflicts within LLM outputs (Jung et al., 2022; Mitchell et al., 2022; Kassner et al., 20223). Conversely, we examine how LLMs handle inconsistent logical knowledge within input.
2.3 Reasoning with Inconsistent Logical Knowledge
Logical reasoning with uncertainty has been a long-standing problem in machine learning and AI. Richardson & Domingos (2006) propose Markov logic networks to address am- biguities caused by inconsistent logical knowledge with uncertainty. Since then, MLNs have been applied across various domains with applications such KB-based question answering (Poon & Domingos, 2009), opinion extraction (de la Vega & Ng, 2016), and video action reasoning (Jin al., 2022). In this work, we leverage MLNs to establish a framework for evaluating LLMs in reasoning over inconsistent knowledge.
Evaluating Reasoning over Logically Inconsistent Knowledge
We start by specifying guidelines to help us define what it means for models to reason over inconsistent knowledge. Concretely, we ground our approach in three key principles: (1) maximal internal consistency within our knowledge of the world (Harmon-Jones & Mills, 1999; Peppas, 2008); (2) integrating uncertainty into the reasoning process (as opposed to binary true-false beliefs) (Dempster, 1968); and (3) prioritizing newly acquired knowledge as becomes available (Piaget, 1977; Delgrande et al., 2004). Driven by these principles, we formally define reasoning over inconsistent knowledge, then introduce two tasks within this formulation.
3.1 Formulation
We first define a first-order logic knowledge base K= F), where (r1, r....... ... In) is set of first order logical rules expressed in natural language, and F F= {fi, f2..., fm set of atomic formulas, also expressed in natural language, and related to the rules in R. For simplicity, we refer to them factual statements below.
Example 1. The set R is composed of the following rules:
r1 =If -Ifa [Person] works at [Companyl, and [Company] is located in [City], then the [Person] is a resident of [City].
r2 [Person) was born in /Cityl, then they are the resident of ICityl.
The set F is composed of the following facts related to R:
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Mining firat-order
logicatrutes
language mapping rules
3. Human varification filters out Implauxibia rulex and Incorrect mappings
Kapperedd was deat Yoegarsj and Porsary kiacoedis E'heas al [havan arcasings the (rawn
WIKIDATA
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Verified rules natural languagee mappings
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[Eaunty).
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Orouping vorified rulas based shared prodicates
Knowledge base creation per g group: Weighing rulos (2) Synthesizing facts
Taxks curation
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Question answeerngg
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(Cergpary, Country
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(Stuctinn, battee Oi))
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Knowledge rectification
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Countay)
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The pipeline of the iKnow curation. Knowledge base creation: (1) We first mine a large set of first-order logic rules candidates from Wikidata (methods detailed in Sec- tion 4.2.1) (2 3) Then, we generate their natural language mappings and infer the variable types; Later, human annotators filter out the implausible rules and incorrect mappings (Section 4.2.1). (4 & 5) We group verified rules based on shared relations, then create KB per group of rules, synthesizing facts for each relation in the rules and assign weights rules (Section 4.2.3). Task construction: we curate two task instances for each KB. We use a MLN engine to derive ground-truth answers and rectifications (Section 4.3).
Figure 2:
Alice works at SmartAl; SmartAl is located in Boston; Alice was born in Chicago.
Each rule represents an If-Then logical connection between premises and implications. For instance, 12 corresponds to the symbolic form (Person, birthplace, City) residency, City), where Person and City are variables that must be instantiated with entities of their respective types, such as Alice and Chicago. The relations birthplace and residency define relationships between these variables. fact is grounding of a relation where variables are instantiated, e.g. (Alice, birthplace, Chicago).
Given query q, the model infers set of consequent facts f with uncertainty, e.g. Alice lives in the city _, based on K, maximizing consistency in knowledge base. We denote S(K UKUF F) as a measure of the internal consistency within a given knowledge base. As discussed above, 5(-) should incorporate uncertainty of knowledge and hence provide a nuanced quantification of consistency.
In this work, we use the formulation of Markov logic networks (MLNs) that allows users to assign priorities in terms of weights w; to each logical rule r;, enabling the integration of uncertainty directly into first-order logic rules. This flexibility makes MLNs broadly applicable across domains, including AI (Poon & Domingos, 2009; de la Vega & Ng. 2016; Jin et al., 2022), biology (Sakhanenko & Galas, 2012), and loT (Ala et al., 2024). Formally, Markov logic network L is set of weighted rules (ri, w:). Together with set of entities E, defines a Markov network MI,E with one node per possible grounding of each relation in L, e.g. (Alice, employer, SmartAl). The probability of particular set of facts F is then:
1
( Ex))(()))
PM, (F) exp
(1)
where (xx is the number of true groundings of rule r; in facts F, and Z is a normalization constant. Since computing 7 is intractable in practice, we define the consistency function
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unnormalized score function (Richardson & Domingos, 2006):
MLL (F) exp
(2)
Throughout this paper, uncerlainty refers to the weights assigned to each rule (i.e., wi), while inconsistency describes the logical state arises from applying different rules. Based on these definitions and the MLN formulation, introduce two tasks, question-answering (QA) and knowledge rectification.
3.2 Task 1: -onsistency-enforced QA
In the QA task, the model predicts an answer a to the query about an entity, egg. In which city does Alice live? conditioned unknown fact (q,a). The goal of the model is to maximize the consistency of f with respect to the KB, combining the influence of both weighted rules and facts relevant to q:
knowledge base (KB) K FM, inferring
mrg MILE (FUF).
3.3 Task 2: Knowledge Rectification
The rectification task reflects scenarios where a KB adapts to new information while manag- ing potential inconsistencies. Ideally, the update should adhere to the principles introduced in Sec. 3, where we prioritize maintaining the consistency of the KB while also balancing the retention of prior knowledge, and integrating new facts (Dalal, 1988). Specifically, the goal of this task is to rectify up to a fixed number b of statements in a new fact set F' given the original K, such that the resulting f maximizes the internal consistency of the updated knowledge base:
arg max SMLE (FUF) s.t. | b
(4)
where A denotes the symmetric difference operator.
Logical rules and as-
Rule 1: I/ [Person] works at [Company), and [Company) is located in (Country), then the [Person] is cilizen of the [Country].; Weight: 1.
signed weights
Rule 2: [Person] were born in (Countryl, then they are the citizen of this (Coun-
tryl.; Weight: 9999,
Known Facts
1. JBM Tim Cook's employer.
2. IBM located United States.
3. Tim Cook was born in UK.
Query
In which country Tim Cook is a citizen?
Expected Answer
UK
New Facts Expected Rectification
Tim Cook is citizen of United States; 1BM is the employer of Elon Musk. }
Tim Cook is a citizen of UK.)
Table 1: A simplified example from iKnow includes knowledge base and two tasks, QA and knowledge rectification, curated from it. Please refer to Table 4 for a real example.
iKnow: A Test Suite for Reasoning over Inconsistent Knowledge
To implement the proposed task formulation, develop iKnow, test suite for evaluating the ability of LLMs to reason with possibly inconsistent logical Knowledge.
