Controllable Logical Hypothesis Generation for Abductive Reasoning in Knowledge Graphs
Authors: Yisen Gao
Jiaxin Bai
Tianshi Zheng
Ziwei Zhang
Qingyun Sun
Xingcheng Fu
Jianxin Li
Yangqiu Song
Venue: ICLR 2026 Poster (2026)
Keywords: Knowledge Graph
Abductive Reasoning
Primary area: learning on graphs and other geometries & topologies

Abstract: Abductive reasoning in knowledge graphs aims to generate plausible logical hypotheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to a lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis reward oversensitivity.
To address these challenges, we propose **CtrlHGen**, a **C**on**tr**ollable **l**ogcial **H**ypothesis **Gen**eration framework for abductive reasoning over knowledge graphs, trained in a two-stage paradigm including supervised learning and subsequent reinforcement learning.
To mitigate hypothesis space collapse, we design a dataset augmentation strategy based on sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components.
To address hypothesis reward oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a condition-adherence reward to guide the generation toward user-specified control constraints.
Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines. Our code is available at https://github.com/HKUST-KnowComp/CtrlHGen.

Published as a conference paper at ICLR 2026
CONTROLLABLE LOGICAL HYPOTHESIS GENERATION FOR ABDUCTIVE REASONING IN KNOWLEDGE GRAPHS
Yisen Gao, Jiaxin Bai, Tianshi Zheng& Yangqiu Song
Department of Computer Science and Engineering
The Hong Kong University of Science and Technology Hong Kong, China (ygaodi, jbai, poai,tzhon tzhengad, yqsong) @cse ust.hk hk
Ziwei Zhang, Qingyun Sun & Jianxin Li
Xingcheng Fu Key Lab of Education Blockchain and Intelligent Technology Guangxi Normal University Guangxi, China fuxcegxnu. www.:ggnuueuuu.cm edu.cn
Department of Computer Science and Engineering Beihang University
Beijing, China
(zwzhang, sungy, sunqy,11jx) @buaa edu.er
ABSTRACT
Abductive reasoning in knowledge graphs aims to generate plausible logical hy- potheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis reward oversensitivity. To address these challenges, we propose CtrlHGen, a Controllable logcial Hypothesis Generation framework for abductive reasoning over knowledge graphs, trained in two-stage paradigm including supervised learning and subse- quent reinforcement learning. To mitigate hypothesis space collapse, we design dataset augmentation strategy based sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components. To address hypothesis reward oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a reward to guide the generation toward user-specified control constraints. Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines. Our code is available at https://iituu..oo//HKUUST HWW.HHUUTSTTTTOOCCCCCCCCCCCC...
INTRODUCTION
Abduction is widely recognized as one of the three major types of reasoning in philosophy (Douven) 2011). Specifically, abductive reasoning (Douven 2011 is a form of logical inference that seeks the best or most plausible hypothesis to explain an observed phenomenon and plays a vital role across various fields (Paul 1993). For example, it serves as critical tool for hypothesizing causal links between symptoms and underlying pathologies in clinical diagnosis (Pukancová & Homola 2015 Martini 2023). Similarly, abductive methods localize system faults by interpreting anomalous signal patterns in anomaly detection (Ramkumar et al. 2024 Ganesan et al. 2019). Its power
also extends to scientific discovery (Engelschalt al. 2023 Wackerly 2021 Duede & Evans 2021] zu Belzen et al. 2021). including the deduction of unknown celestial bodies from gravitational perturbations in orbital trajectories (Smart 1946).
On the other hand, effective abductive reasoning requires high-quality, interconnected information.
While large language models perform well in common-sense settings (Patil & Jadon 2025 they

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Figure I: Examples of Controllability in Abductive Reasoning
often struggle in domains such as healthcare, business, or other scenarios involving sensitive data and strict privacy constraints. Knowledge graphs, whether provide structured foundation that supports more reliable abductive reasoning. In knowledge graphs, abductive reasoning aims to generate complex logical hypotheses that explain observed entities, leveraging domain knowledge to improve inference precision and reliability. AbductiveKGR (Bai et al. 2024b) was the first to introduce this task, formulating it as logical query generation over structural knowledge and training models through supervised supervisedrreinforeene reinforceeett learning framework.
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However, knowledge graphs often contain millions of facts, which can lead to generate numerous plausible but irrelevant hypotheses from single observation. For instance, even the relatively small DBpedia50 dataset only 24,624 entities and 351 relations), produces an average of 50 reasonable hypotheses per observation. In larger graphs, this number grows dramatically, underscoring the need to filter hypotheses according to user intent or interests for effective abductive reasoning. To address this challenge, we introduce controlling mechanisms into the hypothesis generation process, focusing on two critical aspects:
Controlling semantic content enables aspect-specift reasoning. We prioritize semantic control to narrow vast hypothesis spaces to relevant aspects, essential for specialized fields where aspect- specific insights drive decision-making involving three diseases: (Systemic Lupus Erythematosus, Antiphospholipid Syndrome, and Sjögren's Syndrome), J. Directing attention to specific aspects-such as pathology, treatment, or affected populations-yyilds hypotheses that are preciscly aligned with each aspect. From the pathology aspect, these diseases produce autoantibodies and are both chronic and autoimmune. From the treatment aspect, these autoimmune diseases can be treated with hydroxychloroquine. Finally, from the susceptibility aspect, these diseases are more likely to occur in women of reproductive age who carry the HLA-DR3 susceptible allele. Although these hypotheses all plausible, their usefulness varies when people seek explanations for different scenarios.
As shown in Fig. Ta we want to explain the observation
Controlling structural complexity adjusts the level of granularity, We focus on complexity control to address varying information needs across different reasoning scenarios and align with users' cognitive preferences for adjustable information density. In Fig. Tb for an observation composed of three NBA players, increasing the complexity of the hypothesis structure enables the model to capture richer shared experiences or achievements among them. By adjusting the structural complexity, users can flexibly decide how much information they want to include in the generated hypotheses. Unfortunately, prior work (Bai et al. 2024b) has largely overlooked controllable generation, resulting in hypotheses that are redundant lack meaningful relevance.
Motivated by these, we introduce the task of controllable abductive reasoning, aiming at controllable generation of hypothesis, which leads to better leverage the practical value of abductive reasoning in knowledge graphs. However, when implementing semantic and structural controls on complex long logical hypotheses, we face two critical challenges: (i) Hypothesis Space Collapse: As illustrated in Fig. 2a the number of plausible hypotheses drops sharply as their length increases. This sharp decline severely limits our ability to apply structural complexity control, as the model needs to ensure
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(a) Hypothesis Space Collapse
(b) Hypothesis Reward Oversensitivity
Figure 2: (a) Hypothesis quality (measured in Jaccard) and space size across three logic lengths: short (one predicate), medium (two predicates), and long (three predicates). Valid candidates represent average reference hypotheses per observation. Note the dramatic collapse of hypothesis space as complexity increases. (b) Hypothesis oversensitivity example: Minor errors cause significant Jaccard score drops, creating tension between control adherence and semantic accuracy.
strong understanding of complex logic in order to make correct candidate hypotheses. (ii) Hypothesis Reward Oversensitivity: The previous approach (Bai et al., 2024b) utilized the Jaccard score reward mechanism to enhance the model's understanding of query semanties. However, as illustrated in Fig. 2b] during the model's exploration process, in the Jaccard score, severely disrupting training stability and guiding the model toward incorrect directions.
minor misstep may lead to sharp drop
To tackle these challenges, we propose a Controllable logcial Hypothesis Generation method (CtrlHGen) for abductive reasoning in knowledge graphs. To address the problem of hypothesis space collapse, we introduce a dataset augmentation strategy based on sub-logical decomposition. By leveraging the semantic similarity simpler sub-logics derived from the decomposition of complex hypotheses, this approach enables the model to understand long logical structures, which are composed of these smaller components. The hypothesis generator then trained using a combination of supervised fine-tuning and reinforcement learning. To address the problem of hypothesis reward oversensitivity, we refine the semantic reward function by incorporating Dice and Overlap coefficient to smooth out minor discrepancies between the hypothesis and the target. Additionally, we introduce a -aiitiion-ddeeencee reward to encourage the generation of hypotheses that adhere to the control constraints during exploration. Our main contributions
follows:
We the first introduce the task of controllable abductive reasoning, enabling abductive reasoning in knowledge graphs to better satisfy practical needs by controlling semantic content and structural complexity.
We propose an dnssevvtiionhypothher pair augmentation strategy via sub-logical decomposition to address the challenge of hypothesis space collapse when generating complex logical structures, significantly enhancing the quality of controllable hypotheses.
