Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning
Open accessAbstract
Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving. Our method first utilizes LLMs to translate a natural language problem into a symbolic formulation. Afterward, a deterministic symbolic solver performs inference on the formulated problem. We also introduce a self-refinement module, which utilizes the symbolic solver's error messages to revise symbolic formalizations. We demonstrate Logic-LM's effectiveness on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. On average, Logic-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-of-thought prompting. Our findings suggest that Logic-LM, by combining LLMs with symbolic logic, offers a promising avenue for faithful logical reasoning. Code and data are publicly available at https://github.com/teacherpeterpan/Logic-LLM.
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Written from the paper’s full text.
TL;DR
LOGIC-LM combines LLMs with deterministic symbolic solvers by having the LLM translate natural-language logical problems into symbolic formulations, then offloading inference to solvers and interpreting results back into answers. Across five logical reasoning datasets, it improves over standard prompting by 39.2% on average and over chain-of-thought by 18.4% on average.
Key findings
- LOGIC-LM outperforms standard LLMs and CoT across all five datasets; with GPT-3.5, average improvement is 39.2% over standard prompting and 18.4% over CoT.
- With GPT-4, LOGIC-LM further improves over standard prompting by an average of 24.98% and over CoT by 10.44%.
- Performance gains grow with reasoning depth on ProofWriter: LOGIC-LM outperforms CoT by 7.1%, 5.0%, 12.7%, 20.0%, and 39.4% on depth-0, depth-1, depth-2, depth-4, and depth-5 problems, respectively.
- Self-refinement increases executable symbolic formulations by 5.01% on average, but accuracy tends to stagnate in later rounds even as executability continues to rise.
Methods
- Design: three-stage framework — Problem Formulator (LLM translates NL into symbolic language), Symbolic Reasoner (deterministic solver performs inference), and Result Interpreter (maps solver output to natural-language answer). A self-refinement module revises symbolic formulations using solver error messages.
- Data: five logical reasoning datasets — PrOntoQA, ProofWriter, FOLIO, LogicalDeduction, and AR-LSAT — covering deductive reasoning, first-order logic, constraint satisfaction, and analytical reasoning. Test sizes reported in the paper’s table are PrOntoQA 500, ProofWriter 600, FOLIO 204, LogicalDeduction 300, and AR-LSAT 230; the text separately says AR-LSAT has 231 multiple-choice questions.
- Analysis: compares LOGIC-LM against standard in-context prompting and chain-of-thought prompting using ChatGPT (gpt-3.5-turbo), GPT-3.5 (text-davinci-003), and GPT-4 (gpt-4), with temperature 0 and accuracy as the metric. Symbolic solvers include Pyke, Prover9, python-constraint, and Z3.
Limitations
- Stated: LOGIC-LM’s applicability is bounded by the expressiveness of the symbolic solver, since not all problems can be easily encoded in formalisms such as first-order logic.
- Stated: it depends on in-context learning plus self-refinement to convert NL into symbolic representations, which may struggle with intricate grammar structures such as probabilistic soft logic due to limited demonstrations and context size.
- Evident from the paper’s analysis: self-refinement mainly fixes invalid symbolic forms using solver error messages, but a valid symbolic representation is not necessarily a correct problem formulation; the paper notes accuracy can stagnate even as executable rate increases. Error cases also show GPT-4 struggles with predicate consistency, interpreting expressions like “below” vs. “above,” and FOL grammar.
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Claims the paper makes
6 of 13 cited sources checked · 3 supported · 0 flagged · accuracy not yet measured
- Premisecitation
LLMs still struggle with complex logical reasoning problems.
“Despite the advances of LLMs, they still struggle with complex logical reasoning problems (Liu et al., 2023b).”
Quote in the paperSubstantial claim1 of 1 sources checked- cites Liu et al., 2023b source
- Premisecitation
LLMs occasionally make unfaithful reasoning, i.e., the derived conclusion does not follow the previously generated reasoning chain.
“Recent studies (Golovneva et al., 2023;Ribeiro et al., 2023b;Lyu et al., 2023) found that LLMs occasionally make unfaithful reasoning, i.e., the derived conclusion does not follow the previously generated reasoning chain.”
Quote in the paperSubstantial claim1 of 3 sources checked- cites Golovneva et al., 2023
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Ribeiro et al., 2023b
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Lyu et al., 2023 source
- Premisecitation
LLMs have demonstrated a notable ability to comprehend textual inputs and translate them into formal programs.
“However, they have demonstrated a notable ability to comprehend textual inputs and translate them into formal programs, such as mathematical equations (He-Yueya et al., 2023) or Python codes (Gao et al., 2023).”
Quote in the paperSubstantial claim1 of 2 sources checked- cites He-Yueya et al., 2023 source
- cites Gao et al., 2023
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Findingown data
LOGIC-LM becomes increasingly effective as the required reasoning depth increases.
“We also find that LOGIC-LM becomes increasingly effective as the required reasoning depth increases ( § 4.3).”
- Also stated in: § 4.3 Robustness of Reasoning · hedged
“The results, shown in Figure 3, indicate that LOGIC-LM becomes increasingly effective as the required reasoning depth increases.”
Quote in the paperNot a substantial claim - Also stated in: § 4.3 Robustness of Reasoning · hedged
- Findingown data
GPT-4 has difficulty fully grasping the rules of FOL grammar, evidenced by the invalid generated formula: Rating(subway, y) ∧ y > 9.
“Example 4 exemplifies GPT-4's challenge with fully grasping the rules of FOL grammar, evidenced by the invalid generated formula: Rating(subway, y) ∧ y > 9.”
Quote in the paperNot a substantial claim
- Findingown data
Self-refinement is effective in fixing in-executable symbolic formulations, increasing Exe_Rate by 5.01 on average.
“In Table 3, we find that self-refinement is effective in fixing the in-executable symbolic formulations, increasing the Exe_Rate by 5.01 on average.”
Quote in the paperSubstantial claim - Findingown data
Self-refinement, i.e., incrementally revising symbolic formalizations using the symbolic solver's error messages, is effective.
“Finally, by analyzing the impact of selfrefinement, we highlight the effectiveness of incrementally revising symbolic formalizations when interacting with the symbolic solver ( § 4.4).”
Quote in the paperSubstantial claim - Findingown data
GPT-4 outperforms GPT-3.5 by 48.46% on average for standard prompting.
“GPT-4 outperforms GPT-3.5 by a large margin of 48.46% on average for the standard prompting.”
Quote in the paperNot a substantial claim - Findingown data
The performance of Standard and CoT declines precipitously with escalation of problem complexity.
“The performance of Standard and CoT declines precipitously with the escalation of problem complexity.”
Quote in the paperSubstantial claim - Findingown data
LLM demonstrates high proficiency in transcribing problems into symbolic formats, with near 100% Exe_Rate on ProntoQA, ProofWriter, and LogicalDeduction.
“Generally, LLM demonstrates high proficiency in transcribing problems into symbolic formats, evidenced by its near 100% Exe_Rate on ProntoQA, ProofWriter, and Logi-calDeduction.”
Quote in the paperSubstantial claim - Findingown data
LLMs like InstructGPT and GPT-4 can effectively follow instructions to identify key entities, facts, and rules and translate them into symbolic language following the defined grammar.
“we observe that LLMs, like InstructGPT (Ouyang et al., 2022b) and GPT-4 (OpenAI, 2023), can effectively follow the instructions to identify key entities, facts, and rules present in the problem statement, and then translate these elements into symbolic language following our defined grammar.”
Quote in the paperSubstantial claim - Findingnone given
LOGIC-LM has demonstrated a potent capacity to interpret complex problems into symbolic forms.
“In general, LOGIC-LM has demonstrated a potent capacity to interpret complex problems into symbolic forms.”
Quote in the paperSubstantial claim - Findingown data
Logical forms generated by GPT-4 generally achieve high Exe_Acc, even for the most challenging AR-LSAT dataset.
“We find that logical forms generated by GPT-4 generally achieve high Exe_Acc, even for the most challenging AR-LSAT dataset.”
Quote in the paperSubstantial claim - Findingown data
The declining trend with problem complexity is less prominent for LOGIC-LM.
“However, this trend is less prominent for LOGIC-LM”
Quote in the paperSubstantial claim - Findingown data
GPT-4 generates an incorrect FOL representation in Example 1, stemming from its inability to define appropriate predicates.
“Example 1 shows a case where GPT-4 generates an incorrect FOL representation, stemming from its inability to define appropriate predicates.”
Quote in the paperNot a substantial claim - Findingown data
GPT-4 still makes numerous unfaithful reasoning errors.
“we observe that GPT-4 still makes numerous unfaithful reasoning errors.”
Quote in the paperSubstantial claim - Interpretationown data
Self-refinement serves as an effective tool in aiding the LLM to accurately frame the problem.
“This suggests that selfrefinement serves as an effective tool in aiding the LLM to accurately frame the problem.”
Quote in the paperSubstantial claim - Interpretationreasoning
The high Exe_Rate on ProntoQA, ProofWriter, and LogicalDeduction is somewhat anticipated because their problems are mostly synthetically generated, limiting language variability.
“However, the high performance on these datasets is somewhat anticipated, given that their problems are mostly synthetically generated, limiting language variability.”
Quote in the paperNot a substantial claim- Rests on an assumption: The problems in ProntoQA, ProofWriter, and LogicalDeduction are mostly synthetically generated, limiting language variability.
- Interpretationown data
Offloading the reasoning to symbolic solvers greatly improves faithfulness compared with pure language-based reasoning with chain-of-thought.
“LOGIC-LM also improves CoT by a large margin of 18.4% on average, showing that offloading the reasoning to symbolic solvers greatly improves faithfulness compared with pure language-based reasoning with CoT.”
Quote in the paperSubstantial claim - Interpretationreasoning
The stagnation in accuracy can be attributed to the type of feedback received by the self-refiner, which is the error message from the symbolic solver.
“This can be attributed to the type of feedback received by the self-refiner, which is the error mes- sage from the symbolic solver.”
Quote in the paperSubstantial claim - Interpretationreasoning
LOGIC-LM is a more generalizable framework than prior neuro-symbolic methods because it integrates modern LLMs with symbolic logic without the need for training or designing complex problem-specific modules.