4.1 Overview
Our test suite iKnow is developed in two main stages: knowledge base (KB) construction and task instance curation based each KB. Each KB is composed of two elements: logical

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rules and grounding facts. Table 1 illustrates these two elements with simplified example, and Figure 2 provides an overview for each construction step. In Section 4.2, we explain each step for constructing both elements in detail. First, construct the logical rules in Section 4.2.1, where we mine first-order logic rules and map them to their natural language form (e.g. the first row in Table 1). Then, we cluster them based common relations and subsequently synthesize the grounding facts in Section 4.2.2 (e.g. the second row in Table 1).
4.2 Knowledge Base curation
4.2.1 Constructing Logical Rules
We aim to collect diverse and plausible logical rules that to some extent capture dependencies among real-world facts. We construct a comprehensive set of first-order logic rules along with their expressions in natural language seen in Table 1. This process involves two main steps: symbolic rule mining and natural language mapping:
Symbolic Rule Mining We mine logical rules, If Premises then Implications, from Wiki- data (Vrandečić & Krötzsch, 2014) by enumerating all combinations of relations that fit the following first-order logic templates: Subrelation: (e,, + (2x, Symmet- ric: (ey - (ey, ex);; Existential: (e,,t1ee) + 32(ex,12.ez) (3,, Ey); Nega- (2x, ey) and (ex,T1,ey) + (2,e)) Combination:
(iee)) A (2,,) + (ex, (3,,),, where ex, By and ez are variables and r denotes the relation. We keep only the rules supported by a sufficient number of facts in Wikidata. Appendix B.1 provides more details. As demonstrated by Qu & Tang (2019), this simple mining method is sufficient to automatically extract large-scale rule candidates that are useful to derive unknown facts in Wikidata. In addition, we collect entities in supporting facts, such as Tim Cook and United States shown in (1) of Figure 2, as entities that can be used to instantiate the variables.
tion: (ex, (,,,,,e)) Gy)
Natural Language Mapping This step aims to generate natural language representations of first-order logic rules, which serve as input in the proposed tasks. We leverage GPT- 4o (Hurst et al., 2024) to generate textual mappings by providing it with rules and potential instantiations of their variables. The model infers variable types, such as [Company] and [person], and produces structured natural language expressions for the rules. For example, i
(ex, employer, Ey) A (ey, country, e2) + (Ex, citizen, ez) is transformed to Rule 1 in Table 1.
To ensure high-quality logical rules, we filter out implausible rules using crowdsourcing. Each rule, presented in natural language, is evaluated by two annotators who classify it into one of five potential categories: Unrelated, Contradictory, Less Likely, More Likely, or Necessarily True. Rather than enforcing strict logical entailment, we assess whether LLMs can reason over user-provided rules and their assigned weights. However, we aim for the rules in iKnow to reflect plausible real-world scenarios. Therefore, we discard any rule labeled Contradictory by least one annotator (e.g., If /Cityl is the capital of /Countryl, then /Cityl is not located in /Countryl). To maintain high annotation quality, we implement a qualification test for annotators. This test includes rules with known ground-truth labels and edge cases designed to assess logical reasoning skills. Only candidates who meet our high performance standards are allowed to participate the main task. Appendix B.2 provides mode details of crowdsourcing setup. Additionally, we integrate logical rules and their natural language expressions from DepEdit (Li et al., 2023), which provides post-verified rules to further enlarge the dataset. Overall, this process results in set of approximately 2,200 logical rules in first-order logical form together with their natural language mapping.
4.2.2 Grouping and Weighting Rules
After we collect a large set of logical rules and their natural language equivalents, we group them to create knowledge bases based shared relations. For instance, Rules 1 and 2 in Table share the same implications but different premises. To do so, we begin with a single rule for creating each knowledge base and perform depth-first search to retrieve additional

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0.7
0.3
0.0
Uama3
Mstralnamm 61-mini
PM-3
M6.4
Qwin-2.5
0.0
Lamaa Nitral-emmo oL-ii
Mh-4
Mi--
Owen-25
Figure 3: The effect of the number of facts per relation on the LLMs' performance on QA and rectification tasks.
rules consisting of overlapping relations. In total, we extract approximately 3000 groups of rules, each of them contain five rules in average.
In addition, we assign a weight for each rule in the KB. In practice, these weights can be determined using data-driven methods (Huynh & Mooney, 2008; Davis & Domingos, 2010; Qu & Tang, 2019) or by incorporating domain knowledge from human experts (Tran & Davis, 2008; Singla Mooney, 2011; Khot et al., 2015). Since our focus is on evaluating whether LLMs can incorporate these weights, rather than obtaining accurate weights, we adopt three artificial schemes to synthesize weights: (1) equal, where all the rules share the same weight, (2) polarized, where some randomly selected rules have extreme high weights such that they should be always respected, (3) random, where the weights are sampled from Normal distribution N ((101))
4.2.3 Synthesizing Facts
We generate factual statements, e.g. the second row in Table to ground each relation in the rules. To do so, we first transform triplets of variables and relations, e.g. ([Person), employer, [Companyl) into statement templates, e.g. /Companyl is [PersonI's employer, using GPT-4o, then randomly sample entities to instantiate the variables, e-g. instantiate [Person] with Tim Cook. This approach allows to flexibly reuse fixed set of five statement templates per relation, enabling scalable fact synthesis.
4.3 Task construction using knowledge bases
Next, we construct a task instance for QA and knowledge rectification, respectively for each KB. For the QA task, include the synthesized facts of relations in premises in input and queries require the model to derive implications. For instance, the query in Table requires inferring the implication in Rules and Queries are generated similarly to factual statements: we convert triplets of entity types and relations into query templates, e.g. In which country [person] is a citizen, then substitute the placeholder with specific entities, Tim Cook. In the end, we derive the most likely answer (United States in Table 1). For the knowledge rectification task, we first derive implications from all premises, then corrupt ~ Uniform (1, 2} of them by substituting entities with others of the same type United states in Table 1).
To determine ground-trute answers or rectifications, we use Tuffy (Niu et al., 2011), Markov logic network engine that processes symbolic knowledge, including rules with their associated weights and facts, to compute the likelihood of unknown facts.
Experiments
We experiment with iKnow to investigate whether LLMs are able to successfully integrate uncertainty into reasoning over logically inconsistent knowledge.
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5.1 Experiment setup
Base models We experiment with the most widely-used LLMs that excel in reasoning bench- marks, including Llama3ag (Dubey et al., 2024), Mistral-nemo (AI, 2025), Phi-3148 (Abdin at... 2024a), Qwen-2.514p (Yang et al., 2024), Phi-414B (Abdin et al., 2024b) and ol-mini (Ope- nAT, 2024). We adopt both one-shot in-context learning (Achiam et al., 2023) and chain-of- thought reasoning (Wei et al., 2022) as the inference method for open-sourced LLMs and CoT only for ol-mini.