To mitigate hypothesis reward oversensitivity, we refine the semantic reward function by incorpo- rating Dice and Overlap coefficients to accommodate minor discrepancies between hypotheses and targets, while introducing a condition-adherence reward to ensure better compliance with control constraints, leading to more stable and accurate learning.
Extensive experiments on three datasets demonstrate that our model not only adheres more effec- tively control signals but also achieves superior semantic similarity performance compared to the baseline across multiple evaluation metrics.
2 RELATED WORK
Knowledge Graph Reasoning. Deductive reasoning focuses answering complex logical queries by improving query and answer embeddings (Zhang et al. 2021 Ren et al., 2020 Bai et al. 2022 2023a b. 2024a)). Inductive reasoning, often framed rule mining, ranges from efficient symbolic methods like AMIE (Galárraga et al.) (0113) to embedding- based approaches such as RuLES (Ho al. 2018) and RI RLogic (Cheng al." 2022), though traditional search-based techniques face
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Step1: Hypotheis-Obseervation Pair Construction
O O
Sub-logic
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Step3: Reinforcement Tuning
Condition
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Observation
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Reward Function
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Hypothesis
Semantic Alignment
Condition Adlrerence
[01, 02, 68, (or, 08 03 68, .... 03,
O O O+OOO O+O*O
An overview of our controllable abductive reasoning framework. The process consists of three main steps: (1) Hypothesis- Obssrivtissrroooonn pair construction through sub-logic decomposition to expand the hypothesis space, (2) Supervised training the generative model using augmented hypotheses, and (3) Reinforcement tuning with dual rewards for semantic alignment and condition adherence to balance hypothesis accuracy with control signal compliance.
Figure 3:
scalability challenges. Abductive reasoning was introduced by AbductiveKGR Bai et al. 2024b) using Transformer-basee hypothesis generation, with follow-up work (Bai al. 2025) highlighting its future potential.
A Abductive Reasoning. In natural language inference, o-NLI (Bhagavatula al. 2020 introduced abductive reasoning to commonsense reasoning, where plausible explanations are inferred from observations. Subsequent works proposed various techniques enhance this capability QQin al. 2021 Kadikis et al. 2022 Chan et al. (2023), including extensions to uncommon scenarios Tocusing on rare but logical explanations (Zhao al. al.] 2024). Unlike real-world data in commonsense reasoning. benchmarks like ProofWrites (Tafjord et al. (202T) evaluate formal abductive reasoning within semi- structured texts with explicit logical relationships. Recent studies have explored LLMSs in more challenging open-world reasoning contexts (Zhong et al. [023 Del & Fishel 2023
Thagard 2024)
and abstract reasoning tasks (Liu et al., [024b)]Zheng et al. (2025).
Meanwhile, in the neuro-symbolic domain, Abductive Learning (ABL) Zhou 2019) attempts to integrate machine learning and logical reasoning a balanced and mutually supportive manner. Recent research in this exemplified by systems such ARLC (Camposampiero et al. 2024) and ABL-Refl (Hu et al. (025). focuses on enhancing this integration by introducing novel techniques to improve context-awarente error correction, generalization, and overall reasoning accuracy and efficiency.
METHOD
In this section, we elaborate the proposed CtrlHGen, controllable hypothesis generation method for abductive reasoning in knowledge graphs. The framework of CtrlHGen is shown Fig. 3
3.1 PROBLEM DEFINITION
We define a knowledge graph G (V, R), where V is the set of entities and R is the set of binary relations. A triple (u, u) exists in G if r(u, = true. Following the open-world world assumption (Drummond & Shearer 2006), only the observed graph G is available during training, with missing triples treated as unknown rather than false. The full graph G remains hidden, and G C G.
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The core concepts of abductive reasoning consist of observation and hypothesis. Here, observation in knowledge graph G defined as set of entities O = {01, 02..... )n). where o, E Vi Ví e (I.....,.. A logical hypothesis H is defined query in the form of first-order logic on knowledge graph G, including existential quantifiers()), And(A), Or(V), Not(-). The hypothesis can also be written in disjunctive normal form:
HV4) .....,, V& e1 V... Ven
6 A ... A Tsm,,
where .V...... V& denotes the subset of V. Each ry is defined as either riy r(u, v) or Tiy rru, v), where u and u are either fixed entities from the set (V....., VaJ. or variable vertices V/. which could be any entity on the graph G.
The conclusion of the hypothesis [H]c on a graph G is the set of the variable entities V/ for which H holds true G. Specifically, it can be formulated as:
H = (V: E GVH(V, true).
Definition 3.1 (Controllable Abductive Reasoning in Knowledge Graph). Given a knowledge graph G, an observation O, and a control condition C, the goal of controllable abductive reasoning is to find a hypothesis satisfying:
1. The hypothesis H the most plausible explanation for the observation O. In other words, the conclusion [H]c closely matches the observation O
2. H satisfies the constraints specified by the control condition C.
3.2 OBSERVATION-HHYPOTIISS PAIRS CONSTRUCTION
Sampling. We randomly sample setevaatiinnyppphhssii pairs from the knowledge graph by con- structing hypotheses based predefined logical patterns. Each logical pattern is assigned an equal number of hypotheses to ensure diversity, and the conclusion of hypotheses on the graph are taken as the corresponding observations. Finally, both hypotheses and observations converted into input sequences suitable for the generative model.
Augmentation by sub-logic decomposition. To address the challenge of hypothesis space col- lapse in complex logical patterns, we propose dataset augmentation method based on sub-logic decomposition. Specifically, given hypothesis-obee obbervvation pair (H, O) under complex logical pattern P. we recursively decompose the hypothesis into sub- aub-hypotheses Hagh according to identifi- able sub-logical patterns Puuh- Corresponding sub-observations Oubb are then derived by executing these sub-hypotheses on the knowledge graph G. This process effectively generates additional hypothesis-observale pairs and can be formally described as:
{(H )= = {(((P) H), [ H)]a) P P):
where f(P: sub H) denotes the sub-hypothesis generated based the sub-pattern Pi and the origin hypothesis H, and [f H)lG computes the corresponding sub-observation by querying the knowledge graph to get the conclusion of the sub-hypothesis.
Because each sub-hy -ub-hyyothesis is subset of the original, they closely related both structurally and semantically. This strong alignment enables the model to progressively learn complex logical patterns by building simpler, related sub-patterns. We have reported more details in Appendix A
3.3 SUPERVISED TRAINING OF CONTROLLABLE HYPOTHESIS GENERATION
To enable controllable generation of logical hypotheses, we train a conditional generative model to generate hypothesis sequences guided by given observation and control condition. Specifically, given an observation sequence O = {01,-. ... }. a target hypothesis sequence /l {/I,..., h
and control condition C, the generative model is optimized using an autoregressive loss:
CAR = - (H O,C) = -" log pe (h: N....,,,-1,00
(4)
where 9 denotes the generative model, which we implement using a standard Transformer based decoder-only architecture.
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The training process consists of two stages. In the first stage, the model is trained under an uncondi- tional setting, where the input only consists observation tokens. This allows the model to acquire general capability for hypothesis generation. In the second stage, the model is fine-tuned under different control conditions respectively. The input is formed by concatenating observation tokens with control condition tokens, guiding the model to generate hypotheses that satisfy the constraints.
The control conditions C' are designed from two different perspectives to guide hypothesis generation:
Semantic Focus:
We randomly sample a specific entity or relation from the target hypothesis as a control condition. This guides the model to generate hypotheses grounded in a specific semantic region the knowledge graph. The control condition is directly represented by the token of the selected entity or relation. Formally, C e (Te) or C E {T+). Te and T, represents the token set of entity and relation respectively.
We apply constraints based on the logic structure of the hypothesis. Specifically, we implement three types of structural control: (1) strictly enforcing a predefined logical pattern, where each logical pattern is represented
Structural Constraint:
Lisp-like language with operator tokens following previous work in KG reasoning (Bai al.) (024b). (2) constraining the number entities involved, encoded using a special token [ne] that indicates hypotheses with exactly n entities. Formally, C {[ne]], where is an Integer. (3) constraining the number of relations used in the generated hypothesis, encoded using a token [nx], where [nr] denotes hypotheses containing exactly relations. Formally, C' [[r]], where is Integer.
3.4 REINFORCEMENT LEARNING
To improve the generalization ability on unseen knowledge graphs and better adhere to the specified control conditions, we further fine-tune the generative model using reinforcement learning. The reward function is constructed from two perspectives: semantic alignment and condition adherence.