“In contrast, we propose a more generalizable framework that integrates modern LLMs with symbolic logic without the need for training or designing complex problem-specific modules.”
Quote in the paperNot a substantial claim - Interpretationown data
Logic-LM significantly improves performance over pure LLMs and chain-of-thought prompting techniques.
“We introduce Logic-LM, one instantiation of such a framework, and demonstrate how it significantly improves performance over pure LLMs and chainof-thought prompting techniques.”
Quote in the paperSubstantial claim - Interpretationreasoning
The reasoning in LOGIC-LM is guaranteed to be faithful as long as the problem formulation is correct.
“Using this approach, the reasoning is guaranteed to be faithful as long as the problem formulation is correct since the answer A is the result of executing deterministic algorithms (e.g., forward/backward-chaining) embedded within the symbolic reasoner.”
Quote in the paperSubstantial claim - Interpretationown data
Transforming problems into logical forms remains a challenging task for modern LLMs, due to the intricacies of FOL formulation, the innate flexibility of natural language, and the complexity of global problem comprehension.
“These error cases underscore that transforming problems into logical forms remains a challenging task for modern LLMs, due to the intricacies of FOL formulation, the innate flexibility of natural language, and the complexity of global problem comprehension.”
Quote in the paperSubstantial claim - Interpretationown data
The discrepancy in Exe_Rate underscores inherent challenges associated with converting real-world problems into their logical equivalents.
“This discrepancy underscores the inherent challenges associated with converting real-world problems into their logical equivalents.”
Quote in the paperSubstantial claim - Premisecitation
Symbolic inference engines are faithful and transparent because their reasoning is based on symbolic-represented knowledge and follows well-defined inference rules that adhere to logical principles.
“In contrast, symbolic inference engines, such as expert systems (Metaxiotis et al., 2002), are faithful and transparent because the reasoning is based on symbolic-represented knowledge and follows well-defined inference rules that adhere to logical principles.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Metaxiotis et al., 2002
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationown data
Robust reasoning capabilities provided by external solvers substantially mitigate performance degradation for complex reasoning problems.
“indicating that the robust reasoning capabilities provided by external solvers substantially mitigate performance degradation for complex reasoning problems.”
Quote in the paperSubstantial claim - Interpretationown data
The results highlight the benefit of combining LLMs with external symbolic solvers for logical reasoning.
“This highlights the benefit of combining LLMs with external symbolic solvers for logical reasoning.”
Quote in the paperSubstantial claim - Interpretationown data
The high Exe_Acc accentuates the potential of symbolic solvers in bolstering the model's logical reasoning prowess, contingent on precise translation of problems into symbolic forms.
“Such performance accentuates the potential of symbolic solvers in bolstering the model's logical reasoning prowess, contingent on the precise translation of problems into symbolic forms.”
Quote in the paperSubstantial claim - Interpretationreasoning
CoT's forward-chain reasoning style aligns well with problems in the PrOntoQA and ProofWriter datasets.
“This reasoning style aligns well with problems in the PrOntoQA and ProofWriter datasets.”
Quote in the paperSubstantial claim - Interpretationreasoning
LOGIC-LM may face difficulties when dealing with logical representations with intricate grammar structures, such as probabilistic soft logic.
“While this method has proven to be effective, it may face difficulties when dealing with logical representations with intricate grammar structures, such as probabilistic soft logic.”
Quote in the paperNot a substantial claim
- May combine two claims. 17
- Classified as probably not a substantial claim. 13
May combine two claims.
PremisecitationPrior neuro-symbolic methods suffer from limitations such as hand-crafted or specialized module designs that are not easily generalizable, or brittleness due to the difficulty of optimization.
“Although prior works (Mao et al., 2019;Gupta et al., 2020;Manhaeve et al., 2021;Cai et al., 2021;Tian et al., 2022;Pryor et al., 2023) also propose neuro-symbolic methods to combine neural networks with symbolic reasoning, these methods suffer from limitations such as hand-crafted or specialized module designs that are not easily generalizable, or brittleness due to the difficulty of optimization.”
Quote in the paperSubstantial claim2 of 3 sources checked- cites Mao et al., 2019 source
The Training Paradigm (p. 6) says curriculum learning is essential to joint optimization, and Appendix E (p. 19) reports that training can fail to converge without it. But the paper describes NS-CL as robust and demonstrates several forms of generalization (p. 2); it does not support the unqualified claim that its module design is not easily generalizable or that the trained method is brittle. (LLM, conf=0.86)
Experimental — accuracy not yet measured - cites Gupta et al., 2020
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Manhaeve et al., 2021 source
The Related Work section describes limitations of some prior neuro-symbolic methods, including restricted expressivity, and §7.3 identifies an approach specialized for NLP tasks. It does not establish that prior methods generally rely on hand-crafted modules that are hard to generalize or are brittle because optimization is difficult. Page numbers were not available in our copy. (LLM, conf=0.78)
Experimental — accuracy not yet measured
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe main enhancement of GPT-4 lies in its ability to carry out complex reasoning.
“This aligns with the assertion that the main enhancement of GPT-4 lies in its ability to carry out complex reasoning (OpenAI, 2023).”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites OpenAI, 2023 source
The Observed Safety Challenges section (p. 44) says GPT-4 improves on earlier models in reasoning, but also names knowledge retention and coding. The report does not identify complex reasoning as GPT-4’s main enhancement. (LLM, conf=0.86)
Experimental — accuracy not yet measured
May combine two claims.
Findingown dataChain-of-thought prompting yields comparatively less substantial or even negative improvements on FOLIO, LogicalDeduction, and AR-LSAT, with improvements of 11.75%, 9.41%, and -3.2%, respectively.
“While integrating CoT generally enhances LLM performance, we find its benefits comparatively less substantial or even negative on FOLIO, LogicalDeduction, and AR-LSAT, with a modest improvement of 11.75%, 9.41%, and -3.2%, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataGPT-4's Exe_Rate is notably less promising on FOLIO and AR-LSAT, with scores of 79.9% and 32.6%, respectively.
“When it comes to datasets comprising real-world, expertly crafted problems, such as FOLIO and AR-LSAT, GPT-4's performance is notably less promising, with Exe_Rate scores of 79.9% and 32.6% respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataLOGIC-LM achieves an average improvement of 39.2% over standard prompting and 18.4% over chain-of-thought prompting.
“On average, LOGIC-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-ofthought prompting.”
- Also stated in: § Problem Goal Answer · boosted
“Our evaluations show that the strategy of integrating LLMs with symbolic solvers performs significantly better than purely relying on LLMs for logical reasoning, with an average improvement of 39.2% over the standard prompting and 18.4% over the chain-of-thought prompting ( § 4.1).”
- Also stated in: § 4.1 Main Results · plain
“With GPT-3.5, our method outperforms standard LLM on all datasets, with an average improvement of 39.2%.”
Quote in the paperSubstantial claim- Also stated in: § Problem Goal Answer · boosted
May combine two claims.
Findingown dataLOGIC-LM significantly outperforms standard LLMs and chain-of-thought across all datasets.
“Logic-LM significantly outperforms standard LLMs and CoT across all datasets.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAs rounds of self-refinement increase, the percentage of executable formulations consistently increases, leading to an enhancement in final performance.
“We find that as the rounds of self-refinement increase, the percentage of executable formulations consistently increases, leading to an enhancement in the final performance.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).
Findingnone givenThere remain certain difficulties in accurately understanding the semantics of the problem.
“Nonetheless, there remain certain difficulties in accurately understanding the semantics of the problem.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataLOGIC-LM outperforms CoT by 7.1%, 5.0%, 12.7%, 20.0%, and 39.4% on depth-0, depth-1, depth-2, depth-4, and depth-5 problems, respectively.
“LOGIC-LM outperforms CoT by 7.1%, 5.0%, 12.7%, 20.0%, and 39.4% on depth-0, depth-1, depth-2, depth-4, and depth-5 problems, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataLOGIC-LM improves GPT-4 by an average of 24.98% for standard prompting and 10.44% for chain-of-thought prompting.
“By delegating the reasoning to symbolic solvers, our method can further improve GPT-4 by an average of 24.98% and 10.44% for standard prompting and CoT prompting, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataChain-of-thought prompting yields improvements of 51.59% on ProntoQA and 33.82% on ProofWriter.
“On the contrary, the benefits of CoT on ProntoQA and ProofWriter are 51.59% and 33.82%, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningAccuracy tends to stagnate in subsequent rounds of self-refinement, even though Exe_Rate continues to increase.
“However, the accuracy tends to stagnate in subsequent rounds, even though the Exe_Rate continues to increase.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningCompared to CoT, integrating symbolic solvers is better suited to nonlinear reasoning styles, yielding more marked improvements on FOLIO (+21.85%), LogicalDeduction (+45.67%), and AR-LSAT (+24.14%).
“Compared to CoT, the integration of symbolic solvers is better suited to these reasoning styles, hence yielding a more marked improvement on FO-LIO (+21.85%),LogicalDeduction (+45.67%), and AR-LSAT (+24.14%).”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone givenIn LOGIC-LM, multi-step logical reasoning is delegated to external symbolic solvers, transitioning the challenge of LLM from problem-solving to problem representation.
“In LOGIC-LM, multi-step logical reasoning is delegated to external symbolic solvers, thereby transitioning the challenge of LLM from problemsolving to problem representation.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductreasoningFor reproducible results, the temperature was set to 0 and the response with the highest probability was selected from LLMs.
“For reproducible results, we set the temperature to 0 and select the response with the highest probability from LLMs.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductnone givenThe robustness analysis randomly selected 300 examples from each ProofWriter subset, ensuring a balanced label distribution.
“We randomly selected 300 examples from each subset of ProofWriter, ensuring a balanced label distribution.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningLOGIC-LM's applicability is inherently bounded by the expressiveness of the symbolic solver; not all problems can be easily encoded in first-order logic.
“As a consequence, the model's applicability is inherently bounded by the expressiveness of the symbolic solver, for example, not all problems can be easily encoded in first-order logic.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductreasoningFor un-executable cases where the symbolic solver does not return an answer due to grammar errors, the method falls back on using chain-of-thought to predict the answer.
“For these un-executable cases, we fall back on using chain-of-thought to predict the answer.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Interpretationown dataA plausible explanation for CoT's performance pattern is that CoT emulates human forward-chain reasoning: beginning with known facts and sequentially deriving new conclusions until the goal is met.