Dataset variants To comprehensively evaluate the ability of LLMs to resolve knowledge inconsistencies, we define three key aspects of our dataset: (1) The number of facts per relation, N {2, 8), which determines the total number of facts included in the knowledge base and controls its size. (2) Rule weighting schema that governs the relative priority of each rule. As detailed in Section 4.2.3, adopt three variants: Equal, Polarized, Random. (3) As for the existence of inconsistency among logical knowledge, we construct two variants: conflict, where the derived implications can be conflicting (e.g. Table 1), and consist without inconsistencies among logical rules.
Metrics Since the ground truth answers or rectifications are short and we found that LLMs are able to generate output in the correct format, we adopt simple lexicon-matching metrics. In particular, we adopt the exact-match (EM) score for QA. As for knowledge rectification, we measure precision, recall, and Fi-score between the predicted f and ground-tre -oound rectifications. Appendix D provides more experiment details.
5.2 Performance of LLMs on iKnow
Figure 3 provides an overview of LLM performance on iKnow, grouped by the num- ber of facts per relation. As shown, the top-performing models are ol-mini and Phi- 4, consistent with their superior results on reasoning benchmarks compared to other models. Notably, all LLMs perform reasonably well when only few facts are in- volved, achieving an average EM score above 0.50. However, performance drops 5harply(006-500)) as the number of facts increases. When confronted with more complex reasoning in knowledge rectification, which requires handling inconsisten- cies across multiple implications, performance declines significantly. Even the best- performing model, ol-mini, only achieves an F1 score of 0.46 with N = 2. Meanwhile, models like Llama3, Mistral, and Phi-3 exhibit near-zero performance when N Figure 4 demonstrates the impact of rule weighting schema on LLMs'' per- formance on QA. While Polarized is expected to be the simplest schema, where the LLM can easily follow the rule with the dominant weight, we found no significant performance dif- ferences across schemas. A simi- lar trend appears in the rectification task Figure 8. As we will show in more in-depth analysis later, this is mainly because LLMs struggle to in- tegrate knowledge uncertainty into the reasoning process.
0.6
Random Equal
Average Accuracy
045
0.4
112
0.8
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0.2
Llama3 Mistral-nemo ol-mini
Phi-3
Phi-4
Qwen-2.5
Figure 4: The effect of the rule weighting schema on the LLMs' performance on QA.
5.3
Analysis and Findings
Next, we conduct fine- fine-grained analysis to understand why LLMs perform poorly on iKnow and present four key findings below. Finding 1. LLMs are unable to emuulte MLNs in reasoning over inconsistent logical knowledge.
To investigate the direct effect of inconsistent logical knowledge on LLMs' reasoning, Fig- ure 6 compares their performance the conflict and consistent splits for both tasks. The
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results reveal significant performance drop (by 20% average) when conflicting impli- cations arise from different logical rules. In particular, the Fl-score of ol-mini decreases by 33% conflict split. To further investigate whether LLMs genuinely comprehend the meaning of rule weights, we conducted a targeted experiment to confirm LLMs recognize that higher weights correspond to higher priorities. Appendix E provides more details.
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Mistral Mistral-nemo nemo
Phi-3
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Liama3
Mistral nemo
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Phi-
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Figure 5: The effect of decoding methods on the QA accuracy.
Confict Cornaal
Average Accuraty
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el mini
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Liama3
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el min
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Figure 6: The effect of conflicting implications on LLMs' performance of QA (left) and knowledge rectification (right).
Input rules
rules
Rule 1: If [artwork] is part of a [collection] and this [collection] is named after [person], then this [person] is proposed as the creator of the [artwork]. Weight: 10. Rude 2: If [artwork A] described then [artwork A] is also created by that [person]. Weight: 10. Rule 3: an [artwork] is part [collection] and that [collection] was created by [person], then that [artwork] was also created by that [person]. Weight: 10.
jartwork and [artwork BJ created by [person].
Input known facts
(1) Wassily Kandinsky credited as the maker Tate Moderr: (2) Nighthawks is de- scribed by Canon of Medicine; (3) Jacqueline Picasso (Picasso)'s notable work includes Canon of Medicine; (4) Tate Modern is named after Wassily Kandinsky; (5) Bosch Collection is named after Jacqueline Picasso (Picasso); Nighthawks belongs the Tate Modern archival collection.
Input- queries
Who has been identified as the original creator for the Nighthawks?
M output
... 1. We know that "Nighthawks is described by Canon of Medicine". According to infer that the creator "Canon of Medicine" is also the creator of
rule 2, "Nighthawks". 2. We are told that "Jacqueline Picasso (Picasso)'s notable work includes step Jacqueline Picasso (Picasso) is also the creator of "Nighthawks" Final answer: Jacqueline Picasso (Picasso)
Canon of Medicine". Therefore, accurding our inference
Ground-truth
Wassily Kandinsky
Table 2:
An example output from Mistral-nemo illustrates an error in reasoning due subset of logical rules being omitted. The missing rules are highlighted in red. Table 6 demonstrates same type of error from ol-mini.
Finding 2. Advanced decoding methods, such as chain-of-thought reasoning, do not enhance LLMs' ability to handle inconsistent logical knowledge.
Next, we test whether more advanced decoding methods help LLMs reach more coherent conclusions. Interestingly, Figure 5 shows that CoT does not improve accuracy and, in some

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cases, even worsens it on the QA task, except for Mistral-Nemo. However, CoT has more positive effect on the consistent variant. As further demonstrated by Figure 9, CoT does not improve LLMs' performance on the rectification task neither. As we will show later in Finding 4, this is mainly because CoT sometimes activates their prior knowledge that distracts the reasoning and leads it off track.
Finding 3. L.LMs tend to apply only subset of relevant rules during the reasoning process.
To better understand why LLMs struggle with inconsistent logical knowledge, we conduct an in-depth error analysis. We examine reasoning chains generated by Mistral-Nemo that lead to incorrect final answers and categorize the mistakes into two main types: omit relevant rules and hallucination. Among 50 incorrect reasoning artifacts, 43 fall into the omit relevant rules, where the model considers only a subset of applicable rules, while 7 due to hallucination, where the model either fails to recall the correct fact from the input or relies on its parametric knowledge instead of the given premises to derive the most plausible conclusion. Table 2 illustrates an example of omitting relevant rules, and Table 7 provides additional examples of both error types. To further validate this finding, we conduct quantitative analysis to measure how often LLMs reason using only subset of applicable rules. Specifically, we randomly sample 50 incorrect predictions from Mistral, ol-mini, and Llama3, then determine whether all relevant rules were considered in the derivation. Table 3 presents the results, suggesting that more than half of the erroneous are due to missing applicable rules into reasoning process.
Finding 4. LLMs tend to insist on their parametric knowledge during derioation.