Semantic Alignment:
This reward assesses the semantic consistency between the generated hypothe- sis conclusion [ and the corresponding observation O. We adopt the Jaccard similarity coefficient as the primary reward due to its strict evaluation of set-level agreement. However, the high sensitivity of hypotheses can lead to sharp reward fluctuations in response minor errors. To mitigate this, we integrate two supplementary metries:the Dice similarity coefficient and the Overlap similarity coefficient, which provide smoother gradients and greater tolerance slight mismatches. The final semantic reward Rsem is computed as a weighted combination of these metrics, defined as:
Rsem ([H) G, O) > [[H] O) + +A2 Dice([H) G, O) + À3 (verlap([H]c..) [[H] n
| n X2 [H]a] - |
2|[H|G no)
(5)
+ A min([[H[a),10))
[M]
where Åι X2, and As are hyperparameters. G denotes the observable knowledge graph during training, which serves as a reliable and leakage-free proxy for evaluating abductive reasoning quality.
Condition Adherence: This reward encourages the model to generate hypotheses that satisfy the given control condition C. We formulate it as a binary-valued function: if the generated hypothesis Il satisties the condition C, the reward is 1; otherwise, it is O. The final adherence performance is evaluated by computing the proportion of generated hypotheses that meet the condition. Formally, the reward function is defined as:
- f1 0, otherwise.
1,, if satisfies C,
Reond (H,C)
Jointly capturing condition adherence and semantic alignment, the overall reward function ft is formulated as:
R(H,O, = a Rumm (H, 0) -z) R H C):
where a E 10 is a hyperparameter that balances the contributions of semantic alignment and condition adherence.
Since abductive reasoning often involves generating multiple plausible hypotheses rather than a single answer, it is important ensure overall hypothesis quality. To achieve this, we Group Relative

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Policy Optimization (GRPO) (Shao et al. 2024), which promotes consistent improvement across set of sampled hypotheses per observation, instead of optimizing individual outputs. Specifically, GRPO updates the model xe by maximizing the expected reward over group of hypotheses H H...... H2 sampled from the same observation O and control condition C. The objective is:
H.l
To( 10, C, hiret) Ri BDxL (To [ J.. T0 (hs,, C, hi,ct)
[(0) = (O (HOO,C)
H
(8)
where & is the number of sampled hypotheses per observation. The normalized reward RC is obtained by applying intra-group normalization over { (fi..... R. A KL term constrains the policy ma from drifting too far from the reference model Tiet with B controlling its strength. Gradient clipping is also used to stabilize training.
EXPERIMENT
4.1 EXPERIMENT SETTINGS
Dataset. We conduct experiments on three widely used knowledge graph datasets: DBpedia50 (Auer et al. 2007), WNISRR (Bordes et al., 2013). and FB15k-237 (Toutanova & Chen 2015). Follow- ing (Bai et al. 2024b), each dataset is split into training. validation, and test sets with an 8:1:1 ratio. Under the open- world assumption, incrementally build Guain Gvalid and Grest where each graph includes all previous edges.
Observation-i Enservaaton-Hyoooessii Pair. Following prior KG reasoning work (Ren et al. 2020), adopt the 13 predefined logical patterns in Fig. 4 for hypothesis sampling. Each observation contains no more than 32 entities. To evaluate generalization, the validation and test sets include entities not during training, with the test set covering more unseen entities. For sub-logic decomposition, we chose five complex logical patterns (up, 3in, pni, pin, inp) to break down.
Evaluation Metrics. The quality of generated hypotheses is evaluated in terms of semantic similarity and condition adherence. For seman- tic similarity, we use Jaccard, Dice and Overlap score, with Giest used to compute [H.... G... dur- ing testing. For condition adherence, we regard it binary classification problem and calcu- late Accuracy. In addition, Smatch score (Cai & Knight 2013) is also used to quantify the struc- tural similarity corresponding to the generated hypothesis H and the reference hypothesis Heer- can measure how similar the nodes, edges and their labels are by representing the hypothesis as a graph. It is an evaluation metric for Abstract Meaning Representation (AMR) graphs, which directed acyclic graphs with node types (variable and concept) and three edge types (in- stance, attribute, and relation). Given a predicted graph Gp and a gold graph Gg. Smatch(G,p. G3) computed by finding an approximately optimal mapping between the variable nodes of the two graphs and matching their edges. Following the settings of Bai et al. (2024b), we transform the hypothesis graph G (H) into an AMR graph GA(H) by adding virtual nodes and instance edges, and then calculate Smatch. In short, Smatch is used to measure the degree of similarity between the generated hypothesis and the ground truth in the test set. It should be noted that Smatch is only a reference metric, as the generated hypotheses do not need to be the same the reference hypotheses.
2i
pri
Figure 4: Thirteen predefined logical types.
Implementation Details. We adopt a 12 layers decoder-only Transformer architecture (Radford al. 2019 Vaswann et al. (2017) for the hypothesis generation model and use the AdamW optimizer. All experiments are conducted on 4 Nvidia A6000 48GB GPUs. Additional hyperparameter settings and other experiment details reported in Appendix B
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Table The results of controllable abductive reasoning under different conditions. (Result: average score + standard deviation. Bold: best; Underline: runner-up. cannot be evaluated.)
Semantic Similarity
Condition Adherence Accuracy
Dataset
Condition
Jaccard
Dice
Overlap
Smatch
uncondition
21.4
69.3
82.3
61.4
pattern
65.5 +0.33
43.0
83,9 #0.27
98.9 +0.9
82.34..10
FB15k-237
relation-number
65.1
72.7+a.31
83.5
99.4+0.14
40.2
entity-number
63. 20.33
71.54
82.7
86.3
65.7 20.10
specific-entity
64.3
2..38
82.420.31
98.9 98.9 10
71.2
specific-relation
63.3
71,4
82.6
29.5
64.8 2.1.
uncondition
72.6
74.2#t..3
85.2
56.4+00220
pattern
80.8 20.0
93.5 86.8
13.3
WNISRR
relation-numher
24.0
77.4
86.3
95.3++0.25
78.9+0.20
entity-number
73.2
77.9+0.35
87.2
85 $5.2+00.0
65. +
specific-entity
73.620.38
75.6
86.2+0.3a
89. 39.020.31
65 6..2+
specific-relation
73.0
0.33
a0.30
96.1
60.8
uncondition
64.3
06.2
79.5
51.0 51.0
pattern
73.8
76.6+0.36
86.8
88.4
79.2++0.20
DBpedia50
relation-number
72.1
76.1
87.5
80.6
79.1+0.22
entity-number
75.220.37
80.3.10.5
92.4
84.0
63.3
specific-entity
23.7
78.7
88.4
79.6 79.6
62.9:0.22
specific-relation
75.220.31
80.6
93.7 20.20
84.2
60.3
Table 2: Average scores on FB15k237 datasets under five conditions
Model
Jaccard
Dice
Overlap
Accuracy
Smatch
GPT-40 + 2-hop subgraph
2.4 10.0
3.1
5.3
77.5
37.9
Kimi K2 + 2-hop subgraph
3.1 10.11
4.7.0.17
8.5
71.6.0..4
42.4.10.2
Grok-3 + 2-hop subgraph
2.5 0.59
3.710.12
6.910.21
75.610.38
43.5
DeepSeek- V3 2-hop subgraph
2.199
2.840.11
6.3
73.9 10.33
41.8
DeepSeek-Vi V3 + RAG
5.3
6.7+0.17
10.440.46
76,640.35
41,8
GPTS(Thinking) 2-hop subgraph
18.7+0.32
21.940.35
37.3
00.8
32.9 +0.27
CtrlHGen
60.33
71.9 #0.31
83.0
96.640.84
73.3
4.2 EXPERIMENT RESULTS AND ANALYSIS
We evaluated the quality and controllability of generated hypotheses three datasets under five conditions: pattern, iilattonnnumber entity-number, specific-entityy and specific-relation relation (see Sec- As baselines,
AbductiveKGR (Bai et al., 2024b) under unconditional settings (denoted as uncondition) to highlight the improvements of our approach. The results are reported in Table [ We further compare several advanced LLMs, including GPT-4o Achiam et al. (2023). Kimi K2 (Team et al. (2025), Grok-3 (xAl 2025), and Deepseek-V2 (Liu et al. 2024a). on FB 15k337 dataset under five conditions. For these models, 2-hop subgraphs of observation entities in triple form are included as part of the prompt to compensate for their lack of KG structural knowledge. For all LLMs above, we did not use the thinking mode. And their temperatures are uniformly set to 0.0. In addition, we also added one of the most advanced reasoning models, GPTS, and adopted the thinking mode. At the same time, we constructed an attempt to combine the raw model DeepSeek- V3 with RAG. Average results across five conditions reported in Table 2 with details provided in Appendix C.I.