“that CoT emulates human forward-chain reasoning: beginning with known facts and sequentially deriving new conclusions until the goal is met.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningBy incorporating LLMs with symbolic solvers, one can exploit the robust natural language understanding capabilities of LLMs to precisely represent the problem using symbolic representations, while also taking advantage of the logical faithfulness and transparency offered by symbolic solvers.
“By incorporating LLMs with symbolic solvers, we can exploit the robust natural language understanding capabilities of LLMs to precisely represent the problem using symbolic representations, while also taking advantage of the logical faithfulness and transparency offered by symbolic solvers.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
InterpretationreasoningBy defining additional problem-specific formulations, the LOGIC-LM framework retains the flexibility to accommodate a wider range of reasoning tasks.
“By defining additional problem-specific formulations, our framework retains the flexibility to accommodate a wider range of reasoning tasks.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Study design and conductreasoningModel performance was evaluated based on the accuracy of selecting the correct answer.
“Since all examples are formed as multiple-choice questions, we evaluate model performance based on the accuracy of selecting the correct answer.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationAR-LSAT is particularly challenging, with state-of-the-art models only achieving performance slightly better than random guessing.
“AR-LSAT is particularly challenging, with state-of-the-art models only achieving performance slightly better than random guessing (Liang et al., 2022;Ribeiro et al., 2023a).”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites Liang et al., 2022 source
Checked before — its earlier verdict is held back until a new check runs.
- cites Ribeiro et al., 2023a
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Interpretationown dataThis inconsistency is a recurring issue in GPT-4's symbolic form generation, illustrating that the model sometimes struggles to maintain an overarching understanding of the problem when forming logical symbols.
“This inconsistency is a recurring issue in GPT-4's symbolic form generation, illustrating that the model sometimes struggles to maintain an overarching understanding of the problem when forming logical symbols.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Study design and conductreasoningTo ensure fair comparisons, the same in-context examples were used for all models.
“To ensure fair comparisons, we use the same in-context examples for all models.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone givenThe flexible design of LOGIC-LM facilitates integration of a more diverse set of symbolic solvers.
“The flexible design of LOGIC-LM facilitates this integration.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
InterpretationreasoningThe difficulty with intricate grammar structures arises from the difficulty in conveying complex grammatical rules to the language model through a limited number of demonstrations within a constrained context size.
“This arises from the difficulty in conveying complex grammatical rules to the language model through a limited number of demonstrations within a constrained context size.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
InterpretationreasoningThe wide range of reasoning tasks that we can instantiate our LOGIC-LM framework on shows its general applicability.
“The wide range of reasoning tasks that we can instantiate our LOGIC-LM framework on shows its general applicability.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
The main obstacle in using symbolic solvers for logical reasoning is accurately translating natural language problems into symbolic representations.
“The main obstacle is how to accurately translate a problem into symbolic representations, considering the inherent ambiguity and flexibility of natural language.”
The paper relies on this without support.
Language models have inherent limitations such as the inability to access up-to-date information, take actions, or perform precise mathematical reasoning.
“Language models have inherent limitations such as the inability to access up-to-date information, take actions, or perform precise mathematical reasoning.”
The paper relies on this without support.
Many analytical reasoning problems can be formulated as SAT problems.
“Many analytical reasoning problems can be formulated as SAT problems.”
The paper relies on this without support.
A lot of real-world analytical reasoning problems can be represented as problems of solving a system of equations.
“A lot of real-world analytical reasoning problems can be represented as problems of solving a system of equations.”
The paper relies on this without support.
For complex problems, generating the correct logical form may become challenging for LLMs.
“For complex problems, generating the correct logical form may become challenging for LLMs.”
The paper relies on this without support.
While logic programming efficiently represents common deductive reasoning problems, it may fail to represent more complex first-order logic problems.
“While the logic programming language efficiently represents common deductive reasoning problems, it may fail to represent more complex first-order logic (FOL) problems.”
The authors state this as an assumption.
The complexity of formally representing a problem statement in logical form should remain relatively constant, regardless of whether the questions require simple or complex reasoning.
“Ideally, the complexity of formally representing a problem statement in logical form should remain relatively constant, regardless of whether the questions require simple or complex reasoning.”
The paper relies on this without support.
The problems in ProntoQA, ProofWriter, and LogicalDeduction are mostly synthetically generated, limiting language variability.
“given that their problems are mostly synthetically generated, limiting language variability.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Existing neurosymbolic approaches typically operate at the level of the full problem or the full reasoning trace.
“but they typically operate at the level of the full problem or the full reasoning trace.”
From Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming (2026) · cites this paper as Pan et al. [2023]
The Problem Goal Answer passage and §3.2 describe Logic-LM as a neuro-symbolic method that formulates the problem and goal for a symbolic solver, supporting the full-problem part of the claim. Section 2 discusses prior neuro-symbolic work but does not say that such approaches typically operate at the level of the full problem or the full reasoning trace. (LLM, conf=0.76)
Experimental — accuracy not yet measuredLOGIC-LM creates a deterministic symbolic solver that expresses reasoning in a specific symbolic format to obtain actual results.
“LOGIC-LM [15] creates a deterministic symbolic solver that expresses reasoning in a specific symbolic format to obtain actual results.”
From ChatLogic: Integrating Logic Programming with Large Language Models for Multi-Step Reasoning (2024) · cites this paper as [15]
The Problem Goal Answer passage describes LOGIC-LM using an LLM to convert a problem into a symbolic formulation, then a deterministic solver to perform inference. Section 3.2 says the framework calls a task-dependent external solver; it does not say LOGIC-LM creates that solver or that the solver itself expresses the problem in symbolic form. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe improvement aligns with recent research integrating LLMs with symbolic reasoners for various reasoning tasks.
“This aligns with recent research integrating LLMs with symbolic reasoners for various reasoning tasks (Olausson et al., 2023;Pan et al., 2023).”
From TReMu: Towards Neuro-Symbolic Temporal Reasoning for LLM-Agents with Memory in Multi-Session Dialogues (2025) · cites this paper as Pan et al., 2023
Logic-LM partially addresses the grounding bottleneck by using LLMs as translators from natural language to formal logic, but the translation stage itself introduces an additional failure mode.
“Logic-LM Pan et al. [2023] partially addresses this issue by using LLMs as translators from natural language to formal logic, but the translation stage itself introduces an additional failure mode.”
From Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming (2026) · cites this paper as Pan et al. [2023]
Existing neurosymbolic approaches either internalize rules through retraining with logic-informed objectives, or rely on hand-crafted formal grammars specified per domain.
“Existing neurosymbolic approaches either internalize rules through retraining with logic-informed objectives de Souza et al. [2025], or rely on hand-crafted formal grammars specified per domain Pan et al. [2023], Chen et al. [2022, 2023].”
From Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming (2026) · cites this paper as Pan et al. [2023]
Recent neurosymbolic approaches either translate natural-language problems into formal representations and delegate reasoning to external solvers, or inject symbolic structure into the reasoning process to improve faithfulness and controllability.
“Recent neurosymbolic approaches either translate natural-language problems into formal representations and delegate reasoning to external solvers Pan et al. [2023], Olausson et al. [2023], or inject symbolic structure into the reasoning process to improve faithfulness and controllability Xu et al. [2024], Lyu et al. [2023].”
From Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming (2026) · cites this paper as Pan et al. [2023]
Symbolic constraints can improve reasoning reliability.
“These approaches show that symbolic constraints can improve reasoning reliability”
From Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming (2026) · cites this paper as Pan et al. [2023]
Neither the Neuro-Symbolic Concept Learner [11] nor Logic-LM [13] pose a viable approach for the current work due to the complexity of questions expected for a KBQA system and the authors' interest in leveraging the generative power of an LLM.
“Neither [11] nor [13] pose a viable approach in this current work, however, due to the complexity of questions expected for a KBQA system, and our subsequent interest in leveraging the generative power of an LLM to answer inputted queries.”
From ProSLM: A Prolog Synergized Language Model for explainable Domain Specific Knowledge Based Question Answering (2024) · cites this paper as [13]
LLM outputs in formal domains remain prone to errors.
“While LLMs can generate logic programs, their outputs in formal domains remain prone to errors [15].”
From ADVENT: LLM-Driven Automatic Predicate Invention for ILP (2026) · cites this paper as [15]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
LOGIC-LM does not outperform CoT on every dataset
MajorThe across-all-datasets claim conflicts with Table 2: on PrOntoQA, ChatGPT with LOGIC-LM scores 61.00 versus 67.80 with CoT, and GPT-4 with LOGIC-LM scores 83.20 versus 98.79 with CoT.
“1. Logic-LM significantly outperforms standard LLMs and CoT across all datasets.”
“| PrOntoQA | 47.40 | 67.80 | 61.00 | 51.80 | 83.00 | 85.00 | 77.40 | 98.79 | 83.20 |”
AR-LSAT test-set size differs between text and table
MinorThe dataset description states that the test set has 231 questions, while the dataset-statistics table lists 230.
“We use the test set which has 231 multiplechoice questions.”
“| AR-LSAT | AR | 230 | 5 |”
Reasoning-depth discussion refers to a nonexistent depth-4 group
MinorThe reported ProofWriter depth groups are 0, 1, 2, 3, and 5; the discussion instead calls the fourth group depth 4.
“depth-0, depth-1, depth-2, depth-4, and depth-5 problems, respectively.”
“The problems in these subsets require 0, <=1, <=2, <=3, and <=5 hops of reasoning, respectively.”
Oldest-vehicle answer has the wrong option letter
MinorThe convertible is option B in the stated choices, but the answer labels it option A.
“A) The convertible is the oldest.”
“A) The tractor is the oldest.B) The convertible is the oldest.C) The minivan is the oldest.”
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Language Models are Few-Shot Learners
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BackgroundMethodChain-of-Thought Prompting Elicits Reasoning in Large Language Models
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“”, these models are able to answer questions with explicit reasoning steps (Wei et al., 2022b; Kojima et al., 2022).”