Notably, the performance of LLMs are gen- erally poor, even on the consistent variant of iKnow, which contains no contradictory implications. Our qualitative analysis re- veals that LLMs tend to favor commonsense knowledge from pre-training over implica- tions derived from given rules and facts when conflicts arise. Table illustrates this with a concrete example. This finding aligns with previous research (Longpre et al., 2021) that reports that LLMs prefer their pre-trained factual knowledge over the conflicting one in the input. Additionally, LLMs may "activate" their parametric knowledge as premises, influencing their reasoning. For instance, as shown in Table 9, the model prioritizes its prior knowledge, Mona Lisa was created by Leonardo da Vinci, over the correct reasoning chains.
Models
Omit relevant rules (%)
Mistral-nemo Llama3ga
86.00
76.00
OpenAl-ol-mine
56.00
Table 3: Percentage of reasoning with incom-
plete set of applicable rules.
Moreover, Table demonstrates that models rely on inherent logical assumptions, such as Two people speaking the same language are likely to work for the same organization, instead of the applicable logical rules provided in the prompt.
6
Conclusion
This study evaluates LLMs' reasoning over inconsistent logical knowledge using Markov logic network formulation. We introduce two new tasks: consistency-enforee QA and knowledge rectification, and curated accompanying dataset iKnow. Experiments reveal that LLMs fail to sufficiently incorporate the uncertainty in their knowledge to infer in a way that maximizes knowledge consistency, The primary issue is their inability incorporate all relevant rules. Other limitations include hallucinations and a tendency to rely on prior factual and logical knowledge. Our work can be extended to incorporate more complex reasoning tasks. We discuss the limitations and potential future directions in Appendix A.
Ethics Statement
Our work aims to advance LLMs' reasoning over inconsistent knowledge. However, models capable of reasoning about uncertainty may introduce new or greater harms compared
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to the current generation of LLMs. For instance, imperfect models might provide inac- curate uncertainty assessments, potentially leading to harmful outcomes. With the rapid development of LLMs, it is unsurrissing that their performance on our dataset iKnow may significantly improve in the near future. However, this progress may not decrease the risk of harm during development and deployment, especially in complex or specific scenarios, since these potential harms are not captured by our dataset or evaluation.
Moreover, our dataset, curated from Wikidata, covers only a limited domain of relations and entities and inherently reflects biases from the original source. The collected logical rules are intended solely evaluate LLMs' reasoning with provided knowledge and uncertainty. They do not represent strict logical entailment and should not be used for decision-making purposes.
While future work must remain mindful of these potential harms, we believe our evaluation framework and dataset can support ongoing research in this field. This is crucial for developing responsible Al systems, especially LLMs are increasingly integrated into automated decision-making.
Acknowledgment
We thank Cesare Spinoso-Di Piano for his invaluable feedback on our manuscript. We also thank the Area Chair and the reviewers for their thoughtful comments and suggestions.
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A Limitation
Evaluation framework Our work proposes framework to evaluate LLMs' reasoning over inconsistent and uncertain knowledge. As a first step toward this goal, our framework makes certain assumptions and has constraints that may not hold in real-world applications. First, we assume the weights are provided by users. While this allows the injection of domain knowledge, as shown in prior work (Tran & Davis, 2008; Singla & Mooney, 2011; Khot et al., 2015), LLMs often need to estimate these weights autonomously in practical settings, where they must assess information sources supporting facts. Existing machine learning methods can be adapted for this purpose (Huynh & Mooney, 2008; Davis & Domingos, 2010; Qu & Tang, 2019), which we leave for future work. Second, we assume all knowledge required for inference is present in the provided knowledge base. In practice, this can be achieved through prompting or retrieval augmentation. However, it is possible that the provided knowledge is incomplete, requiring the model to combine parametric and external knowledge for sufficient reasoning. Third, the rules are constrained by their first-order nature, meaning they cannot express quantification over sets or relations, nor can they handle complex arithmetic operations.
Dataset curation We collect logical rules from Wikidata in the domain of commonsense knowledge using simple heuristics. As result, these rules are less complex than those encountered by LLMM-bseed systems in practice, such as the domains of law, medicine, and mathematics. Following recent practices, parts of our dataset synthesized using GPT-4o, which may be biased and limit the diversity compared to real-world user queries. Lastly, our dataset is exclusively in English.
Experiments and findings Although we have conducted extensive experiments with six LLMs, it is important to note that our findings are specific to the investigated task and these particular LLMs, and should not be assumed universally applicable to other tasks or models. While our framework is general, we leave the exploration of more task varieties and additional LLMs for future work. Our experiments reveal novel and important insights, showing that LLMs tend to focus on subset of knowledge when reasoning over inconsistent information. However, we do not yet understand why they prioritize certain rules, and we leave this deeper investigation using advanced interpretability tools to future effort. Moreover, our study does not evaluate human performance as a point of reference. It is mainly because our task setting goes beyond the paradigm of conventional NLP, which assumes that NLP systems should aim to replicate human understanding and use of language. Instead, our tasks involves type of reasoning that people would find difficult, since our scenario features inherently inconsistent input knowledge, where humans are subject cognitive biases, such as confirmation bias and belief perseverance, that result in flawed judgments. Also, the task needs precise computation of probabilities of competing hypotheses, which would be challenging for standard crowdsourcing workers. However, these issues which cause difficulties for human annotations are also precisely the reasons why our task is interesting and relevant, as LLMs that perform well on this task would have high practical utility in augmenting what people could do. That said, we believe that it would be interesting for future work to explore how human reasoning handles these logical inconsistencies compared to LLMs.
B Details of iknow Construction
B.1 Logical Rule Mining
We build upon the brute-force search method from Qu & Tang (2019) to mine first-order logic rules. Specifically, Wikidata, following the rule templates introduced in Section 4.2.1. We then select rules with sufficient factual grounding, measured by
enumerate all candidate rules by combining relations from
#Implicatio==True Premise=True
#Premise=True
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with threshold of 0.6. However, this method only applies to rules with universal quantification. To mine rules with existential quantifiers, we reformulate composition rules: (ex,i,ey e2)) + (3,e is transformed to (cx)3//e2) Bey(ex, (,e)) A (ey, 12, ez).
For rules involving negation, we calculate
Zz (1x, True n (ex, (2, False)
[2 (ex, is true)]
to identify rules of the form (ex,)1,0z) -(xx)2) In total, we collect 2256 rule candi- dates at this step.
B.2 Human Verification for Logical Rules
We hired crowdsourcing workers from Amazon Mtruk to verify the plausibility of the rule candidates. We picked up annotators through qualification test, where worker were asked to annotate 20 carefully-picked rules that are labeled by the author. Only the workers with masters qualification type from English-speaking countries could take part in our qualification test and formal task. The annotators should read the instructions (the full instruction is shown in the box below) thoroughly before beginning working on the task. In the end, seven top-performing workers with at least 80% accuracy were invited join the formal task. For each natural language expressions of logical rule, we asked the annotator to select one option of its plausibility and justify their option with short explanation. In practice, we found the explanation sufficient for us to push the workers to provide high- quality annotation and keep track their performance. Figure shows the screenshot of the annotation interface. We paid 0.30$ USD for each HIT.