tion 3.3
Compared to AbductiveKGR (uncondition), our model shows notable improvements in semantic similarity under conditional constraints, with most condition condition-adherence accuracies exceeding 80%. This improvement likely stems from the additional guidance provided by the control conditions (we further provide a case Section 4.5 whether the model can handle irrelevant control condi- tions). Structural conditions generally outperform semantic-focused ones in semantic similarity,
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with the fxee-format pattern condition achieving the best results. While both specific-entity and specific-relation conditions similarly enhance semantic similarity, the model shows a clear adherence preference for specifie-relation
On the other hand, the performance of LLMs remains very poor, even on common-senss knowledge graphs. We attribute this issue to two main factors. First, LLMs lack the ability to fully comprehend structured data, while this task requires generating correct structured query graphs rather than merely capturing semantic meaning. Moreover, when the number of observed entities large, their two-hop subgraphs expand rapidly, producing lengthy textual representations that further challenge the model. Second, the knowledge embedded in LLMs may conflict with that of the knowledge graph. For example, given an observation set containing several singers including Justin Bieber and Kendrick Lamar, Grok-3 classified them as singers who have made hip-hop music, whereas the knowledge graph, Justin Bieber is not hip-hop singer. Such contradictions can significantly affect performance on certain sppeifc data. For more analysis, please refer to Appendix C.T
4.3 ABLATION STUDY
We studied the influence of two proposed components of CtrlHGen, dataset augmentation based on sub-logical decomposition and the reward function.
Sub-logical Decomposition. We evaluate 13 logical patterns on DBpedia-50 using predefined patterns as conditions. The evaluation is conducted under two settings: one with the data augmentation strategy and one without it. As shown in Fig. [ sub-logical decomposition significantly improves the Jaccard Index, especially for complex patterns involving disjunctions and negations, while maintaining similar Accuracy between two settings. This indicates that the improvement in long logic is due to the enhanced understanding of the internal logical structure rather than relying on external prompts. Notably, improvements also appear on simple patterns (e.g.. 1p), indicating the model benefits from decomposing logic into simpler sub-components.
Reward Function. We investigate different reward functions on WNI8RR with the "pattern" condition. The results has been shown in Table 3 Reinforcement learning notably improves generalization and reduces accuracy variance compared to supervised learning. Removing Dice and Overlap rewards weakens performance, indicating that Jaccard alone is too strict and may hinder convergence. Excluding the condition-adherrnce reward slightly improves semantic similarity but harms condition adherence, confirming our reward design effectively balances both objectives. We further analyzed the possible reasons why semantic similarity slightly decreased when conditional adherence was introduced in Appendix C
Ablation Study Results (Jaccard)
Ablation Study Results (Accuracy)
1.0
0.8
0.0
Jancard Score
0.6
Accuraty
0.8
0.4
0.2
Logicel Pattern
Logical Pattern
(a) Jaccard Score
(b) Condition Adherence Accuracy
Figure 5: Results of ablation studies for the sub-logical decomposition.
4.4 VISUALIZATION
To evaluate controllability, we sampled 100 hypothesis-ooserratiie pairs from the FB15k-237 test set for each category defined by the number of relations (1, 2, or 3) in the reference hypothesis.
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Table 3: Results of ablation studies for the reward function.
Semantic Similarity
Condition Adherence
Model
Average
Jaccard
Dice
Overlap
Accuracy
Smatch
CtrlHGiw/o RI.)
40.5
75.8
83.7
81.5
79.0
78.3
CurHG(ww Dice and Overlap)
74.8
78.2+0.33
85.
90.3 00.25
82.0=0.15
82.1
CirlHG(wo Condition Adherence) CtrlHG
77.5 1.033
80.610.31
87.8
68.3 1:0.0
25.0
78.0
27.0+0.34
80.8+0.31
86.8
93.5 23.54
83.3
84.3
We compared the number of predicate relations in generated hypotheses under two settings: with and without relation-numbe constraints. As shown in Fig. 6 without conditional constraints, the model tends to generate hypotheses with a larger number of predicate relations, making it difficult to generate hypotheses with only one relation. However, when conditional constraints are applied, the majority of generated hypotheses align with the expected number of predicates. This experiment further demonstrates the strong controllability of our model.
Distribution of Hypotheses without Condition
Distribution of Hypotheses with Relation-number
80
condi--rrtattonn
cond-1iretation
1-l-reettttonn
cond-2-ralatonn
cond-2-ielation
70
condin 3-relaiions
80
condin 3-relalions
60
0.0
0.0
Percentage
50
Percentage
60
0.0
40
0:0
30
0.0
20
0.0
20
0.0
10
0
1-relation
2-relations
3-relations
1-relation
2-relations
3-relations
(a) Without condition constraint
(b) With relation-numben condition
Figure 6: Visualization of Relation-number Distribution in Generated Hypotheses
4.5
CASE STUDY
To demonstrate our controlbility we present two representative cases from FB15k-237, with results provided in Appendix. In the first case (Fig (). the observation consists of four music genres: (Blues, Jazz, Rhythm_an aarthm_and__a Blues, Bebop]. As the logical pattern conditions grow complexity, the model produces increasingly fine- mme-ggrinedd answers. For instance, under the basic "Ip" pattern it identifies their common parent genre, while more complex patterns enable it to retrieve finer details such as artists associated with these genres. In the second case shown in Fig. 9 it focuses specific entities. For strongly related entities such as Yahoo, the model is able to identify clear connections with the observation set. Even for entities with weaker relationships, such as two movies, the model can still capture hidden associations between them. Surpringsingly. for seemingly unrelated entities like BAFTA_ Award Baa__Best__ouul Sound, the model is able to generate high-semantic-quality hypotheses by leveraging the logical "or" operator, while still ensuring adherence to the given constraints.
5 CONCLUSION
In summary, this paper introduces a new task of controllable abductive reasoning in knowledge graphs to address the limitation of controllability in the existing method. To tackle the challenges when control generating long and complex logical hypotheses, we propose a data augmentation strategy based on sub-logic decomposition, along with smoother semantic and constraint-adheree reward functions. Experimental results demonstrate that our approach significantly improves the controllability and overall quality of the generated hypotheses.
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6 ACKNOWLEDGEMENTS
The corresponding author is Yangqiu Song. We owe sincerely thanks to all authors for their valuable efforts and contributions. The authors of this paper are supported by the ITSP Platform Research Project (TTS/18923FP)) from ITC of Hong Kong, SAR, China, and the AoE (AoE/E-601 60/44-N,, the RIF (R6021-20) and the GRF (16205322) from RGC of Hong Kong. SAR, China and the National Natural Science Foundation of China (No.6246200) and No.62302023).
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A DETAILS FOR OBSERVATION-HYPOTREE SAMPLE
Given knowledge graph G and predefined logical pattern P. the algorithm begins by sampling random node v and recursively constructs a hypothesis such that is one of its conclusions and the hypothesis conforms to the logical type specified by P. During the recursive process, the algorithm examines the current operation in the hypothesis structure. If the operation is projection, the algorithm randomly selects incoming edge (u, v) of node v, then recursively generates sub-hypothesis rooted at node u according to the corresponding subtype of P. the operation intersection, the algorithm recursively constructs sub-hypotheses using the same node for each subtype, since all sub-hypotheses must conclude with v. If the operation is union, it applies the recursion to one subtype using node v, and to the remaining subtypes using randomly selected nodes. This is because, under union, only one of the sub-hypotheses needs to have as its conclusion.
For the sub-logic decomposition, we decompose hypothesis into its sub-logical hypothesis Hab based on the type of reference hypothesis H. For example, a logical pattern "inp" can be decomposed into two sublogical patterns "2p". Then we calculate the corresponding conclusions of these two "2p" logical hypotheses respectively sub-observations, thereby constructing the sub-logic observation- hypothesis set.
B MORE EXPERIMENT DETAILS
For all experiments, we set the learning rate to le-5 and use batch size of 256 during supervised training. The supervised training process consists of two stages. In the first stage, the model is trained for 400 epochs, including a 50-epoch warm-up phase. In the second stage, which involves conditional supervised training, we train for 50 epochs with a 5-epoch warm-up. For reinforcement learning, smaller batch size of 32 is used, and each group samples candidate answers. The hyperparameters \1, X2 and aa are to 1.0, 0.5, and 0.5, respectively. And then set 0.5.
B. SMATCH
Smatch (Cai & Knight 2013) is an evaluation metric for Abstract Meaning Representation (AMR) graphs which are directed acyclic graphs with node types (variable and concept) and three edge types (instance, attribute, and relation). Given a predicted graph Gp and a gold graph Gg. Smatch(G,p Gg) is computed by finding an approximately optimal mapping between the variable nodes of the two graphs and matching their edges. Following the settings of Bai et al. (2024b), we transform the hypothesis graph G(H) into an AMR graph GA(H) by adding virtual nodes and instance edges, and then calculate Smatch. In short, Smatch is used to measure the degree of similarity between the generated hypothesis and the ground truth in the test set.