BackgroundMethodInfluentialSelf-citationTraining language models to follow instructions with human feedback
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BackgroundMethodEnergy and Policy Considerations for Deep Learning in NLP
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Training Language Models to Follow Instructions with Human Feedback
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Large language models are zero-shot reasoners
Kojima, T., Gu, S. (., Reid, M., Matsuo, Y., & Iwasawa, Y. (2022) · Advances in Neural Information Processing Systems 35 · doi:10.52202/068431-1613 · Cited by 2,013 · cited 2× · see citing works
“, these models are able to answer questions with explicit reasoning steps (Wei et al., 2022b; Kojima et al., 2022).”
BackgroundSymPy: symbolic computing in Python
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Emergent Abilities of Large Language Models
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“AR-LSAT is particularly challenging, with state-of-the-art models only achieving performance slightly better than random guessing (Liang et al., 2022; Ribeiro et al., 2023a).”
BackgroundAlgorithms for Constraint-Satisfaction Problems: A Survey
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“Constraint satisfaction problems (CSPs) (Kumar, 1992) aims to find the value assignment of a set of objects that satisfy a number of constraints.”
BackgroundSelf-Consistency Improves Chain of Thought Reasoning in Language Models
Wang, X., Wei, J., Schuurmans, D., Le, Q., Chi, E., Narang, S., Chowdhery, A., & Zhou, D. (2022) · arXiv · doi:10.48550/arxiv.2203.11171 · Cited by 829 · cited 2× · see citing works
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BackgroundMethodSelf-citationSelf-Refine: Iterative Refinement with Self-Feedback
Madaan, A., Tandon, N., Gupta, P., Hallinan, S., Gao, L., Wiegreffe, S., Alon, U., Dziri, N., Prabhumoye, S., Yang, Y., et al. (2023) · Advances in Neural Information Processing Systems 36 · doi:10.52202/075280-2019 · Cited by 755 · see citing works
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Training Verifiers to Solve Math Word Problems
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Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models
Srivastava, A., Rastogi, A., Rao, A., Shoeb, A. A. M., Abid, A., Fisch, A., Brown, A. R., Santoro, A., Gupta, A., Garriga-Alonso, A., et al. (2022) · arXiv · doi:10.48550/arxiv.2206.04615 · Cited by 569 · see citing works
HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face
Shen, Y., Song, K., Tan, X., Li, D., Lu, W., & Zhuang, Y. (2023) · arXiv · doi:10.48550/arxiv.2303.17580 · Cited by 477 · cited 2× · see citing works
“…with access to external tools and resources, such as the information retriever (Nakano et al., 2021; Shi et al., 2023; Lazaridou et al., 2022), calculator (Cobbe et al., 2021), code interpreter (Wang et al., 2022), planner (Liu et al., 2023a), and other pre-trained models (Shen et al., 2023).”
BackgroundHuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face
Shen, Y., Song, K., Tan, X., Li, D., Lu, W., & Zhuang, Y. (2023) · Advances in Neural Information Processing Systems 36 · doi:10.52202/075280-1657 · Cited by 475 · see citing works
Socratic guiding questions in synthetic arithmetic data: matched LoRA runs (revision v2)
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“Although prior works (Mao et al., 2019; Gupta et al., 2020; Manhaeve et al., 2021; Cai et al., 2021; Tian et al., 2022; Pryor et al., 2022) also propose neuro-symbolic methods to combine neural networks with symbolic reasoning, these methods suffer from limitations such as hand-crafted or specialized module designs th…”
BackgroundTowards Reasoning in Large Language Models: A Survey
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Artificial intelligence: foundations of computational agents
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The Lean Theorem Prover (System Description)
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“These works demonstrate the proficiency of LLMs in translating a considerable fraction of mathematical problems into formal specifications defined in tools like SymPy (Meurer et al., 2017), Isabelle/HOL (Paulson, 1994), and Lean (de Moura et al., 2015).”
BackgroundMethodLeast-to-Most Prompting Enables Complex Reasoning in Large Language Models
Zhou, D., Schärli, N., Hou, L., Wei, J., Scales, N., Wang, X., Schuurmans, D., Cui, C., Bousquet, O., Le, Q., et al. (2022) · arXiv · doi:10.48550/arxiv.2205.10625 · Cited by 380 · cited 1× · see citing works
“, 2022b) that generates explanations before the final answer and the least-to-most prompting (Zhou et al., 2022) that breaks the problem down into simpler components that can be solved individually.”
BackgroundSelf-citationWebGPT: Browser-assisted question-answering with human feedback
Nakano, R., Hilton, J., Balaji, S., Wu, J., Ouyang, L., Kim, C., Hesse, C., Jain, S., Kosaraju, V., Saunders, W., et al. (2021) · arXiv · doi:10.48550/arxiv.2112.09332 · Cited by 272 · see citing works
Holistic Evaluation of Language Models
Liang, P., Bommasani, R., Lee, T., Tsipras, D., Soylu, D., Yasunaga, M., Zhang, Y., Narayanan, D., Wu, Y., Kumar, A., et al. (2022) · arXiv · doi:10.48550/arxiv.2211.09110 · Cited by 255 · see citing works
Self-citationSelf-Refine: Iterative Refinement with Self-Feedback
Madaan, A., Tandon, N., Gupta, P., Hallinan, S., Gao, L., Wiegreffe, S., Alon, U., Dziri, N., Prabhumoye, S., Yang, Y., et al. (2023) · arXiv · doi:10.48550/arxiv.2303.17651 · Cited by 219 · see citing works
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Transformers as Soft Reasoners over Language
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“Recent works in adapting large language models for logical reasoning tasks can be broadly categorized into two groups: 1) fine-tuning approaches that optimize LLMs’ reasoning ability through fine-tuning or training specialized modules (Clark et al., 2020; Tafjord et al., 2022; Yang et al., 2022), and 2) incontext lear…”
BackgroundPAL: Program-aided Language Models
Gao, L., Madaan, A., Zhou, S., Alon, U., Liu, P., Yang, Y., Callan, J., & Neubig, G. (2022) · arXiv · doi:10.48550/arxiv.2211.10435 · Cited by 155 · cited 1× · see citing works
“, 2023) or a Python interpreter (Gao et al., 2022; Chen et al., 2022) into LLMs can greatly enhance performance by offloading numerical calculations.”
BackgroundNeural probabilistic logic programming in DeepProbLog
Manhaeve, R., Dumančić, S., Kimmig, A., Demeester, T., & De Raedt, L. (2021) · Artificial Intelligence · doi:10.1016/j.artint.2021.103504 · Cited by 131 · cited 2× · see citing works
“Although prior works (Mao et al., 2019; Gupta et al., 2020; Manhaeve et al., 2021; Cai et al., 2021; Tian et al., 2022; Pryor et al., 2022) also propose neuro-symbolic methods to combine neural networks with symbolic reasoning, these methods suffer from limitations such as hand-crafted or specialized module designs th…”
BackgroundChen, W., Ma, X., Wang, X., & Cohen, W. W. (2022) · arXiv · doi:10.48550/arxiv.2211.12588 · Cited by 125 · cited 2× · see citing works
“, 2023) or a Python interpreter (Gao et al., 2022; Chen et al., 2022) into LLMs can greatly enhance performance by offloading numerical calculations.”
BackgroundSelf-citationProofWriter: Generating implications, proofs, and abductive statements over natural language
Tafjord, O., Dalvi, B., & Clark, P. (2021) · Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021 · doi:10.18653/v1/2021.findings-acl.317 · Cited by 122 · cited 7× · see citing works
“We randomly selected 300 examples from each subset of ProofWriter, ensuring a balanced label distribution.”
MethodInfluentialLLM+P: Empowering Large Language Models with Optimal Planning Proficiency
Liu, B., Jiang, Y., Zhang, X., Liu, Q., Zhang, S., Biswas, J., & Stone, P. (2023) · arXiv · doi:10.48550/arxiv.2304.11477 · Cited by 104 · cited 3× · see citing works
“…with access to external tools and resources, such as the information retriever (Nakano et al., 2021; Shi et al., 2023; Lazaridou et al., 2022), calculator (Cobbe et al., 2021), code interpreter (Wang et al., 2022), planner (Liu et al., 2023a), and other pre-trained models (Shen et al., 2023).”
BackgroundEvaluating the logical reasoning ability of chatgpt and GPT-4
Liu, H., Ning, R., Teng, Z., Liu, J., Zhou, Q., & Zhang, Y. (2023) · arXiv · doi:10.48550/arxiv.2304.03439 · Cited by 100 · cited 2× · see citing works
“…with access to external tools and resources, such as the information retriever (Nakano et al., 2021; Shi et al., 2023; Lazaridou et al., 2022), calculator (Cobbe et al., 2021), code interpreter (Wang et al., 2022), planner (Liu et al., 2023a), and other pre-trained models (Shen et al., 2023).”
BackgroundNeural Module Networks for Reasoning over TextPreprint
Gupta, N., Lin, K., Roth, D., Singh, S., & Gardner, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.04971 · Cited by 94 · see citing works
Teaching Large Language Models to Self-Debug
Chen, X., Lin, M., Schärli, N., & Zhou, D. (2023) · arXiv · doi:10.48550/arxiv.2304.05128 · Cited by 77 · cited 2× · see citing works
“Recent works (Chen et al., 2023; Madaan et al., 2023) have adopted similar ideas to improve code generation, by teaching LLMs to debug their predicted programs via fewshot demonstrations.”
BackgroundTalking About Large Language ModelsPreprint
Shanahan, M. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2212.03551 · Cited by 69 · cited 1× · see citing works
“While chain-of-thought may imitate human reasoning processes, the fundamental nature of LLMs remains that of black-box probabilistic models, lacking a mechanism to guarantee the faithfulness of reasoning (Shanahan, 2022).”