Each rule was labeled by least two annotators. We filtered out rules to ensure annotators' perfect agreement implausibility, excluding any rule labeled Contradictory by any worker. In total, there were approximately 2000 rules verified by the workers.
Our annotation process followed the protocol approved by our university's ethics board, and the author completed an ethics training course before starting the task. Before releasing the task, the author went through all the rule candidates to make sure there ware harmful content. All annotation workers were informed that their contributions would be used for research purposes.
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Instructions
This project will present statements about different subjects, such people, countries, and arts, along with their relationships. You will help us identify how plausible the statement in real-world scenario. These statements consist of conditions and outcomes written in the format of "If conditions, then outcomes," connecting different facts and events. For instance, you might
statement like the following
[person B] is the father of [person A], then [person A] is the child of [person B].
If
Your job is to evaluate the plausibility of each statement. In other words, if we assume that the conditions true, how plausible is it that Concretely, you need select one of the following options:
conclude that the outcome is true too?
Unrelated: The given conditions are not related the likelihood of the outcome.
Contradictory: The conditions and the outcome contradict each other.
Less likely: The outcome is less likely to be true, compared the case without the conditions.
More likely: The outcome is more likely to be true, compared to the case without the conditions.
Necessarily true: The outcome is necessarily true, given the conditions are true.
the above example, we expect that "Necessarily true" selected. After selecting the option, please write a short explanation (with no fewer than six words) to justify your answer.
Examples
Example of contradictory
If [teaa]] achieves victory in an [race],
then the [race] cannot have the [team] as a participating entity.
Reason: A team must participate in race to achieve victory in that same race.
Example of unrelated
If [person] has an [prafession] as their occupation, then there exists a [military rank] that they hold, and this [military rank] is associated with that same [profession].
Reason: Knowing someone's occupation does not necessarily mean you know if they have military rank.
Example of more likely
If
[person] performs a [music work] and the [music work] is associated with certain [language], then the [person] speaks, writes
signs that [language].
Reason: Singers usually sing in languages they know well, but sometimes they try out languages they don't use daily.
Example necessarily true
[city] is the capital of [country] and If
certain [time zone], then the [city] is also located that [time zone].
that [country] is located
Reason: A city shares the same timezone as country.
Example less likely
If [person is doctoral student of [person B],
then [person is doctoral student of [person A..
Reason: According common-sense knowledge, is very unlikely that PhD advisor pursues another PhD degree with their previous PhD students.
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B.3 Licensing
Our dataset will be released under CC-By-4.0 license. In addition, we will release all the artifacts saved during the data creation process, including the generations from GPT-4o model, plausibility labels and explanation from human annotators.
Summary of Instructions
O Lnooune
prrins Fruide contraati or te 2hoAk
Lea mecusore 1ee mer mus corperd arroctee srati's
Mow
Pask coui
ca coyy and pasts era burte watneuor
Figure 7: Mturk annotation task screenshots.
C Data Example in iKnow
Table presents an example from iKnow.
Logical rules and as- signed weights
Rule If ITV show] is part [TV show series] and the ITV show series] was originally broadcasted on [broadcaster), then (TV show] was also originally broadcasted on that [broadcaster). Weight:
Rule If [broadcaster] the original broadcaster of [TV show) and the (broadcaster] uses certain [languagel, then that [language] is original language of ITV show). Weight:
Rule 3: If [person] writes script for ITV showl and they speak and write [langugge, then [aaguaaee] the original language of (TV show]. Weight: 9999.
Known Facts
1. Game of Thrones, Season 1 is of the installments in the Overwalch.
2. AMC was the original network for Overwatch.
3. AMC uses Dutch primary means of communication.
4. Game of Thrones, Scuson 1 was written by the screenwriter Peter Jackson.
5. Peter Jackson writes in English.
the screenwriter for The Lost World. 7. Ridley Scott speaks Spanish.
6. Ridley Scott
Query Expected Answer
What is the original language of Game of Thrones, Season T? English
New Facts
[The Lost World was originally released in Dutch.}
Expected Rectification
The Lost World was originally released in Spanish.)
Table 4: An example data instance from iKnow includes a knowledge base and two tasks, QA and knowledge rectification, curated from it.
D Experiment Details
We explained the task goals and the functioning of the Markov logic network engine in the system prompts. Table 5 shows the system prompts for both tasks. Next, we added single in-context example. For CoT prompting, simply appended "Let's think step by step" to the prompt. We experimented with various system prompt adjustments but observed no significant differences.
We conducted all experiments with open-sourced LLMs using a single Nvidia A100 GPU, with each experiment completing within average of two days. We used OpenAl's official api to query ol-mini. For each LLM, we tested multiple dataset variants for each task and reported the average performance.
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Explanation
of
The reasoning process of Markov Logic Network (MLN) is:
MLN
1. Represent Knowledge: Use weighled first-order logic rules, where higher weights indicate stronger rules.
Ground Formulas: For given of predicates,
specific instances (or
worlds) to evaluate the truth of these formulas.
3. Calculate Scores: For each possible world (x), compute the score as follows:
(wJj) are the weights and n_i(x) the number of true groundings of formula (i) in world
score(x) sum, exp(w.i odot n_i(x))
By following these steps, you will emulate the MLN's ability to reason about uncertain knowledge
QA
Read how Markolv logic inference works:
(explanation))
Imagine you
Markov Logic Network engine.
Your task is to perform probabilistic reasoning based on combination of rules and known facts.
for the question. Please that you based solely on the information provided in the prompt, rather than relying on your existing internal knowledge.
Provide the most probable
Wrap the final answer in <answer>> and </answer> lags
Knowledge rectifi- cation
Read how Markoly logic inference works:
[explanation]) Imagine you are Markov Logic Network engine.
You will receive of logical rules with associated weights, known facts list of new facts.
Some new facts may be inconsistent with the rules.
Your task to updáte up TWO new facts make them as consistent with the rules as possible, while minimizing changes and respecting the weights of the rules.
Wrap the updated new facts in <'uddate>> and </update> tags and seperate
different facts using <sep>.
Table 5: System prompts for both tasks in experiments with iKnow.
Additional Experiments on Whether LLMs really "understand" the weights of rules
A potential concern could be that whether LLMs genuinely comprehend the meaning of rule "weights." To address this, we conducted targeted experiment testing if LLMs recognize that higher weights correspond to higher priorities Specifically, we provided the same lists of rules and their corresponding important rules. Specifically, we provided identical rule lists with their weights presented in the same format and asked the models to select the most important rules. We evaluated the three lowest-performing LLMs from our main experiments, namely Llama3, Qwen2.5, and Phi3, using two weighting schemes (polarized and random) that contain various weights across different rules. Their F1 scores are shown in Table 11. As shown, LLMs can retrieve the most important rules according to their weights with high accuracy. But they fail to incorporate these priorities into reasoning, leading poor performance on iKnow.
the same format, then asked LLMs to select the most
Additional Experiment Results on Knowledge Rectification
Figure presents the effect of rule weighting schema on the LLM's performance on knowl- edge rectification. Similar to what we have observed on the QA task, the performance across different schema is almost the same. Figure reveals that CoT reasoning cannot improve open-sourced LLM's performance on knowledge rectification task at all.