C
MORE RESULTS
C.I DETAILED RESULTS
Here, we reported our detailed results of LLMs' performance in Table 4 We also showed prompts in Fig 7 We found that large language models are sometimes greatly influenced by semantics, thus neglecting the role of correct structure. For example, when the observation is (Librarian, Lawyer, Mathematician, Physicist, Scientist-GB), Grok-3 will answer whether they are working a library in a law-related profession. However, the correct query for reference the occupation of Gottfrie Wilhelm von Leibniz or the occupation of those influenced by Italo Calvino. In this example, the large language model found the most relevant semantic content but ignored that they could not meet all situations. Even more strangely, large language models sometimes include the entities within observations [Fever, Fatigue, Headache). LLMs did not find any drugs that could treat them diseases with these three symptoms. Instead, it included these three observed entities and predicates belonging to certain symptom in its logical assumptions. That is, these observations are symptoms of fever, Headache and Fatigue. We believe this is because the large language model has not fully understood the structural relationship, thus confusing the contents of the input edge and the output edge.
the hypotheses they generate. Given an observation
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Input: Observation, Logic Patterns, 2-hop subgraph, condition
Formmt Specification):
'answer: <hypothesis>'.
[Instructions]: Do not add quotes, explanations, or extra text and only replace <hypothesis> with your generated content.
[Task]: Now you need do the abductive reasoning in knowledge graphs. The observation (consist of entity id and semantic) is <observation>.
Your task is to generate the hypothesis whose form is first order logic in <logic patterns>, where means intersection, u means union, n means negation. p denotes the relation and e is the entity.
Here the related 2-hop subgraph <2-hop subgraph> for you, which may help you. For each (u.v u the source node, the target node, is the relation. Each form is 'id: Semantic content'.
Now generate the hypothesis, with the format the <logic patterns>. Please note that you need to make sure the hypothesis you generate satisfy the <condition>.
Figure 7: Prompt Example.
On the one hand, found that GPTS(Thinking) has achieved significant performance improvement Firstly, the model can follow the control conditions in most cases. Secondly, higher semantic similarity achieved under all five conditions. In contrast, models are more likely generate hypotheses with higher semantic similarities under the control of semantic content than under structural control. This might be because the model itself is better at capturing based on semantics compared to structured reasoning. However, they still have a considerable gap compared to CtrlHGen, indicating that abductive reasoning tasks with structured knowledge remain challenging for advanced large language models.
the other hand, Deepseek-V? V3 with RAG has improved performance under the condition of semantic control, but the results remains almost unchanged under the condition of structural control. We believe this can be attributed to two primary reasons: First, RAG primarily enhances semantic retrieval, enabling the model to fetch more semantically relevant context. It offers limited benefit when precise structural constraints are imposed, as these require strict path conformance rather than semantic relevance. Second, the provided 2-hop subgraph already serves highly informative prompt. Since the depth of all 13 predefined logical patterns is 2, this 2-hop subgraph covers most of the structural information required for hypothesis generation.
The consistently poor performance under structural control instead reveals the models' persistent weakness in complex structural reasoning over graphs. Compared to standard KGQA, which only requires interpreting and following one given logical chain, abductive reasoning is fundamentally more challenging: it demands that the model simultancously consider all relevant logical chains surrounding a set of observed entities and abduce the single most explanatory multi-hop hypothesis. This inverse, open-ended search process imposes significantly greater demands on structural understanding and logical synthesis, an area where current LLMs still fall short.
We also compared the experimental results of GPT5 (thinking) under different temperature settings on FB 15k37 dataset under the "patttern' condition. The results are shown in Table We found that a temperature of 0.0 can ensure a balance between semantic similarity and condition adherence. Excessively high temperatures may enhance the ability to explore, thereby improving semantic similarity, but they will significantly reduce condition adherence.
C.2 ANALYSIS FOR CONDITION ADHERENCE REWARD
We have further analyzed the ablation study presented in the paper, comparing the performance of each logical pattern with and without the Condition Adherence(CA) reward. The results are summarized in Table Table
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Table 4: The results of controllable abductive reasoning under different conditions. (Result: average score + standard deviation.)
Semantic Similarity
Condition Adherence Smatch
Dataset
Condition
Jaccard
Dice
Overlap
Accuracy
pattern
4.7.0.19
4..00
7.220.26
85.3
55.640.29
relation-number
1.940.08
2.8
5.4
74.420-49
44.1 44.1
entity-number
2.240.08
3.
6.0
84.3 20.36
45.3
GPT-4o + 2-hop subgraph
specific-entity
2.
3.240.14
2.0
20.7 20.8
specific-relation
0.9 0.9
1.340.us
2.4
65.5
23.8
pattern
3.140.10
4.640.11
7.740.22
82.4
50.2+40.11
relation-number
2.410.09
3.640.12
8.5
71.1 10.49
47.0
entit-nummbr
2.240.09
3.210.12
6.0
62.3
35.8
Kimi K2 + 2-hop subgraph
specific-entity
4.240.18
5.710.20
10.8
69.0
38.4
specific-
3.6
5.240.15
9.5
73.4
40.5
pattern
3.810.11
5.7
12.0
23.07
61.2.10.24
relation-number
1.8
2.8
4.6.0.17
10.45
40.0
entity-number
1.940.07
2.8
4.9
70.9
42.2
Grok-3 2-hop subgraph
specific-entity
2.7
3.740.14
6.020.22
26.3
38.820.25
specific-relation
2.340.08
3.440.11
7.2
35.420.25 77.2
pattern
2.740.10
4.0
7.1
79. +0.50
47.2
relation-number
0.9
1.340.06
5,5
70.6 400311
39.1 39.140.32
entity-number
1.3
1.740.
3,440.16
69. 20.29
40.3
Deepseek-V3 2-hop subgraph
specific-entity
3.7
4.7.0.11
10.2
20.8
41.610.25
specific-relation
1. 1.720.09
2.340.11
5.4
74.220.28
40.6
pattern
14.840.30
17.440.32
30.640.42
83.8
71.5
Ellation-numbr
14.6+0.30
17.1 20.32
31.5
96.640.17
56.8
GPTS(Thinking)+2-opp subgraph
entity-number
17.8
22.0.0.33
10.9
95.3 10.21
54.2.10.19
specific-entity
24. 10.36
27.4
40.1
31.9 94.2
specific-relation
22. 10.34
25.810.37
39.610.46
94.5
18.1
pattern
2.840.09
3.840.22
6.1
78. 28.5
48 48.2220.55
Illation-numbe
1.6+0.08
2.340.11
3.8
69.3
34.5
entity-number
0.840.04
1.440.07
3.8
39.2. 72.3
Deepseek-Ve -3 RAG
specific-entity
13.7
15.440.33
23.0
80.84
25.9
specific-relation
7.640.27
10.5
15.4
80.2
06.8
Table 5: Temperature sensitivity experiment.
Semantic Similarity
Condition Adherence
Temperature
Average
Jaccard
Dice
Overlap
Accuracy
Smatch
1=1.
15.840.31
18. 18.2+0.33
28.5
75.3+0.43
68 68.440.18
41.2
t05
13.440.28
15.8 17.4 17.4
28.840.41
79.2+
69. +0.18
41.2
0.0
14.8
30.640.42
83.8 +0.37
71.5
43.6
For logical patterns involving negation (such as 2in, pin, and inp), we observed that even without conditional adherence rewards, the model is often able to identify the correct logical structure its own and achieve higher accuracy. In these cases, enforcing constraint adher- ence may overly limit the model's 's exploratory flexibility, leading to suboptimal semantic performance.
In contrast, for logical patterns that involve only intersection (such pi, ip. 2i, 3i), found a strong correlation between improved constraint satisfaction and enhanced semantic similarity. Without reinforcement signals guiding the model to comply with constraints, it tends to generate alternative formats that deviate from the intended structure, resulting in decreased semantic quality.
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Interestingly, for the '3in' pattern, the model appears to strike balance between intersection and negation: regardless whether constraints are enforced, the resulting hypotheses exhibit comparable semantic similarity.