BackgroundREPLUG: Retrieval-augmented black-box language models
Shi, W., Min, S., Yasunaga, M., Seo, M., James, R., Lewis, M., Zettlemoyer, L., & Yih, W.-T. (2023) · arXiv · doi:10.48550/arxiv.2301.12652 · Cited by 65 · cited 1× · see citing works
“…work has begun to augment language models with access to external tools and resources, such as the information retriever (Nakano et al., 2021; Shi et al., 2023; Lazaridou et al., 2022), calculator (Cobbe et al., 2021), code interpreter (Wang et al., 2022), planner (Liu et al., 2023a), and…”
BackgroundInternet-augmented language models through few-shot prompting for open-domain question answering
Lazaridou, A., Gribovskaya, E., Stokowiec, W., & Grigorev, N. (2022) · arXiv · doi:10.48550/arxiv.2203.05115 · Cited by 64 · see citing works
Code4Struct: Code Generation for Few-Shot Event Structure Prediction
Wang, X., Li, S., & Ji, H. (2023) · Proceedings of the conference - Association for Computational Linguistics. Meeting · doi:10.18653/v1/2023.acl-long.202 · Cited by 63 · see citing works
Self-citationAutoformalization with Large Language ModelsPreprint
Wu, Y., Jiang, A. Q., Li, W., Rabe, M. N., Staats, C., Jamnik, M., & Szegedy, C. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2205.12615 · Cited by 62 · see citing works
Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought
Saparov, A., & He, H. (2022) · arXiv · doi:10.48550/arxiv.2210.01240 · Cited by 46 · cited 5× · see citing works
“, 2021), PrOntoQA (Saparov and He, 2023), FOLIO (Han et al.”
BackgroundInfluentialFifty Years of Prolog and Beyond
KÖRNER, P., LEUSCHEL, M., BARBOSA, J., COSTA, V. S., DAHL, V., HERMENEGILDO, M. V., MORALES, J. F., WIELEMAKER, J., DIAZ, D., ABREU, S., et al. (2022) · Theory and Practice of Logic Programming · doi:10.1017/s1471068422000102 · Cited by 40 · cited 1× · see citing works
“The Prolog logic programming language (Clocksin and Mellish, 2003; Körner et al., 2022) is arguably the most prominent symbolic language to describe deductive reasoning problems.”
BackgroundROSCOE: A Suite of Metrics for Scoring Step-by-Step ReasoningPreprint
Golovneva, O., Chen, M., Poff, S., Corredor, M., Zettlemoyer, L., Fazel-Zarandi, M., & Çelikyılmaz, A. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2212.07919 · Cited by 37 · cited 2× · see citing works
“Recent studies (Golovneva et al., 2023; Ribeiro et al., 2023; Lyu et al., 2023) found that LLMs occasionally make unfaithful reasoning, i.”
BackgroundNeuPSL: Neural Probabilistic Soft Logic
Pryor, C., Dickens, C., Augustine, E., Albalak, A., Wang, W. Y., & Getoor, L. C. (2023) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2023/461 · Cited by 36 · see citing works
Self-citationFOLIO: Natural Language Reasoning with First-Order Logic
Han, S., Schoelkopf, H., Zhao, Y., Qi, Z., Riddell, M., Zhou, W., Coady, J., Peng, D., Qiao, Y., Benson, L., et al. (2022) · arXiv · doi:10.48550/arxiv.2209.00840 · Cited by 35 · see citing works
Entailer: Answering Questions with Faithful and Truthful Chains of Reasoning
Tafjord, O., Mishra, B. D., & Clark, P. A. (2022) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2022.emnlp-main.134 · Cited by 31 · see citing works
Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal ProofsPreprint
Jiang, A. Q., Welleck, S., Zhou, J., Li, W., Liu, J., Jamnik, M., Lacroix, T., Wu, Y., & Lample, G. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2210.12283 · Cited by 29 · cited 1× · see citing works
“However, they have demonstrated a notable ability to comprehend textual inputs and translate them into formal programs, such as mathematical equations (He-Yueya et al., 2023) or Python codes (Gao et al., 2023).”
BackgroundGenerating Natural Language Proofs with Verifier-Guided Search
Yang, K., Deng, J., & Chen, D. (2022) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2022.emnlp-main.7 · Cited by 29 · see citing works
Abductive Learning with Ground Knowledge Base
Cai, L.-W., Dai, W.-Z., Huang, Y., Li, Y.-F., Muggleton, S., & Jiang, Y. Y. (2021) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2021/250 · Cited by 23 · cited 1× · see citing works
“Although prior works (Mao et al., 2019; Gupta et al., 2020; Manhaeve et al., 2021; Cai et al., 2021; Tian et al., 2022; Pryor et al., 2023) also propose neuro-symbolic methods to combine neural networks with symbolic reasoning, these methods suffer from limitations such as hand-crafted or…”
BackgroundFaithful Chain-of-Thought Reasoning
Lyu, Q., Havaldar, S., Stein, A., Zhang, L., Rao, D., Wong, E., Apidianaki, M., & Callison-Burch, C. (2023) · arXiv · doi:10.48550/arxiv.2301.13379 · Cited by 23 · cited 1× · see citing works
“Recent studies (Golovneva et al., 2023; Ribeiro et al., 2023b; Lyu et al., 2023) found that LLMs occasionally make unfaithful reasoning, i.e. , the derived conclusion does not follow the previously generated reasoning chain.”
BackgroundSolving Math Word Problems by Combining Language Models With Symbolic Solvers
He-Yueya, J., Poesia, G., Wang, R. E., & Goodman, N. D. (2023) · arXiv · doi:10.48550/arxiv.2304.09102 · Cited by 16 · cited 3× · see citing works
“However, they have demonstrated a notable ability to comprehend textual inputs and translate them into formal programs, such as mathematical equations (He-Yueya et al., 2023) or Python codes (Gao et al., 2023).”
BackgroundZhong, W., Wang, S., Tang, D., Xu, Z., Guo, D., Chen, Y., Wang, J., Yin, J., Zhou, M., & Duan, N. (2022) · Findings of the Association for Computational Linguistics: NAACL · doi:10.18653/v1/2022.findings-naacl.177 · Cited by 14 · see citing works
SatLM: Satisfiability-Aided Language Models Using Declarative Prompting
Ye, X., Chen, Q., Dillig, I., et al. (2023) · neural information processing systems · doi:10.52202/075280-1974 · Cited by 14 · see citing works
Weakly Supervised Neural Symbolic Learning for Cognitive Tasks
Tian, J., Li, Y., Chen, W., Xiao, L., He, H., & Jin, Y. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i5.20533 · Cited by 10 · cited 2× · see citing works
“Although prior works (Mao et al., 2019; Gupta et al., 2020; Manhaeve et al., 2021; Cai et al., 2021; Tian et al., 2022; Pryor et al., 2022) also propose neuro-symbolic methods to combine neural networks with symbolic reasoning, these methods suffer from limitations such as hand-crafted or specialized module designs th…”
BackgroundSTREET: A Multi-Task Structured Reasoning and Explanation BenchmarkPreprint
Ribeiro, D., Wang, S., Ma, X., et al. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2302.06729 · Cited by 10 · cited 3× · see citing works
“Recent studies (Golovneva et al., 2023; Ribeiro et al., 2023; Lyu et al., 2023) found that LLMs occasionally make unfaithful reasoning, i.”
BackgroundSelf-citationOpenAI, Achiam, J., Adler, S., Agarwal, S., Ahmad, L., Akkaya, I., Aleman, F. L., Almeida, D., Altenschmidt, J., Altman, S., et al. (2023) · arXiv · doi:10.48550/arxiv.2303.08774 · cited 4×
“This observation aligns with the GPT-4 technical report’s assertion that the main enhancement of GPT-4 lies in its ability to carry out complex reasoning (OpenAI, 2023).”
BackgroundResultInfluentialCode4Struct: Code Generation for Few-Shot Event Structure Prediction
Wang, X., Li, S., & Ji, H. (2022) · arXiv · doi:10.48550/arxiv.2210.12810
Self-citation
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- Stephen Bach, Matthias Broecheler, Bert Huang, and Lise Getoor. 2017. Hinge-loss markov random fields and probabilistic soft logic. Journal of Machine Learning Research (JMLR), 18(1):1-67.
- Kostas S. Metaxiotis, Dimitris Askounis, and John E. Psarras. 2002. Expert systems in production planning and scheduling: A state-of-the-art survey. Journal of Intelligent Manufacturing, 13(4):253-260. · DOI
- Danilo Neves Ribeiro, Shen Wang, Xiaofei Ma, Henry Zhu, Rui Dong, Deguang Kong, Juliette Burger, An- jelica Ramos, William Yang Wang, Zhiheng Huang, George Karypis, Bing Xiang, and Dan Roth. 2023b. STREET: A multi-task structured reasoning and ex- planation benchmark. In Proceedings of the 11th International Conference on Learning Representa- tions (ICLR). · DOI
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Sorted by citations
Hadi, M. U., Al-Tashi, Q., Qureshi, R., Shah, A., Muneer, A., Irfan, M., Zafar, A., Shaikh, M. B., Akhtar, N., Hassan, S. Z., et al. (2023) · doi:10.36227/techrxiv.23589741.v4 · Cited by 173 · see citing works
Ma, Y., Cao, Y., Hong, Y. S., & Sun, A. (2023) · Findings of the Association for Computational Linguistics: EMNLP (Findings of EMNLP) · doi:10.18653/v1/2023.findings-emnlp.710 · Cited by 154 · see citing works
“…Chowdhery et al. 2022; Touvron et al. 2023) have shown remarkable abilities on various NLP applications such as factual question answering (Yu et al., 2023; Sun et al., 2023), arithmetic reasoning (Chen et al., 2022a; Qian et al., 2023) and logical reasoning (Jung et al., 2022; Pan et al., 2023).”
BackgroundEnhancing emergency decision-making with knowledge graphs and large language models
Chen, M., Tao, Z., Tang, W., Qin, T., Yang, R. C., & Zhu, C. (2024) · International Journal of Disaster Risk Reduction · doi:10.1016/j.ijdrr.2024.104804 · Cited by 112 · see citing works
Pan, L., Saxon, M., Xu, W., Nathani, D., Wang, X., & Wang, W. Y. (2024) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00660 · Cited by 86 · see citing works
Self-citationKamoi, R., Zhang, Y., Zhang, N., Han, J., & Zhang, R. (2024) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00713 · Cited by 82 · see citing works
Olausson, T., Gu, A., Lipkin, B., Zhang, C., Solar-Lezama, A., Tenenbaum, J., & Levy, R. (2023) · Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing · doi:10.18653/v1/2023.emnlp-main.313 · Cited by 57 · see citing works
“Second, Logic-LM employs a self-refinement strategy, which has shown promise across code generation and NLP tasks (Zhang et al., 2023b; Chen et al., 2023a; Peng et al., 2023; Madaan et al., 2023; Olausson et al., 2023) but which we do not consider here.”