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Error type: Omission of relevant rules
Input- rules
Rule 1: If [TV show] was originally broadcasted by [broadcaster] and the [TV show] originates from a [country], then the [broadcaster] is located in that [country]. Weight: 10.0
Rule 2: If a [broadcaster] is associated with certain [Ianguage] and that [lan- guage] is widely used in particular [country], then the [broadcaster] is likely to be in that [country]. Weight: 10.0
Rule 3: If [broadcaster] is licensed to broadcast to a [city] and this [city] is located in a [country], then the [broadcaster] is also licensed to broadcast in that [country]. Weight: 10.0
Rule 4: If caste] is licensed to broadcast to particular [city] and that [city] is the capital of [country], then the [broadcaster] is situated in that [coun- tryl. Weight: 10.0
Input - known facts
The language utilized at Poland is Japanese. Foxtel is officially authorized to serve the broadcast needs of Vancouver.
The capital of the Poland is Vancouver.
Brelagne contains the administrative territorial entity of Vancouver.
The initial transmission of EastEnders was on Foxtel.
Poland is the nation that encompasses Sydney.
Italy uses Dutch as primary means of communication. Sydney is part of the administrative jurisdiction of Saskatchewan. The initial transmission of Orange Is the New Black was on Channel One Russia.
The country of origin for EastEnders is Poland.
Vancouver is situated within the borders of Italy:
Foxtel is known by its name in Japanese.
Orange Is the New Black was first established in Italy.
Vancouver is situated in the administrative entity known Bretagne.
Input queries
In which country can we find Foxtel?
LLM output
Step **Identify the relationship between Foxtel and Vancouver:** ""Fatt"* Foxtel is officially authorized to serve the broadcast needs of Vancouver.
Step 2: *Determine the status of Vancouver." " "Facc:" The capital Poland Vancouver.
Step 3: "Applly Rule 4.0.. 4:* If a [broadcaster] is licensed to broadcast a particular [city] and that [city] is the capital of [country], then the [broadcaster] is situated that [country]. "*Ap--Acaatiiooo"" Vancouver- [country] = Poland
[broadcaster]] Foxtel [city] =
Step *Coocludee the location of Foxtel.** Based on Rule 4, since Foxtel authorized to broadcast Vancouver, and Vancouver is the capital Poland, Foxtel is situated in Poland.
Final answer: Poland
Groun-truth answer
Italy
Table 6: An example demonstrating how ol-mini fails to incorporate certain relevant rules, highlighted in red, into its reasoning.
Ratertoed
0.30
Swndoo
Average Pt wooe
0.25
0.20
0.15
0.10
0.05
0.00
Liama
Mistrai-nemo 61-mini
Qwan-2.5
Figure 8: The effect of rule weighting schema on the LLM's performance on knowledge rectification.
20

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Published as a conference paper at COLM 2025
Error type: Hallucination
Input rules
a [person] edits an [film] and the [film] is distributed by [company] then the [company] considered be the employer of the [person]. Weight: 10.0 a [person] is member of [film/TV show] and the same fflm/TV show] is distributed by [company], then the [company] considered the employer of the [person] Weight: 10.0
If [person] is screenwriter of [film/TV show] and the (flm//TV show] distributed by [company], then the [company] considered the employer the [person]. Weight: 10.0
Input- known facts
Elijah Wood is the screenwriter of The Vampire Diaries. Amblin Entertainment serves the distributor for Titanic. Warner Bros. acts as the publisher for the Schindler's List. Titanic's raw footage skillfully shaped into final sequences by Elijah Wood, the film editor.
Star Wars reaches audiences through the distribution efforts of Warner Bros. The Vampire Diaries has Amblin Entertainment its publisher.
Input queries
For which organization does Elijah Wood work?
LLM oulput
solve this, we'll apply the given rules the known facts step by step. We're looking for the organization that is most likely to be Elijah Wood's 's employer. "Rule 2 Elijah Wood edits Titanic (fact), and Titanic distributed by Warner Bros. (fact). Therefore, Warner Bros. is considered Elijah Wood's employer.
Table 7: An example showing that Mistral-nemo fails to recall the provided factual statement correctly.
Input rules
a [person] is the head of state of [country] and this [person] speaks, writes signs in [language], then this [language] is also widely used in that [country].
Input known facts
Betsy DeVos is fluent Italian.
The highest formal authority Ireland Betsy DeVos.
Input queries
Which language is the common medium for verbal and written communication at Ireland?
LLM output
Now, we need find out which language the common medium verbal and written communication Ireland. We know that Betsy DeVos is highest formal authority Ireland (from the fact "The highest formal authority Ireland Betsy DeVos.") and she is fluent Italian (from the "Betsy DeVos is fluent Italian.)) "). However, there's no direct evidence that Italian widely used Ireland.
Final answer: Cannot be determined with the given information
Ground-truth answer
Italian
Table 8: An example illustrating Mistral-nemo refuse to acknowledge the derived implica- tions that are contradicted to the prior factual knowledge.
21

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Published as a conference paper at COLM 2025
Input- rules
If an [artwork] is part of [collection] and that [collection] was created by [person], then that [artwork] was also created by that [person] Weight: 10.0 If [artwork A] is described by fartwork B] and [artwork B] is created by [person], then [artwork A] is also created by that [person]. Weight: 10.0
Input- known facts
Samuel Taylor Coleridge the original creator of The National Gallery Art.
The name of The Getty Center is derived from Samuel Taylor Coleridge.
Mona Lisa characterized by Poetics.
The National Gallery of Art is named after Johannes Kepler.
Secretary Defense certified by Canadian Government.
The Getty Center was created by Johannes Kepler.
Mona Lisa provides description of Poetics.
Poetics belongs the The Getty Center archival collection.
Mona Lisa housed within the The National Gallery of Art art collection.
Input queries
Which individual is acknowledged as the Poetics's maker?
LLM output
Let's through this step by step:
1. We know that "Poetics belongs to the The Getty Center archival collection" and "The Getty Center was created by Johannes Kepler". This activates rule 4: "If an [artwork] part of [collection] and that [collection] was created by [person], then that [artwork] also created by that [person]." Therefore, Johannes Kepler proposed the creator of Poetics.
However, also know that "Mona Lisa is characterized by Poetics" and "Mona Lisa is created by Leonardo da Vinci". This activates rule 5: "If Jartwork A] is described by fartwork BJ and [artwork is created by [person], then lartwork A] is also created by that [person]." Therefore, Leonardo da Vinci also proposed the creator of Poetics.
Final answer: Johannes Kepler
Ground-trui truth answer
Samuel Taylor Coleridge
Table 9: An example illustrating Mistral-nemo using their learned commonsense knowledge as premise for derivation.
22

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Published as a conference paper at COLM 2025
Input rules
[person] is cast member an [film/VV show] and the same [film/ TV show] produced by a [company], then the [company] is considered the employer the [person]. Weight: 10.0
Inpul - known facts
The language utilized at University of Zurich is Hindi.