Table 6: Ablation Results of Jaccard Score
logical pattern
2in
pin
inp
pni
up
2u
3in
1p
2p
pi
ip
CulHGen((woo RL)
63.6
68.1
67.6
65.2
67.0
81.9
69.2
75.4
79.3
72.6
73.8
70.1
74.8
CtrlGGen(w/o CA)
76.2
75.9
72.3
71.1
71.6
85.3
70.4
91.2
85.1
75.8
82.1
78.9
71.9
CurHGenn
71.7
73.2
69.7
69.1
70.3
84.9
70.2
91.3
85.3
76.4
82.8
79.8
77.2
Difference
-45
-277
-2.6
2.0
-13
-0.4
-0.2
0.1
0.2
0.6
0.7
0.9
5.3
Table 7: Ablation Results of Condition Adherence Accuracy
logical pattern
pin
inp
pni
up
2u
3in
1p
2p
pi
ip
CulHGen (w/o RL)
58.7
60.1
98.2
78.7
98.5
93.9
93.2
45.5
84.6
88.5
91.4
96.7
70.6
CuiHGen (w/o CA)
82.4
84.7
78.7
79.1
91.6
97.0
34.2
65,9
74.8
57.0
58.4
76.9
16.5
CtrlHGen
84.5
98.6
84.4
85.8
98.7
96.3
95.4
89.0
96.4
98.2
98.3
98.6
90.1
C.3
MORE BASELINES
Here, we incorporated the data augmentation strategy proposed in Logic-Gen (Asai & Hajishirzi 2020) as additional baseline. We also compared with our method CtrlHGen and AbductiveKGiR without data augmentation but only by introducing conditional tokens. Since these two methods don't employ reinforcement learning for conditional control, we report results after supervised training, ensuring fair comparison. We conducted experiments on the DBpedia50 dataset and selected 'pattern' and "specific-relation" respectively to represent structural control and semantic control. The results reported in Table 8 and and
The experiments reveal that, while Logic-Gen's data augmentation indeed improves the model's overall grasp of logical patterns, it remains inferior to our sub-logic decomposition approach. We believe this is because the sub-logic decomposition forces the model to deeply understand and compose longer, more intricate logical chains step-by-step, leading substantially stronger reasoning capability on complex hypotheses. It more effectively mitigates hypothesis space collapse, thereby significantly enhancing compliance when strict structural conditions are imposed.
Table 8: Results DBpedia50 dataset under the 'pattern' condtion.
Semantic Similarity
Condition Adherence
Model
Jaccard
Dice
Overlap
Accuracy
Smatch
A token
68.2
73.2
80.6.0.29
66.610.47
77.5
Logic-Gen
69.5
73.5
79.9
65.9 10.44
77.5
CtrlHGen
70.1
74.0+0.31
80.8+0.29
73.1
80.8+0.17
C.4
CASE STUDY
In this section, we show the results of two case study in Fig and Fig
C.5
CASE
In this section, implemented simple yet highly interactive multi-round dialogue system that automatically adjusted control conditions based on the user's evolving intentions and the outcomes of previous rounds. We leveraged large language model (DeepSeck-V?) V3)) to intelligently select appropriate control conditions according to the user's expressed intent. The prompt used for this condition-selectinn LLM is presented in Fig. TO At each turn, the LLM generated updated control
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Table 9: Results on the DBpedia50 dataset under the 'specific-relation" condition.
Semantic Similarity
Condition Adherence
Model
Jaccard
Dice
Overlap
Accuracy
Smatch
AbductiveKGRR + condition token
40.3
73. 73.040..3
86.4
78.6=0.40
58.0
Logic-Gen
73 73.4 70.4
88.0 88.0
75.9
54.9
CtrlHGen
+0.33
77.2
90.7
80.0=0.40
51.640.23
Observation: Blues, Jazz, Rhythm and blues, Bebop
Condition1: Logical Pattern 1p
Hypothesis 1: H V/ Parenl_genre Hard Harddbbp, Vz) Interpretations The music genre that originates from the Hard_bop genre. Conclusion 1: Blues, Jazz, Rhythm and blues, Bebop.
Jaccard Score: 1.0
Condition2: Logical Pattern 2p
Hypothesis 2: H V3 Parent Drreettgeenr((P... V2) genre(McCor Tyner, P:)
Interpretations 2: The musical genre that originates from the genre which is associated with the artist Mcyor_Tyner.
Conclusion 2: Blues, Jazz, Rhythm and blues, Bebop.
Jaccard Score: 1.0
Condition3: Logical Pattern ip Hypothesis 3: H V, Parent_ DrrrettggenreHHnne CaareeHHrdddooo) Vτ) A (Rao_Roooyeaeeeae Pt) A Menre(MoCoy__Tymee Pt)
Interpretations 3: The musical genre that originates from the Hard_bop genre and is associated with the artist Roy Haynes and McCoy Tyner.
Conclusion 3: Blues, Jazz, Rhythm and blues, Bebop. Jaccard Score: 1.0
Figure 8: Case study of Logic Control.
conditions by jointly considering the hypothesis produced in the previous round, its derived con- clusions, the corresponding Jaccard similarity score, and the current user input. These dynamically selected conditions were then passed back to the core hypothesis generation model. A complete interaction example is shown in Fig.
In this case, the initial observation consisted of four songs. In the first round, the user expressed interest in connections related to the acoustic guitar. The system accordingly generated a relatively broad hypothesis that slightly over-covered the observed entities. the second round, the user asked who the artist was; the LLM selected sspecific-relation as the control condition to focus the generation. Although a relevant hypothesis was produced, remained somewhat vague. Consequently, in the third round, the user requested simpler logical structure. The L.MM responded by enforcing the simplest available logic pattern, successfully revealing that all four songs were authored by Tracy Lawrence. Finally, wishing to explore the observation more deeply, the user sought additional related information. The LLM then imposed a relation count three as the control condition, prompting the model to generate richer, more complex hypothesis that incorporated two different associated artists.
Through this multi-round interaction, the system seamlessly combines structural and semantic control signals, gradually improving the relevant hypotheses closely related to the user's 's constantly evolving exploration goals. It demonstrates the potential of our method in weal-world scenarios.
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Observation: Avid Technology, Intel Corporattn,,nnn IBM, Microsoft Corporation, Seat- Mar_Meresss, Walmart, Cisco_Systent Inc., Golden_ State___________e Warriors, Seattle Seattle_Supesoniie Supersonics, Los Los_Angele__Kingg San_Jose_Sharks, Pixar, Amazon.com, eBay
Condition Entity contains Amnokin_Aces
Hypothesis 1: I1 V/ Employ(V,, P.) A Film_crew_ree SaaeeeSSokinAaaee Pt) Interpretations 1: The organization/conpany that employs people who have served as a member in the film Smokin Aces.
Conclusion 1: Ticcnooyhy..gg. Intel_Corpone Les__Cororratin, IBM, Microsoft Microsoft_ Corporation, Seat- Mle_Mariners Walmart, Cisco_ Lesso_Systems, Inc., Golden_Staie Starir_arrrrrssss Los Los_Ange jos__Ageles_aii Kings, Lan_Jos__Sharke Pixar, Amazon.com, eBay.
Warriors, Seattle_Supersonies,
Jaccard Score: 1.0
Condition 2: Entity contains The Phantom
Hypothesis 2: H = V/ Employ(V;, P:) A Film_crme sarn__ee______ (eeurrooe(Thh,, Taate__hhntom, P?) Interpretations 2: The organization/company that employs people who have served as crew member in the film Thhe_hantom
Conclusion 2: Avid Technology, Intel Corporation, IBM, Microsoft Corporation, Seat- tle Mariners, Walmart, Cisco Systems, Inc., Golden State Warriors, Seattle Supersoniss,s,,,s Los Angeles Kings, San Jose Sharks, Pixar, Amazon.com, cBay.
Jaccard Score: 1.0
Condition 3: Entity contains Yahoo
Hypothesis 3: H
Vy
Employ(V,, P:) A -Employed (P;, Y ('ahoo) A
Employed( Pt, Avid Technology)
Interpretations 3: The organization/company that employs people who have never been employed by Yahoo, but have been employed by
Conclusion 3: wrid_Technology. Intel_ _hee_ooororainnn IBM, Microsoft_Cororrainnn Corporation, Seat- tle__Ma Mariners, Walmart, Cisco_ Lisco_Systems Inc., Golden Grolde_SState____ Warriors, Seattle_ Suatre_SSppsssniess Los Angeles Kings, San_Jose_Shaal Pixar, Amazon.com, eBay. Jaccard Score: 1.0
Condition 4: Entity contains BAFTA BAFTA_Award, _estterot________ Deut_S
Hypothesis 4:
H Employ(V; Po) A Noninuted___o BAFT SAITA_Auue A_warrd_ Barnuurddoo_BeeSSSowwan _Bes_SSoud) Employed Pr, Los Angeles_King
Interpretations 4: The organization/company that employs people who have been nomi- nated for BAFTA Award for Best_ Soundd have been employed by Los Los_les Kings. Award
Conclusion 4: Avid_ Technooooyllgy, litel_Corporatinn IBM, Microsoft_ _Corh_Caaionn, Seat- tle _l__arrnerr, Walmart, Cisco Lisco_Systems Inc., Golden Stadtn Warriors, Seattle_ Surtrseesspsss,icss Los_Angeles Kings, Lan_Jose_Shaae Pixar, Amazon.com. eBay.