MethodLLM-Based Agents for Tool Learning: A Survey
Xu, W., Huang, C., Gao, S., & Shang, S. (2025) · Data Science and Engineering · doi:10.1007/s41019-025-00296-9 · Cited by 69 · see citing works
“Similarly, Logic-lm [94] transforms described problems into first-order formal logic (FOL [7]).”
Pallagani, V., Muppasani, B. C., Roy, K., Fabiano, F., Loreggia, A., Murugesan, K., Srivastava, B., Rossi, F., Lior Horesh, C., & Sheth, A. (2024) · Proceedings of the International Conference on Automated Planning and Scheduling · doi:10.1609/icaps.v34i1.31503 · Cited by 62 · see citing works
“…and planning involves transforming natural language instructions into structured planning languages (Wong et al. 2023; Kelly et al. 2023; Yang 2023; Pan et al. 2023; Xie et al. 2023; Yang, Ishay, and Lee 2023; Lin et al. 2023c; Sakib and Sun 2023; Yang et al. 2023b; Parakh et al. 2023; Yang et al.…”
Large Language Models Can Learn Temporal Reasoning
Xiong, S., Payani, A., Kompella, R., & Fekri, F. (2024) · Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · doi:10.18653/v1/2024.acl-long.563 · Cited by 47 · see citing works
Nie, T., Sun, J., & Ma, W. (2025) · Artificial Intelligence for Transportation · doi:10.1016/j.ait.2025.100003 · Cited by 56 · see citing works
“Hybrid models that combine LLMs with symbolic solvers (Pan et al., 2023), constraint programming, or external simulation tools (Gao et al., 2024a) are emerging.”
A survey on knowledge-enhanced multimodal learning
Lymperaiou, M., & Stamou, G. B. (2024) · Artificial Intelligence Review · doi:10.1007/s10462-024-10825-z · Cited by 35 · see citing works
ArgMed-Agents: Explainable Clinical Decision Reasoning with LLM Disscusion via Argumentation Schemes
Hong, S., Xiao, L., Zhang, X., & Chen, J. (2024) · 2024 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) · doi:10.1109/bibm62325.2024.10822109 · Cited by 21 · see citing works
Machine Learning in FCAPS: Toward Enhanced Beyond 5G Network Management
Mekrache, A., Ksentini, A., & Verikoukis, C. V. (2024) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2024.3395414 · Cited by 19 · see citing works
A Survey of Reasoning with Foundation ModelsPreprint
Sun, J., Zheng, C., Xie, E., Liu, Z., Chu, R., Liu, J., Xu, J., Ding, M., Li, H., Geng, M., et al. (2023) · doi:10.31219/osf.io/ac4sp · Cited by 51 · see citing works
Self-citationBioPlanner: Automatic Evaluation of LLMs on Protocol Planning in Biology
O’Donoghue, O., Shtedritski, A., Ginger, J., Abboud, R., Ghareeb, A. E., & Rodriques, S. G. (2023) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/2023.emnlp-main.162 · Cited by 26 · see citing works
OpenHands: An Open Platform for AI Software Developers as Generalist Agents
Wang, X., Li, B., Song, Y., Xu, F. F., Tang, X., Zhuge, M., Pan, J., Song, Y., Li, B., Singh, J., et al. (2024) · arXiv · doi:10.48550/arxiv.2407.16741 · Cited by 24 · see citing works
Self-citationLogic Augmented Multi-Decision Fusion Framework for Stance Detection on Social Media
Zhang, B., Jun, M., Fu, X., & Dai, G. (2025) · Information Fusion · doi:10.1016/j.inffus.2025.103214 · Cited by 12 · see citing works
A Survey of Task Planning with Large Language Models
Zhai, W., Liao, J., Chen, Z., Su, B., & Zhao, X. (2025) · Intelligent Computing · doi:10.34133/icomputing.0124 · Cited by 16 · see citing works
Arithmetic Reasoning with LLM: Prolog Generation & Permutation
Yang, X., Chen, B., & Tam, Y.-C. (2024) · Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 2: Short Papers) · doi:10.18653/v1/2024.naacl-short.61 · Cited by 12 · see citing works
LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks
Kambhampati, S., Valmeekam, K., Guan, L., Verma, M., Stechly, K., Bhambri, S., Saldyt, L., & Murthy, A. (2024) · arXiv · doi:10.48550/arxiv.2402.01817 · Cited by 11 · see citing works
“Several efforts (e.g. Liu et al. (2023); Pan et al. (2023); Xie et al. (2023)) advocate using LLMs only as glorified translators–for converting reasoning problems embedded in textual format to symbolic representations, which are then pawed off to external classical symbolic solvers (with all their…”
BackgroundORFS-agent: Tool-Using Agents for Chip Design Optimization
Ghose, A., Kahng, A. B., Kundu, S., & Wang, Z. (2025) · ACM/IEEE Workshop on Machine Learning for CAD (MLCAD) · doi:10.1109/mlcad65511.2025.11189204 · Cited by 13 · see citing works
“Blending BO with symbolic reasoning [42] [52] yields targeted, adaptive flows.”
Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models
Liu, J., Huang, Z., Liu, Q., Ma, Z., Zhai, C., & Chen, E. (2025) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2025.3556367 · Cited by 11 · see citing works
“Nevertheless, behind these successes, numerous studies have indicated that the current LLMs are still prone to exhibit logical errors when solving problems [10], [11], [12], [13].”
ChatLogic: Integrating Logic Programming with Large Language Models for Multi-Step Reasoning
Wang, Z., Liu, J., Bao, Q., Rong, H., & Zhang, J. (2024) · 2024 International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn60899.2024.10650138 · Cited by 8 · see citing works
“Despite facing challenges in multi-step logical tasks involving contemporary information or complex logical sequences [9], emerging approaches like self-consistency [10] show promise in enhancing performance, particularly in areas such as arithmetic and common sense reasoning.”
BackgroundLoRP: LLM-based Logical Reasoning via Prolog
Di, Z., Zhang, C., Lv, H., Cui, L., & Liu, L. (2025) · Knowledge-Based Systems · doi:10.1016/j.knosys.2025.114140 · Cited by 11 · see citing works
DSPy-based neural-symbolic pipeline to enhance spatial reasoning in LLMs
Wang, R., & Sun, K. (2025) · Neural Networks · doi:10.1016/j.neunet.2025.108022 · Cited by 8 · see citing works
Design Patterns for Large Language Model Based Neuro-Symbolic Systems
de Boer, M., Smit, Q. T. S., van Bekkum, M. A., Meyer-Vitali, A., & Schmid, T. (2025) · Neurosymbolic Artificial Intelligence · doi:10.1177/29498732251377499 · Cited by 9 · see citing works
“Secondly, we test validity and usefulness of the Box-ology and our extensions in this field on example architectures and applications, such as ChatGPT, KnowGL, GENOME and Logic-LM.”
Tapia-Mandiola, S., & Araya, R. (2024) · AI · doi:10.3390/ai5040093 · Cited by 11 · see citing works
Advancing Few-Shot Named Entity Recognition with Large Language Model
Xiao, Y., Zou, J., & Yang, Q. (2025) · Applied Sciences · doi:10.3390/app15073838 · Cited by 7 · see citing works
An LLM-Enabled Multi-Agent Autonomous Mechatronics Design Framework
Wang, Z., Lo, F. P.-W., Chen, Q., Zhang, Y., Chen, L., Chen, X., Yu, Z., Thompson, A. J., Yeatman, E. M., & Lo, B. P. L. (2025) · IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw67362.2025.00404 · Cited by 7 · see citing works
Vakharia, P., Kufeldt, A., Meyers, M., Lane, I., & Gilpin, L. H. (2024) · Lecture Notes in Computer Science · doi:10.1007/978-3-031-71170-1_23 · Cited by 5 · see citing works
“Neither [11] nor [13] pose a viable approach in this current work, however, due to the complexity of questions expected for a KBQA system, and our subsequent interest in leveraging the generative power of an LLM to answer inputted queries.”
BackgroundMethodCausal Reasoning in Large Language Models using Causal Graph Retrieval Augmented Generation
Samarajeewa, C., Silva, D. D., Osipov, E., Alahakoon, D., & Manic, M. (2024) · Conference on Human System Interactions · doi:10.1109/hsi61632.2024.10613566 · Cited by 7 · see citing works
“In [18], Pan et al. propose an approach to improve logical reasoning capabilities by combining large language models with symbolic solvers.”
BackgroundGraph of Logic: Enhancing LLM Reasoning with Graphs and Symbolic Logic
Alotaibi, F., Kulkarni, A., & Zhou, D. (2024) · IEEE International Conference on Big Data (BigData) · doi:10.1109/bigdata62323.2024.10825450 · Cited by 5 · see citing works
Agile Logical Semantics for Natural Languages
Manca, V. (2024) · Information · doi:10.3390/info15010064 · Cited by 5 · see citing works
ToM-LM: Delegating Theory of Mind Reasoning to External Symbolic Executors in Large Language Models
Tang, W.-Z., & Belle, V. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-71170-1_20 · Cited by 5 · see citing works
A dataset for evaluating clinical research claims in large language models
Zhang, B., Bornet, A., Yazdani, A., Khlebnikov, P., Milutinovic, M., Rouhizadeh, H., Amini, P., & Teodoro, D. (2025) · Scientific Data · doi:10.1038/s41597-025-04417-x · Cited by 8 · see citing works
Li, Y., Fu, X., Verma, G., Buitelaar, P., & Liu, M. (2025) · arXiv · doi:10.48550/arxiv.2510.24476 · Cited by 4 · see citing works
“Contemporary research has increasingly explored the integration of symbolic reasoning [104, 145] with LLMs to improve the logical consistency and reliability of model reasoning processes.”
Schmidt, D. M., & Cimiano, P. (2025) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2024.1406857 · Cited by 5 · see citing works
“…tasks requiring a structured prediction, e.g., event extraction (Lu et al., 2021), syntactic and semantic parsing (Roy et al., 2024), symbolic expression generation like SMT formulas (Pan et al., 2023; Sun et al., 2023) or SQL query generation from text (Scholak et al., 2021; Lin et al., 2020).”