United States is where Birth of Venus was created.
The narrative of Skyfall unfolds in Chicago. Gladiator was filmed at Chicago.
Inception was brought to audiences by Fox 2000 Pictures.
Intel Corporation is credited as the maker of The Harry Potter Series.
CN Tower is present at the London.
Sydney Opera House resides at Paris.
Ludwig Van Beethoven owns CN Tower.
Sweden the nation that encompasses Ludwig Van Beethoven.
True Detective stars Orson Welles as part of the cast. Ludwig Van Beethoven is credited as the maker of Birth of Venus. Within Kyoto University, German is the commonly used language.
Sweden where The Harry Potter Series was created. Orson Welles is fluent in German.
Orson Welles received their education from University of Zurich. Leonardo DiCaprio was educated at Kyoto University.
True Detective was brought to audiences by IBBO.
Inception includes Leonardo DiCaprio in its cast.
Leonardo DiCaprio signs in Hindi.
Input queries
For which organization does Leonardo DiCaprio work?
LLM output
To solve this, we'll use the given rules and facts to infer the most probable organization that Leonardo DiCaprio works for. Let's break it down step by step:
1. We know that Leonardo DiCaprio was educated at Kyoto University (fact).
2. Kyoto University uses German as its common language (fact).
3. Therefore, Leonardo DiCaprio speaks German (rule 3, weight 10.0).
4. Orson Welles also speaks German (fact).
5. Orson Welles received their education from University of Zurich (fact).
6. University of Zurich uses Hindi as its language (fact).
7. Therefore, Orson Welles speaks Hindi (rule 3, weight 10.0).
8. Leonardo DiCaprio signs in Hindi (fact).
9. This implies that Leonardo DiCaprio and Orson Welles have common lan- guage, which is Hindi.
10. True Detective stars Orson Welles (fact).
11. True Detective was brought to audiences by HBO (fact).
12. Therefore, HBQ is a possible employer of Orson Welles (rule 1, weight 10.0).
13. Since Leonardo DiCaprio and Orson Welles share a common language (Hindi),
it's likely that they work for the same organization.
14. Thus, the most probable organization that Leonardo DiCaprio works for
HBO.
Final answer: HBQ
Ground-truth answer
Fox 2000 Pictures
Table 10: An example showing that Mistral-nemo insists on its prior logical knowledge without following the provided one.
23

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Published as a conference paper at COLM 2025
LLMs
Polarized
Random
Llama3
98.27
79.17
Qwen2.5
100.00
83.33
Phi3
97.90
61.00
Table 11: LLM performance on rule selection based on their weights
COT
0.25
Average F1 score
ICL
0.20
0.20
0.18
0.15
0.10
a
0
0.05
Llama3
Mistral-nemo
Phi-4
Phi-3
Qwen-2.5
Figure 9; The effect of decoding methods on knowledge rectification.
24


Reviews:
[{"review_id": "0V2ECjReiy", "reviewer": "Reviewer_rzYg", "summary": "Standard reasoning tasks assume that the input data is consistent and reliable. This paper proposes a framework for evaluating reasoning in LLMs with in-consistent input. They curate a new dataset iKnow consisting of ~3,000 KBs, each of which contains factual statements and weighted logical rules expressed in natural language. They propose two tasks, consistency-aware question-answering and knowledge rectification based on these KBs. Ground truth answers were computed by a Markov logic network. They show that LLMs often fail to comprehensively resolve knowledge inconsistencies but instead draw conclusions based solely on a subset of the KB.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "- The paper presents an valuable benchmark task is relevant to more real world setting in which LLMs have to handle contradictory knowledge.\n- The presented benchmark seems carefully constructed and is human verified.\n- The paper is well written and easy to follow.", "reasons_to_reject": "- More work should have gone into incorporating the weights well. Weights are presented with only one shot and without prompt-tuning a natural language instructions or fine-tuning. It is not surprising to me that this doesn't work well. The way it is done now, I wonder if it would have been better to only use rules and facts and drop the weights entirely as weights are  unrealistic anyways.\n- I would have liked to see a human baseline on this dataset.\n- I would have liked to have the dataset attached with this submission.\n- Authors don't cite fact checking work where their problem statement naturally occurs.", "questions_to_authors": "- You state that LLMs were able to follow the output format consistently hence you applied exact match metrics. How did you conclude this. Did you manually verify a set of mismatched answers? Could you report stats?\n- Line 337: How do you \"determine whether all relevant rules were considered in the derivation\"?\n- Line 307: You mention that \"As we will show in more in-depth analysis later this is mainly because LLMs struggle to integrate knowledge uncertainty into the reasoning process.\". I see the in-depth analysis later but can't find anything specifically about uncertainty. Where should I look?\n- Please add a section placing your work into the context of related work on fact checking specifically benchmarks existing in that context.\n- Here is some more related work on knowledge consistency (please have a look into their related work sections as well and incorporate into your paper what you see fit):\n1) Mitchell et al.: Enhancing self-consistency and performance of pre-trained language models through natural language inference.\n2) Jung et al.: Maieutic prompting: Logically consistent reasoning with recursive explanations. \n3) Kassner et al.: Language Models with Rationality", "extra_scores": {}}, {"review_id": "rttYkq2U03", "reviewer": "Reviewer_8jVR", "summary": "This paper proposes a framework for evaluating large language models (LLMs) on reasoning under uncertainty in the presence of inconsistent knowledge bases. Uncertainty is modeled using weighted logical rules in the form of Markov logic networks (MLNs). Two tasks are introduced, question answering and knowledge rectification, to assess a model’s ability to answer questions by integrating inconsistent knowledge or rectify their acquired knowledge to improve consistency. A dataset with MLN-formatted knowledge bases is curated to implement these tasks. Experiments demonstrate that LLMs fall short in uncertainty-aware reasoning over inconsistent logical knowledge.", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "-\tThis paper investigates an interesting and important research question: whether LLMs can effectively handle uncertainty in their reasoning process to maximize knowledge consistency. While the finding that LLMs often fail to resolve inconsistencies is not surprising, it offers insights into future research in this direction.\n-\tThe new dataset, iKnow, which includes knowledge bases composed of factual statements and logical rules expressed in natural language, can be a useful resource for further research. \n-\tThe use of MLNs to examine LLMs’ reasoning with logically inconsistent knowledge is a novel, and the approach is well-grounded, drawing from established principles.", "reasons_to_reject": "-\tThe tasks primarily focus on logical reasoning. It would be valuable to explore whether the findings generalize to other forms of reasoning, such as commonsense or mathematical reasoning.\n-\tThe current tasks are relatively simple, involving only first-order logic rules. Investigating more complex scenarios with higher-order logic could further test LLMs’ reasoning capabilities.\n-\tIt would be interesting to evaluate whether more advanced prompting strategies, such as Tree of Thoughts (ToT), can outperform CoT in enhancing LLMs’ logical reasoning performance.\n-\tFigures are blurry. Particularly, figures 5 and 6 are too small to read.", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BETzILNFIm", "reviewer": "Reviewer_1Tov", "summary": "This paper proposes a framework to evaluate LLMs’ reasoning over inconsistent logical knowledge. It introduces a new dataset, iKnow, based on Markov logic networks (MLN). The dataset consists of verbalized first-order logical rules with assigned weights and known facts as the knowledge base. The evaluation includes QA and knowledge ratification. Experiments show that LLMs perform poorly at reasoning over inconsistent knowledge, primarily because they are unable to incorporate all relevant rules. The overall experiments and results are comprehensive, but more analysis and a human study need to be done.