Jaccard Score: 1.0
Figure 9: Case Study of Entity Semantic Control.
D THE USE OF LLMS
In this paper, large language models (LLMs) were employed exclusively for language refinement, such as improving grammar, clarity, and readability of the manuscript. They were not utilized in any stage of the research process itself, including the formulation of ideas, experimental design, data collection, analysis, or interpretation of results.
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Observation, Hypothesis(last round), Condition(last (aapddaJaccrd_scooeeeee round), Intention, Logie Patterns
Input:
[Instructions]:
Do not add quotes, explanations, or extra text and only replace <hypothesis>
with your generated content.
[Task]: Now am doing the abductive reasoning in knowledge graphs. The observation (consist of entity id: semantic) is Observation. I have generated hypothesis <Hypothesis> under the condition <Condition>. The conclusion of this hypothesis <conclusion>. And the jaccard score between the conclusion and the observation is <Jaccard scoress My intention is that <Intention>, Now your task is to adjust the condition and my model will generate new hypothesis under the condition make the jaccard score between the conclusion and the observation higher and conforms to my intention.
[Format Specification]: The condition can be one of them 'pattern', 'entitynumber', 'entity', 'relation', 'relationnumber'. For the pattern, first-order logical hypothesis format including <l.ogic Patternsz. If you choose this condition, your response must be condition: <pattern: <pattern names. For the entitynumber, you can specify the number of entities the hypothesis. If you choose this condition, your response must be condition: <entitynumber: <number>. For the entity, you specify the entities in the hypothesis. If you choose this condition, your response must be condition: <entity: <entity_nanie __mmes.______.. For the relation, you specify the relations in the hypothesis. If you choose this condition, your response must be condition: <relation: <relation _attion___ee,____ For the relationnumber, you can specify the number of relations in the hypothesis. If you choose this condition, your response must be condition: <relationnumber: <number>.
can specify the corresponding
Figure 10: Prompt for LLM.
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Observation: Alibis (song). _See It Now_ (songs, If the Good Die Young, Some- Soly_Paints_the Wall
Intention 1: I want to know about the connection between these songs and the guitar. Condition Entity contains Acoustic _gitar.
Hypothesis 1: H V7 W orrof Artist(V,, Pt) Instrumntto (Acoustic_gutte Pt) Interpretations 1: The songs that are the work of the artist whose instrument Acous- tic go__guitr.
Alibis (sonn_, _See_ Ste__t__Nooe Now Nowoosss))g), If thed Giod_Die Die__oueg,, Some- mody_Paintss Wall, If Had Lrie__rrdeeeeeteee Jaccard Score: 0.66
Conclusion 1:
Intention 2: I want to know which artist is the author of these songs. Condition Relation contains WorkofArtist.
Artist (V, P:) A Associate AssociateArriis((KK AreeeieeelssssseKeeMMMl P:) Hypothesis 2: H Vz Worko, Artisitrtst
Interpretations 2: The songs that are the work of the artist whose associateArtist is Ken_ Men_Mellons.
Conclusion Asonis_(song), LSee_ -See__l_Noww(som) If_ Dioee__GooDDDeeYOOo Young, Some- body Paints the Wall.
Jaccard Score: 1.0
Intention 3: This is too complex. want to make the logic simpler.
Condition 3: Logic Pattern 1p.
Hypothesis 3: H = Vy W Workof Artistttisst,, Tracy_raaaoeo Lawrence)))
Interpretations The songs that are the work of the artist T Lawrence.
Conclusion 3: Alibis (obis_,song), __See_ It NNw_wWwwwnnn If the
Die_Young, f_odh_oGod_ Good Die Young, Some-
body_Paints the Wall.
Jaccard Score: 1.0
Intention 4: I want to know more. Let's explore more. Condition 4: Logic contains 3 relations.
Hypothesis 4:
H
V2
Musicband( Pt)
Arsisiateerttist(Jooss Logan Logan_(countnn (country_singer P:)
ArsociateAAttss(( Lee_Melloss__ P.)
Interpretations 4: The songs that are played by the musical band whose associate artists are Josh www__aaggnnnnunnnn singer) and Ken_ sen_Mellons.
Conclusion 4: Alibis Alibis(ssong), __See It Now [so_ns,ng), If the the_GGoo Die dii_n, Some- body Paints the Wall.
Jaccard Score: 1.0
Figure 11: Case Study of Multi-round Dialogue.
22


Reviews:
[{"review_id": "6NlC1lmiUT", "reviewer": "Reviewer_e8d8", "summary": "In this paper, the authors introduce a model called CONE, which aims to generate logically consistent hypotheses from a given premise. They are allowing fine-grained control over the desired logical relationship. The key innovation is the integration of natural logic into the generation process. In this proposed method, rather than relying solely on learned patterns or black-box transformers, they decompose logical relationships at the token level and apply compositional rules to reason about the entire sentence. They have trained a RL model using the curated data. The results demonstrate superiority compared to raw LLMs.", "questions": "Is the thinking mode activated for Grok-3? It would be great if authors explained the experimental setup of the LLMs in detail. Often in such tasks, specific hyperparameters can change the performance. For instance, in deterministic scenarios, like diagnosis, it is recommended to use temperature 0 to avoid randomness. It would be great if authors include such consideration in their tests.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "1-\tThis paper is the first to formally define controllable abductive reasoning over knowledge graphs (KGs). It is an important task as it can be used in many downstream tasks where KG statements, such as causal-effect or factual statements, exist or could be inferred.\n2-\tThe proposed framework is novel and addresses the challenges of the task. Authors have introduced a two-stage framework for sub-logic decomposition for data and an RL with a dual reward design that balances semantic alignment and control adherence.\n3-\tThe paper is well-structured, uses clear formulations, and provides a detailed training setup, metrics, and open-source code, supporting reproducibility (Appendices A & B).", "weaknesses": "1-\tMore baselines are needed. Current baselines cannot really demonstrate the true contribution of the paper. I recommend that authors include methods that try to address the same challenge. For instance, Logic-Gen [1] can be a good candidate:\nAsai, A., & Hajishirzi, H. (2020). Logic-guided data augmentation and regularization for consistent question answering. arXiv preprint arXiv:2004.10157.\n2-\tSome of the LLMs that are used for comparison do not have reasoning capability. For instance, while GPT 4o may have general reasoning power, the thinking mode is not included, the same for Kimi K2. For such a task where reasoning is important, it is better to use more advanced models. GPT 5, GPT 5-mini, Qwen 3 with Thinking tokens enabled, etc., are all good options. I am not sure what the rationale was behind choosing Kimi K2, as it is mostly good at coding benchmarks. I recommend that authors briefly explain the reason for their choice of LLMs.\n3-\tThe way context is provided to baseline LLMs is questionable. It seems the entire 2-hop subgraph is dumped into the prompt, and a non-thinking LLM was supposed to reason based on that. It would be much better if at least a RAG set-up were used to make it more realistic. Or if raw LLM was the purpose, as mentioned in the second point, a more advanced LLM should be used.", "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": "QHPQziGrPC", "reviewer": "Reviewer_MTp7", "summary": "This paper introduces CtrlHGen, a framework for controllable logical hypothesis generation in abductive reasoning over knowledge graphs. The authors identify two key challenges in this setting. (1) Hypothesis space collapses when generating long and complex logical hypotheses. (2) Reward oversensitivity when reinforcement learning overly biases toward specific metrics. To address these, the paper proposes sub-logical decomposition for dataset augmentation and smoothed semantic rewards to balance semantic quality with user-specified control constraints. Experiments on three benchmark datasets demonstrate improved controllability and semantic similarity compared to baselines.", "questions": "- How does CtrlHGen handle contradictory or mutually exclusive hypotheses under control constraints?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper clearly motivates the need for controllable abductive reasoning, which is underexplored in KG reasoning.\n\n\n- The introduction of smoothed semantic rewards and condition-adherence reward is a thoughtful way to mitigate oversensitivity.", "weaknesses": "- Unclear problem definition. It is unclear to me the difference between abductive KG reasoning and rule-based link prediction. It would be better to add more explanations.\n\n- Method limitation. It seems that the data sampling method relies on predefined logical patterns. How can the proposed method be generalized to other different KGs?