InfluentialLLM-Driven Knowledge Extraction in Temporal and Description Logics
Duranti, D., Giorgini, P., Mazzullo, A., Robol, M., & Roveri, M. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-77792-9_12 · Cited by 6 · see citing works
Safety and Trust in Artificial Intelligence with Abstract Interpretation
Singh, G., Laurel, J., Misailovíc, S., Banerjee, D., Singh, A., Xu, C., Ugare, S., & Zhang, H. (2025) · Foundations and Trends® in Programming Languages · doi:10.1561/2500000062 · Cited by 4 · see citing works
Dynamic knowledge correction via abductive for domain question answering
Zhou, Y., Huang, R., Lin, C., Liu, L., & Qin, Y. (2025) · Information Processing & Management · doi:10.1016/j.ipm.2025.104306 · Cited by 3 · see citing works
Final: Combining First-Order Logic With Natural Logic for Question Answering
Shi, J., Ding, X., Hui, S. C., Yan, Y., Zhao, H., Liu, T., & Qin, B. (2025) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2025.3551231 · Cited by 3 · see citing works
“Furthermore, some research efforts [63], [64], [65] leverage language models to convert natural language problems into symbolic formulations, which are then solved using deterministic symbolic solvers.”
Su, P., Xu, R., Wen-bin, W., et al. (2025) · Applied System Innovation · doi:10.3390/asi8060160 · Cited by 3 · see citing works
Prompt2DeModel: Declarative Neuro-Symbolic Modeling with Natural Language
Faghihi, H. R., Nafar, A., Uszok, A., Karimian, H. R., & Kordjamshidi, P. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-71170-1_25 · Cited by 3 · see citing works
Can Large Language Models Put 2 and 2 Together? Probing for Entailed Arithmetical Relationships
Panas, D., Seth, S., & Belle, V. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-71170-1_21 · Cited by 3 · see citing works
Towards Interpretable and Consistent Multi-Step Mathematical Reasoning in Large Language Models
Huang, X., Wang, Z., Liu, X., et al. (2025) · International Symposium on Artificial Intelligence and Intelligent Manufacturing (AIIM) · doi:10.1109/aiim67611.2025.11232978 · Cited by 3 · see citing works
“Wang et al. [1] combined SymPy with LLMs for algebraic manipulation and reasoning, while Yu et al. [2] fused chain-of-thought prompting with rule-based deduction.”
Giabbanelli, P. J., Beverley, J., Dávid, I., & Tolk, A. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5365069 · Cited by 3 · see citing works
SWE-Search: Enhancing Software Agents with Monte Carlo Tree Search and Iterative Refinement
Antoniades, A., Örwall, A., Zhang, K., Xie, Y., Goyal, A., & Wang, W. (2024) · arXiv · doi:10.48550/arxiv.2410.20285 · Cited by 3 · see citing works
“Search methods Various search approaches have been applied to Large Language Models (LLMs) to facilitate System 2 (Kahneman, 2011; Saha et al., 2024; Pan et al., 2023; Bounsi et al., 2024) thinking in non-linear reasoning structures.”
Self-citationEvidence from formal logical reasoning reveals that the language of thought is not natural language
Kean, H., Fung, A., Jaggers, P., Chen, J., Rule, J. S., Benn, Y., Tenenbaum, J. B., Piantadosi, S. T., Varley, R. A., & Fedorenko, E. (2026) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2520095123 · Cited by 2 · see citing works
Neuro-symbolic systems: a perspective of uncertainty management
Li, Z., Yao, Y., Ma, X., & lu, J. (2024) · Scientia Sinica Informationis · doi:10.1360/ssi-2024-0163 · Cited by 2 · see citing works
Semantic-aware query answering with Large Language Models
Atzeni, P., Baldazzi, T., Bellomarini, L., et al. (2025) · Data & Knowledge Engineering · doi:10.1016/j.datak.2025.102494 · Cited by 2 · see citing works
Kabir, I., Reza, M. A., & Billah, S. M. (2025) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra55743.2025.11128818 · Cited by 2 · see citing works
“LOGIC-LM [9] demonstrated the integration of large language models with symbolic solvers for enhanced logical reasoning. a) Components of FOL: FOL consists of predicates , functions , constants , variables , and quantifiers .”
Evaluating Theory of Mind and Internal Beliefs in LLM-Based Multi-agent Systems
Kostka, A., & Chudziak, J. (2026) · International Conference on Computational Collective Intelligence · doi:10.1007/978-3-032-09318-9_2 · Cited by 7 · see citing works
“…applications, like learned models of other agents’ goals and behaviors [17, 35, 19], more advanced integration of LLMs with symbolic reasoning beyond what is provided by ASP-based verification [23, 36, 28], and hybrid approaches to reasoning that leverage both neural and symbolic strengths [31].”
Fine-Tuned Large Language Models for Logical Translation: Reducing Hallucinations with Lang2Logic
Pan, M., Kodakandla, D., & Farooque, M. (2025) · International Symposium on Networks, Computers and Communications (ISNCC) · doi:10.1109/isncc66965.2025.11250432 · Cited by 2 · see citing works
“Recent works such as LogicLLaMA [6] and LOGIC-LM [7] have pioneered advancements in logical reasoning by fine-tuning LLMs for specialized tasks.”
Bridging Large Language Models and Logic Programming
Crocetti, V., & Dragoni, A. F. (2025) · 2025 IEEE International Conference on Metrology for eXtended Reality, Artificial Intelligence and Neural Engineering (MetroXRAINE) · doi:10.1109/metroxraine66377.2025.11340308
“A highly relevant framework, Logic-LM, was recently proposed by Pan et al. (2023) [9].”
DCoL-A: Agentic dual chain of thinking helps LLMs pretend logic solvers
Chen, M., Wu, L.-I., Liu, R., Chang, X., Xue, J., & Li, G. (2026) · Journal of Systems Architecture · doi:10.1016/j.sysarc.2026.103780 · Cited by 2 · see citing works
OrLog: Resolving Complex Queries with LLMs and Probabilistic Reasoning
Hoveyda, M., Piepenbrock, J., de Vries, A. P., et al. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-21289-4_7 · Cited by 2 · see citing works
Modeling Patterns for Neural-Symbolic Reasoning Using Energy-based Models
Dickens, C., Pryor, C., & Getoor, L. C. (2024) · Proceedings of the AAAI Symposium Series · doi:10.1609/aaaiss.v3i1.31187 · Cited by 2 · see citing works
“We compare our predictive performance with the baseline and models presented in Pan et al. (2023) on gpt-3.”
MethodResultLarge Language Models for Logical Fallacy Detection
Teo, N., Huang, D., Cambria, E., & Wang, Z. (2025) · Lecture notes in computer science · doi:10.1007/978-981-96-8197-6_29 · Cited by 2 · see citing works
CSCE: Boosting LLM Reasoning by Simultaneous Enhancing of Causal Significance and Consistency
Wang, K., Zhang, X., Lyu, J., Hu, T., & Ma, H. (2025) · IEEE International Conference on Multimedia and Expo (ICME) · doi:10.1109/icme59968.2025.11209798 · Cited by 2 · see citing works
“Large language models (LLMs) have shown promising potential in solving structured logical reasoning problems [1]–[3], unstructured mathematical reasoning problems [4]– [6] and downstream tasks such as autonomous driving [7], [8].”
Benchmarking Graph Construction by Large Language Models for Coherence-Driven Inference
Huntsman, S., & Thomas, J. (2025) · IEEE ... International Conference on Data Mining workshops · doi:10.1109/icdmw69685.2025.00116 · Cited by 2 · see citing works
“However, the computation of a transformer with L layers on a prompt of length n can be performed using O ( L log n ) bits of memory under common assumptions.”
Can Language Models Pretend Solvers? Logic Code Simulation with LLMs
Chen, M., Li, G., Wu, L.-I., Liu, R., Su, Y., Chang, X., & Xue, J. (2024) · Lecture notes in computer science · doi:10.1007/978-981-96-0602-3_6 · Cited by 3 · see citing works
Case-Based Reasoning in Generative Agents: Review and Prospect
Zhan, H., Wu, Y., Ding, J. L., Xu, B., Yang, L., & Lin, H. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-96559-3_12 · Cited by 1 · see citing works
On the Relevance of Logic for Artificial Intelligence, and the Promise of Neurosymbolic Learning
Belle, V. (2025) · Neurosymbolic Artificial Intelligence · doi:10.1177/29498732251339951 · Cited by 1 · see citing works
“2 More generally, recent approaches seek to incorporate logical solvers as oracles (Persia & Ozaki, 2022) that can validate or disprove the predictions of neural architectures, including LLMs (Miceli-Barone et al., 2023; Pan et al., 2023; Panas et al., 2024; Zhang et al., 2023).”
He, R., Zhang, Y., Zhang, M., et al. (2025) · IEEE/ACM International Conference on Automated Software Engineering Workshops (ASEW) · doi:10.1109/asew67777.2025.00040 · Cited by 1 · see citing works
“Recent work has shown that large language models can generate Boolean logic, propositional logic, and even more expressive systems like predicate logic (first-order logic) [8], [9].”
Trustworthy Machine Learning in the Era of Foundation Models
Han, B. (2025) · IEEE Intelligent Systems · doi:10.1109/mis.2025.3621938 · Cited by 1 · see citing works
From Legal Text to Tech Specs: Generative AI’s Interpretation of Consent in Privacy Law
Kesari, A., Breaux, T. D., Santos, S., Norton, T. B., & Singhal, A. (2025) · International Conference on Artificial Intelligence and Law · doi:10.1145/3769126.3769241 · Cited by 1 · see citing works
“Formal syntax constrains problem spaces, yielding precise and computationally tractable solutions compared to natural language reasoning [21, 23].”
He, Y., Liu, J., Wen, W., Guo, Y., Chen, H., Ma, Y., Ke, W., & Wang, P. (2026) · IEEE Transactions on Emerging Topics in Computational Intelligence · doi:10.1109/tetci.2026.3654446 · Cited by 1 · see citing works
“Meanwhile,inspiredbypreviousworks[46],[47],we constructacandidatedemonstrationpoolof1,000machine-translatedexamplesperdataset,followingaschema-guidedFOL translationframeworkthatensuressyntacticvalidityandlogi-calconsistency.”