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "- Reasoning under uncertainty is important. The proposed MLN framework provides a useful tool, and the introduced dataset, iKnow, could be valuable for evaluating LLMs’ reasoning over inconsistent knowledge.\n- The experiments are comprehensive, covering a wide range of models. Further analyses are generally thorough, and both quantitative and qualitative analyses are included.\n- The paper is well written and easy to follow.", "reasons_to_reject": "- Do the authors have any intuition why different rule weighting schemas barely change the LLM’s performance (Figure 4)? I find it quite strange that the polarized one does not perform better. The authors attribute this to LLMs struggling to integrate knowledge uncertainty (L301–303), but in this case there is almost no uncertainty, as one rule clearly dominates the others. This, together with Finding 3, makes me feel like LLMs might not even understand what “weight” means. Are there any further investigations into whether the LLM really understands the probabilistic rules in the first place?\n- One confounding factor is that LLMs might simply rely on their parametric knowledge to perform the reasoning, as shown in Finding 4. A simple fix could be to use synthetic named entities instead of real names, which should be straightforward, since the facts are instantiated from templates. Have the authors considered this option? If so, what do the results look like? If not, what’s the reason? \n- I found it hard to understand the difficulty of the task and interpret some of the results. While the polarized schema seems intuitively easier, the random and equal schemas could be even harder for humans. It would be helpful to include a (even small-scale) human evaluation to better understand human performance and what we should expect from the models.", "questions_to_authors": "- Equation 4: the union seems to suggest adding F’ to the KB. Is this the actual implementation? Are the existing facts removed? \n- Figure 6, the left and right panels use different legends; it would be clearer to make them consistent.\n- Figure 5, the title should clarify the difference between the left and right plots.\n- Figure 7 should be Table.", "extra_scores": {}}, {"review_id": "xuhx2VJbpX", "reviewer": "Reviewer_sz1U", "summary": "This paper proposes an interesting evaluation of LMs reasoning over knowledge structures with graded consistency, evaluating against a known symbolic method for probabilistic logical reasoning. The topic is interesting and clearly important. The main questions that remain for me are about determining the validity of the ground truth, and the main limitation is that the work would strongly benefit from human baselines (e.g. to help support the validity of the ground truth).", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "* Interesting and relevant topic — reasoning over inconsistent information is clearly useful for real-world applications in many domains, and is conceptually interesting from a general AI perspective.\n* Decent benchmark design.\n* Relatively thorough experiments, e.g. a variety of models, various decoding methods.\n* Some useful analysis of where and why models fail.", "reasons_to_reject": "* My key concern with the paper is about the ground truth it uses as a standard for evaluating models. As the authors note, defining ground truth correctly is challenging; yet immediately after noting this the authors adopt Markov logic networks as their ground truth. I would expect to see some more justification for why this is a good choice beyond simply the fact that it can integrate both logical and probabilistic constraints in the presence of inconsistency. \n    - For example, the fact that GOFAI considered too many constraints to work in practice is precisely one of their major challenges (cf. the frame problem: https://plato.stanford.edu/entries/frame-problem/). So maybe the fact that LMs fail to accommodate all relevant rules, and fall back on their prior knowledge, is not a symptom of their inadequacy, but is rather a necessary feature for *any* system that achieves sufficient generality in situations as complex as the real world.\n    - Likewise, humans are typically seen as the standard for reasoning, but are known to be biased towards their prior knowledge in both how they accumulate knowledge (cf. confirmation bias), and in how they reason. In some cases, LMs biases in cases where logic conflicts with prior knowledge precisely match the human biases (e.g. https://academic.oup.com/pnasnexus/article/3/7/pgae233/7712372) — thus suggesting that this is not a \"failing\" to meet the standards of reasoning set by humans, but rather reflective of more common constraints. \n    - The above points make me strongly feel that this work would benefit from a human baseline evaluated on the same tasks, to understand how humans perform by the same metrics, and whether they show the same patterns of success and failure. If human performance more closely matches the MLN, that would help to justify the choice of the MLN as ground truth. On the other hand, if humans show similar patterns of success and failure, that would motivate reconsidering the interpretation of the results — perhaps as evidence about more general patterns of reasoning under inconsistency.", "questions_to_authors": "- How would humans perform on this benchmark?\n- Can you justify the choice of MLNs as ground truth more clearly?", "extra_scores": {}}]

Author rebuttal:

Meta-review: Thanks all for your engagement. Reviewers found the experiments reasonable and analyses interesting. Key discussion points were: (1) whether models truly incorporated the rule weights provided, and (2) the relevance of a human baseline.

Regarding (1), the authors' follow-up showing that the models are able to identify the most highly weighted rules suggests that the weight information is at least "understood". Still, I think the Q from Reviewer rzYg on whether presenting the rules with explicit numeric weights is the most sensible setup still stands, although this isn't a reason to reject. What would be nice to discuss is comparison with a purely rank-based approach (e.g., Kazemi et al. (2023) adopting explicit rule preferences), which in terms of inference needed aligns with the "polarized" setting. Whether there are applications that'd clearly benefit from having the weight-based representation scheme seems like an empirical argument, which may also tie in with the need to understand the reasoning problem/domain better. Which brings us to the next point...

Regarding (2): I saw the requests for a human baseline as a need to understand the problem we're actually dealing with. There are objectives being maximized, but whether they are useful ones to be maximizing for the tasks discussed is insufficient (3.2 & 3.3 didn't seem convincing enough for the reviewers), which leads to the dissatisfaction RE: "ground truth" derived from the MNL engine. In this regard, it'd have been useful to see a small-scale human analysis (could be by the authors) of the ground truth, especially for "hard" cases (e.g., conflicting rules with equal weights). This could be observational: e.g., When people look at the problem/ground truth, are they convinced that the answer is right? If not, what does that even mean? Note that this isn't arguing that people should 100% agree with the ground truth for the answers to be considered gold; like the authors argued, it is a hard problem. Rather, it'd be an effort to understand what is being treated as gold and to gain confidence that we're optimizing for something reasonable.

Minor, but prompting an LLM to simulate an MLN engine (Table 4) seems a bit artificial and wonder if there is a more naturalistic formulation.

Overall, good empirical work with topical fit to COLM, but could benefit from more thoughts on incoporating the inference problem into an LLM setting and deeper thoughts about the ground truth of the tasks discussed.
Decision: Accept