\n\n\n- Evaluation limitations. While semantic similarity and adherence metrics are reported, the paper could benefit from more qualitative analysis of generated hypotheses (e.g., case studies, error analysis). It is not entirely clear whether the chosen baselines represent the strongest possible competitors in controllable generation or abductive KG 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": "sMHnld2ibY", "reviewer": "Reviewer_y9eJ", "summary": "This paper addresses the lack of controllability in abductive reasoning on knowledge graphs (KGs), where existing methods often generate numerous plausible but irrelevant hypotheses. The authors introduce the new task of controllable hypothesis generation, which allows users to specify constraints on both the semantic content (e.g., focusing on \"pathology\" or \"treatment\") and the structural complexity (e.g., the length) of the desired hypotheses. They identify two primary challenges in generating long, complex hypotheses: \"Hypothesis Space Collapse\" (a sharp drop in the number of valid complex hypotheses) and \"Hypothesis Reward Oversensitivity\" (unstable reinforcement learning due to strict rewards like the Jaccard score). To solve these problems, they propose CtrlHGen, a framework trained in two stages (supervised learning and reinforcement learning). CtrlHGen uses a \"sub-logical decomposition\" strategy to augment the dataset, helping the model learn complex structures. It also introduces a novel reward function that combines \"smoothed semantic rewards\" (using Dice and Overlap scores) with a \"condition-adherence reward\" to ensure generated hypotheses are both accurate and follow the specified constraints. Experiments on three benchmark datasets demonstrate that CtrlHGen significantly outperforms baselines, including modern LLMs, in both adhering to control conditions and maintaining high semantic similarity.", "questions": "The current system is one-shot. A more practical system would be interactive. A user could receive a generated hypothesis, provide feedback (e.g., \"This is too complex,\" \"This part is wrong,\" \"Explore this entity more\"), and the model would use this feedback to refine the hypothesis, making the process a collaborative dialogue. Would it be possible to achieve the interactive system?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Novel and Practical Problem Formulation\n\nThe paper is the first to formally introduce and tackle the task of \"controllable abductive reasoning\" in KGs. This addresses a significant and practical limitation of prior work (AbductiveKGR ), where a single observation can lead to an unmanageable number of \"plausible but irrelevant hypotheses\". By defining clear control mechanisms for semantic content and structural complexity , the paper moves the field toward greater practical utility in real-world applications like clinical diagnosis or scientific discovery.\n\n2. Insightful Diagnosis of Core Challenges\n\nA key contribution is the clear identification and illustration (in Figure 2) of two non-obvious challenges: \"Hypothesis Space Collapse\" and \"Hypothesis Reward Oversensitivity\". Diagnosing why generating complex, controlled hypotheses is difficult (i.e., fewer valid complex examples exist, and minor errors in them cause massive reward drops) provides a strong, logical foundation for the paper's proposed solutions.\n\n3. Novel and Effective Augmentation Strategy\n\nThe \"dataset augmentation strategy based on sub-logical decomposition\"  is an innovative solution to the \"Hypothesis Space Collapse\" problem. By programmatically breaking down complex hypotheses into simpler, semantically related sub-components, the authors create a richer training environment. This allows the model to learn the building blocks of complex logic, which the ablation study confirms significantly improves performance, especially for complex logical patterns.\n\n4. Robust and Well-Justified Reward Function\n\nThe paper intelligently designs a reward function to overcome \"Hypothesis Reward Oversensitivity\". Recognizing that the Jaccard score is too \"strict\" , they smooth the reward landscape by incorporating Dice and Overlap scores. Furthermore, the inclusion of a \"condition-adherence reward\"  directly optimizes for the new task's constraints. The ablation study (Table 3) effectively demonstrates that this dual-objective reward function successfully balances semantic accuracy with constraint adherence.\n\n5. Extensive and Solid Experimentation\n\nThe authors validate their CtrlHGen model thoroughly. They experiment on three standard KG datasets , test against the relevant SOTA baseline (AbductiveKGR) , and include a comparison against four modern LLMs (GPT-4o, Kimi K2, etc.). Their evaluation is comprehensive, using distinct metrics for both semantic similarity (Jaccard, Dice, Overlap) and condition adherence (Accuracy). The ablation studies (Figure 5, Table 3) are particularly strong, as they isolate and confirm the positive impact of their two main technical contributions.", "weaknesses": "1. Limited Scope and Definition of \"Control\"\n\nThe paper defines \"semantic control\" as providing a specific entity or relation from the target hypothesis and \"structural control\" as a predefined pattern or count . This is a good first step, but it's a fairly rigid and limited form of control. In a practical application (like clinical diagnosis ), a user might want to provide more abstract semantic guidance (e.g., \"focus on infectious diseases but not viral ones\") or compositional constraints that are not covered by this framework.\n\n2. High Complexity of the Training Pipeline\n\nThe proposed CtrlHGen framework involves a complex, multi-stage pipeline: (1) sampling pairs, (2) sub-logic augmentation, (3) unconditional supervised training, (4) conditional supervised fine-tuning, and (5) reinforcement learning with a specific optimizer (GRPO). This pipeline has numerous components and hyperparameters (e.g., $\\lambda_{1}, \\lambda_{2}, \\lambda_{3}, \\alpha$), which could make the method difficult to reproduce, tune, and apply to new KGs or different control types.\n\n3. Baseline Comparison Is Not Perfectly \"Apples-to-Apples\"\n\nThe primary baseline, AbductiveKGR, is run in an \"unconditional\" setting  and is then compared to CtrlHGen's conditional results. While this demonstrates the benefit of adding control, it doesn't fully isolate the benefit of CtrlHGen's method. A stronger baseline would have been to adapt AbductiveKGR to be conditional (e.g., by prepending the condition tokens to its input) and then showing that it fails, thereby proving that the sub-logic augmentation and novel reward function are necessary.\n\n4. Scalability to Truly Large-Scale KGs is Untested\n\nThe paper notes that on large KGs, the number of plausible hypotheses \"grows dramatically\". The experiments are conducted on standard benchmarks (DBpedia50, WN18RR, FB15k-237), which are small-to-medium in size. The paper does not provide evidence that the sampling, augmentation, and RL-tuning processes would be computationally feasible or effective on modern, web-scale KGs containing billions of facts.\n\n5. Analysis of LLM Failures is Plausible but Incomplete\n\nThe paper correctly identifies that LLMs perform \"very poor\" and offers plausible explanations, such as a lack of understanding of structured data and knowledge conflicts. However, the LLMs were only provided with a \"2-hop subgraph\" as context. This is a very limited and simple prompting strategy. It's possible that the LLMs' failure is at least partially due to this weak context-providing method, rather than an inherent inability to perform the task. More advanced prompting or retrieval-augmentation strategies would be needed for a more definitive conclusion.", "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": "xWon2wplVG", "reviewer": "Reviewer_wmXZ", "summary": "Abductive reasoning in knowledge graphs facilitates the creation of plausible logical hypotheses to explain observed entities. This article presents a novel and controllable abductive reasoning approach to overcome the limitations of existing methods, which often lack flexibility in real-world applications. To address challenges including overly lengthy hypotheses due to hypothesis space collapse and the high sensitivity of generated outputs, the authors introduce a sub-logic decomposition-based data augmentation technique, combined with meticulously crafted reinforcement learning reward signals. Comprehensive experiments show that the proposed CtrlHGen method effectively resolves these issues, significantly improving the controllability and semantic quality of hypothesis generation.", "questions": "My questions have already been listed in Weakness.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.The controllable abductive reasoning approach for knowledge graphs introduced in this article is both innovative and practically significant. By generating plausible hypotheses tailored to user-specific interests, this method holds substantial value for applications such as recommendation systems and scientific discovery.\n\n2.The writing of this paper is clear and easy to understand. This paper naturally puts forward the significance of controllability, the challenges of achieving controllability and how to solve these challenges.\n\n3.The paper presents convincing experimental results. Evaluations across five distinct settings convincingly demonstrate the proposed method's ability to achieve controllability. Furthermore, ablation studies robustly validate the effectiveness and contributions of the approach.\n\n4.The case studies reveal unexpectedly robust results. When presented with control conditions unrelated to the observed entities, the model adeptly introduces logical disjunctions (OR) to concurrently meet both the control constraints and maintain semantic interpretability. This behavior is both intriguing and highly significant.", "weaknesses": "1.The author did not explore whether some naive methods could be applied to controllable abductive reasoning tasks. For instance, models based on link prediction in KG, or search methods based on subgraph matching.\n\n2.It seems to me that the poor performance of LLMs is very interesting. But the authors should provide a specific case, including the 2-hop subgraph obtained by the large model and its generation results, so as to more clearly demonstrate the reasons for the poor performance of the large model.\n\n3.Following W1 and W2, the poor performance of LLMs may be limited by some naive searches. The author should make an analysis on this point. For example, whether the 2-hop subgraph can contain valid answers.", "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)