MAPPING RESEARCH ON GENERATIVE AI AND CRITICAL THINKING IN EDUCATION
Idrus, N. M., Ghani, N. A. A., & Rahman, H. A. (2025) · International Journal of Education Psychology and Counseling · doi:10.35631/ijepc.1061067 · Cited by 1 · see citing works
DL-ReasonSuite: A Benchmark for Evaluating Description Logic Reasoning in Large Language Models
Olucoglu, M., & Bursa, O. (2026) · Applied Sciences · doi:10.3390/app16041821 · Cited by 1 · see citing works
Hersche, M., Camposampiero, G., Wattenhofer, R. P., Sebastian, A., & Rahimi, A. (2026) · Neurosymbolic Artificial Intelligence · doi:10.1177/29498732261419316 · Cited by 1 · see citing works
Algebraic Semantics for Interpretable Reasoning in Large Language Models
Liu, P., & Li, Y. (2026) · Information Sciences · doi:10.1016/j.ins.2026.123383 · Cited by 1 · see citing works
Neuro-symbolic NLP: taxonomy, assessment, and directions
Chatzikyriakidis, S., & Lappin, S. (2026) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2026.1797587 · Cited by 1 · see citing works
“Logic-LM (Pan et al., 2023) maps natural language to FOL or SAT constraints for solver refinement, boosting performance by 39.2% over standard prompting.”
InfluentialVeriTrans: Fine-Tuned LLM-Assisted NL→PL Translation via a Deterministic Neuro-symbolic Pipeline
Liu, X. M., Kodakandla, D., Srivastva, K., et al. (2026) · doi:10.1145/3805760.3814906 · Cited by 1 · see citing works
neucsestu@CC-MMD 2026: SC-MACA via Multi-Agent Cultural Reasoning for Misogyny Detection
Zhang, S., & Li, Z. (2026) · INTERNATIONAL CONFERENCE ON MULTIMODAL INTERACTION · doi:10.1145/3776574.3832462 · Cited by 1 · see citing works
“Inspired by logical prompting and multi-model refinement [2, 7, 9, 15], the pipeline keeps its intermediate rationales structured enough for downstream learning.”
Trustworthiness Evaluation of Large Language Models
Chen, P., & Liu, S. (2025) · Springer eBooks · doi:10.1007/978-3-031-76770-8_12 · Cited by 2 · see citing works
Rule-Based Moral Principles for Explaining Uncertainty in Natural Language Generation
Atf, Z., & Lewis, P. R. (2025) · IEEE International Conference on Collaborative Advances in Software and Computing (CASCON) · doi:10.1109/cascon66301.2025.00018 · Cited by 1 · see citing works
Giabbanelli, P. J., Beverley, J. R., Dávid, I., & Tolk, A. (2025) · Winter Simulation Conference · doi:10.1109/wsc68292.2025.11338852 · Cited by 1 · see citing works
“However, as shown by Pan et al. (2023) through their experiments with 1 700 code samples in C, C++, Go, Java, and Python, LLMs are not yet reliable enough for code translation, with the reported proportion of correct translations ranging between 2.1% and 47.3%.”
InfluentialLimitations of and Lessons from the Learning of Large Language ModelsPreprint
Oldenburg, R. (2023) · Qeios · doi:10.32388/9fh6ad · Cited by 1 · see citing works
Xu, F., Zhou, T., Nguyen, T., Bao, H., Lin, C., & Du, J. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4805664 · Cited by 1 · see citing works
Not Explainable but Verifiable
Burgess, P., & Shareghi, E. (2025) · doi:10.1093/9780198945215.003.0093 · Cited by 1 · see citing works
Ge, Y., Romeo, S., Cai, J., Shu, R., Sunkara, M., Benajiba, Y., & Zhang, Y. (2025) · arXiv · doi:10.48550/arxiv.2502.01630 · Cited by 3 · see citing works
“These results align with recent research that combines LLMs with symbolic reasoners for various reasoning tasks (Olausson et al., 2023; Pan et al., 2023).”
InfluentialReason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming
Chen, Z., & Ma, M. (2026) · arXiv · doi:10.48550/arxiv.2607.23019
“Logic-LM Pan et al. [2023] translates natural-language problems into formal logic and delegates inference to an external solver.”
InfluentialAlviano, M., Capalbo, M., Gottlob, G., Grillo, L., Kareem, I., Lo Scudo, F., Piccolo, S. A., & Rodriguez Reiners, L. A. (2026) · Journal of Artificial Intelligence Research · doi:10.1613/jair.1.21678
“…fine-tuning of specialized LLMs to support diverse logic tasks (Coppolillo et al. 2024); and (iii) solver-in-the-loop methodologies that use feedback from the solver either to refine the extracted ASP code on the fly (Pan et al. 2023) or to guide the LLM fine-tuning stage (Schrader et al. 2026).”
ADVENT: LLM-Driven Automatic Predicate Invention for ILP
Yu, T., Huang, P.-C., Hsu, C., Ku, C.-T., & Kang, Y. (2026) · 2026 IEEE International Conference on Information Reuse and Integration for Data Science (IRI) · doi:10.1109/iri69576.2026.00025
Legally-Guided Automated Decision-Making System Using Language Model Agents for Autonomous Driving
Wang, Y., Barta, D., Hesse, J., Buchwald, P., & Paschke, A. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-72407-7_17
A dataset for evaluating clinical research claims in large language modelsPreprint
Zhang, B., Yazdani, A., Bornet, A., Khlebnikov, P., Milutinovic, M., Rouhizadeh, H., Amini, P., & Teodoro, D. (2024) · medRxiv · doi:10.1101/2024.10.08.24315103
Identifying Logical Patterns in Text for Reasoning
Armary, P., Vaigh, C. B. E., Spicher, A., et al. (2024) · Proceedings - International Conference on Tools with Artificial Intelligence, TAI · doi:10.1109/ictai62512.2024.00122
“The two best models are Logic-LM [13], which is based on GPT-4 (1.7T parameters) and Mistral (7B parameters).”
InfluentialKinder, L., & Käfer, T. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-78955-7_21
Beyond Training Data: Zero-Shot Mathematical Problem Solving with Large Language Models
Parmar, S. H., & Goriya, M. (2024) · IEEE Conference on Engineering Informatics (ICEI) · doi:10.1109/icei64305.2024.10912380
Zhang, H., Zhu, X., Wang, X., Song, Y., Gu, H., & Ma, L. (2025) · IEEE International Conference on Mobile Data Management (MDM) · doi:10.1109/mdm65600.2025.00024
Self-citationNARS-GPT: An Integrated Reasoning System for Natural Language Interactions
Isaev, P., & Hammer, P. (2025) · Lecture notes in networks and systems · doi:10.1007/978-3-031-99965-9_25 · Cited by 1 · see citing works
A Little Help Goes a Long Way: Tutoring LLMs in Solving Competitive Programming Through Hints
Zhang, Y., Dong, W., Liu, J., Wang, S., Wang, D., Ma, T., Li, Y., & Yang, K. (2025) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2025.3614204
“While prompt-based generation using powerful LLMs such as GPT-4o can produce plausible results, prior work [17], [18] shows that such models often require reliable external guidance to avoid compounding early-stage errors.”
Formal Reasoning for Intelligent QA Systems: A Case Study in the Educational Domain
Tuan, B., Nguyen, A. D., Thai, P., Hua, M., Ngan Pham, L. N., Ngan Pham, T. B., Le, D. N. H., Nguyen, L. S. T., Tran, T.-T., Bui, T., et al. (2025) · Proceedings of the 2nd ACM Workshop in AI-powered Question & Answering Systems · doi:10.1145/3746274.3760392 · Cited by 2 · see citing works
Le, T. D., Thai, P. K., Nguyen, S., Hua, M. T., Pham, N., Bui, T., Quan, T., & Bui, T. V. (2025) · Lecture notes in computer science · doi:10.1007/978-3-032-09318-9_14 · Cited by 1 · see citing works
Zhang, X., Zhang, P., Liu, Q., & Zhao, F. (2025) · Communications in computer and information science · doi:10.1007/978-981-95-4990-0_9
Weng, T.-T., Sun, J.-T., Fu, Z.-X., & Lee, C.-H. (2025) · Communications in computer and information science · doi:10.1007/978-3-032-09945-7_14
Minimal reduct for propositional circumscription
Xie, Z.-T., Wang, Y., Yang, L., & Feng, R. (2025) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2025.1614894
“Within this trend, classical logic techniques are being revisited as essential tools to provide strong guarantees and structured reasoning capabilities that purely statistical methods often lack (Ryu et al., 2025; Ye et al., 2023; Pan et al., 2023; Olausson et al., 2023; Callewaert et al., 2025).”
Three Tiers of Computation in Transformers and in Brain Architectures
Graham, E., & Granger, R. (2026) · ACM Transactions on Intelligent Systems and Technology · doi:10.1145/3844612
FoVer: First-Order Logic Verification for Natural Language Reasoning
Pei, Y., Du, Y., & Jin, X. (2025) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl.a.41
Zheng, X., Li, N., Luan, X., Wang, K., Shi, L., Sun, M., & Wang, H. (2026) · ACM/IEEE International Conference on Software Engineering: Companion Proceedings (ICSE-Companion) · doi:10.1145/3744916.3787820 · Cited by 2 · see citing works
“18) If something likes the cat then it visits the dog.”
- Authors
- Pan, L., Albalak, A., Wang, X., & Wang, W. Y.
- Affiliations
- University of California, Santa Barbara (US)
- Venue
- arXiv
- Publisher
- arXiv
- Published
- 2023
- Pages
- 3806-3824
- arXiv
- 2305.12295
- OpenAlex
- W4389519818
- Semantic Scholar
- 9e9e4df2996bac794c4f04cb887df3e553bae4fd
- Cited by
- 144
- References
- 56
- Citations by year
- 2026: 59 · 2025: 54 · 2024: 25 · 2023: 6
- FWCI
- 25.82
- Type
- conference paper
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- arXiv (Cornell University) (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- National Science Foundation (2048122)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
- Physical Sciences › Computer Science › Artificial Intelligence › Natural Language Processing Techniques
- Keywords
- large language models, symbolic solvers, logical reasoning, self-refinement, chain-of-thought prompting, proof writing, first-order logic, logical deduction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-19.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-19.
Cited sources are checked by gpt-6-sol.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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