Logical Reasoning

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Logical reasoning studies how conclusions follow from facts and rules, including deduction, abduction, induction, and reasoning with uncertainty, exceptions, time, or conflicting information. Classical approaches use formal languages, theorem provers, SAT/SMT solvers, Datalog, and description logics; neuro-symbolic systems combine these tools with learned perception or language models. Current work evaluates systems on first-order logic, syllogisms, rule-based decisions, and compositional puzzles, often using solver-verified benchmarks and proof traces. A central challenge is that correct answers can hide invalid or shortcut reasoning, while systems that verify steps still struggle with long, deep, unfamiliar, or alternative reasoning paths.

Latest papers

163 papers10 papers in the last four weeks, down 17% on the four weeks before. 0.1% of all new papers.

Non-Zero Radius: The Missing Component of Neural Networks
Oct 29, 2026Tiansi Dong, Mateja Jamnik, Pietro LiòLogical Reasoning Neuro-Symbolic Reasoning
Computer Lab, The University of Cambridge · The Alan Turing Institute
Deogen: Automatic Benchmark Generation for Reasoning over Policies
Oct 28, 2026Sam Kouteili, William Liang, Keeran Murray +4Synthetic Benchmark Generation Language Model Reasoning Evaluation
Yale University · Leibniz AI, Inc. · Yale Law School
Query-Driven Learning for Lifted Reasoning
Oct 26, 2026Luise Ge, Brendan JubaLogical Reasoning Symbolic Reasoning
Washington University in St. Louis
P(Yes): 15 $\times$ Improvements via Test-Time Scaling of Decision Models
Oct 18, 2026Lev StamblerLLM Decision-Making Test-Time Scaling
Tear Labs · University of Maryland, College Park
Selective Reasoning for Typed Decision Models: When to Start, Read, and Stop
Oct 14, 2026Bin Zheng, Zheng ChenEfficient Language Model Reasoning LLM Decision-Making
University of Electronic Science and Technology of China
Are AI Decision Models Biased? A Case Study of Jev
Oct 14, 2026Ilaria Imperatrice, Taisia Kameneva, Adam Eric Greenberg +1Cognitive Bias in Language Models LLM Decision-Making
Bocconi University
UZHCL_for_the_win at Touche: Encoder Fine-Tuning, Synthetic Augmentation, and an Underpowered Encoder-LLM Comparison
Oct 12, 2026Stylianos PsychiasComputational Argumentation Logical Reasoning
University of Zurich, Zurich, Switzerland
Knowledge transfer between simple discrete worlds
Oct 10, 2026Silvère Gangloff, Jan HulaLogical Reasoning Compositional Generalization
University of Ostrava
LASER: Defeasible Certificate Search for Long-Range Protocol Dependencies
Oct 10, 2026Zihan Tang, Huibiao ZhuEvidence Retrieval Formal Verification
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China
Mathematical Proof Assistants for Teaching Logic: The LogiKEy Methodology
Oct 6, 2026Christoph Benzmüller, David Fuenmayor, Luca PasettoLogical Reasoning Interactive Theorem Proving
Otto-Friedrich-Universität Bamberg, Germany · Freie Universität Berlin, Germany · University of Luxembourg, Luxembourg
A Simple Doxastic Deontic Logic for Norm-Guided Decision Making
Sep 30, 2026Thorsten Engesser, Agata CiabattoniLogical Reasoning Constrained Optimization
TU Wien
Learning to Prove, Not Just to Answer: Reinforcement Learning from Formal Verification for Natural-Language Logical Reasoning
Sep 29, 2026Qili Zhang, Qianren Mao, Hanze Cai +11Logical Reasoning RL for Language Model Reasoning
Zhongguancun Laboratory · Beihang University · Nanyang Technological University +1
A decision-support system applied to Law: Reasoning and explainability of the decision
Sep 28, 2026Jeremy Bouche-Pillon, Pascale Zarat{é}, Yannick Chevalier +1Logical Reasoning Explainable Artificial Intelligence
IRIT, IRIT-MELODI, IRIT-ADRIA, IRIT-LILaC · IRIT, UT Capitole, IRIT-ADRIA · IRIT-MELODI, IRIT, CNRS
Explaining Textual Entailment with Lexical Entailments: Using LLMs to Supply Lexical Relations for Formal Proofs
Sep 26, 2026Jorryt de Jong, Stefan Moraca, Ettore Cesari +1LLM Reasoning Natural Language Inference
Utrecht University, the Netherlands · Institute for Language Sciences, Utrecht University, the Netherlands
What Do Current Systematic Generalization Tasks Miss? A Reasoning-Centered Analysis
Sep 16, 2026Chengwen Qi, Deheng Ye, Yatao BianLogical Reasoning Inductive Inference
National University of Singapore · Nanyang Technological University
Visual Compliance via Executable Safety Rule Entailment
Sep 16, 2026Jisoo Kim, TaeYoon Kwack, Jinwoo Jang +1Logical Reasoning LLM Guardrails
Sungkyunkwan University
Autoformalizing Argumentative Material Inferences
Sep 15, 2026Xin Quan, Reto Gubelmann, André FreitasLogical Reasoning Interactive Theorem Proving
1Idiap Research Institute, Switzerland · University of Zurich, Switzerland · Department of Computer Science, University of Manchester, UK
Legislating World-Model-Based Planning with Legal Reasoning
Sep 14, 2026Dylan Waldner, Yiannis Kantaros, Guido Governatori +2Logical Reasoning Robot Task Planning
Cognizant AI Lab, USA · Department of Electrical & Systems Engineering, Washington University, USA · School of Engineering and Technology, Central Queensland University, Australia +1
Warrant Theory
Sep 10, 2026Khashayar IraniLogical Reasoning
Birkbeck College, University of London
Three Types of Negation of Triple and its Elements and an Extension of Triple
Sep 8, 2026Zhenghua PanLogical Reasoning Knowledge Representation
School of Mathematics and Data Science, Jiangnan University, Wuxi 214122, China
Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation
Sep 7, 2026Zhenghua PanLogical Reasoning Counterfactual Reasoning
School of Science, Institute of Mathematics and Physics, Jiangnan University, Wuxi 214122, China
DODR: Deterministic Operator-Driven Reasoning in Latent Space
Sep 4, 2026Weicai HuangLogical Reasoning Inductive Inference
Beijing MQPat Technologies, Co., Ltd.
When Decodability Is Not Enough: Logical Validity Representations, Behavioral Dissociation, and Causal Tests in Language Models
Sep 2, 2026Smitha Muthya Sudheendra, Jaideep SrivastavaLogical Reasoning Representation Probing
University of Minnesota, Twin Cities
Do General NLP Embeddings Capture Ontological Reasoning?
Aug 31, 2026Hamed Babaei Giglou, Jennifer D'Souza, Sören AuerLogical Reasoning Text Embedding Evaluation
TIB Leibniz Information Centre for Science and Technology · Hannover, Lower Saxony, Germany · L3S Research Center, Leibniz University of Hannover
Beyond Surface Forms: Symbolic Edits as a Test for Logical Reasoning with LLMs
Aug 31, 2026Ramya Keerthy Thatikonda, Wray Buntine, Ehsan ShareghiLogical Reasoning LLM Evaluation
Department of Data Science & AI, Monash University · ∃Department of Computer Science, University College London
Evidential-Based Higher-Order Set Argumentation Framework
Aug 28, 2026Shuai TangComputational Argumentation Logical Reasoning
Constrained Entity Selection under Partial Knowledge for LLM-Based Knowledge Graph QA
Aug 25, 2026Emanuel KitzelmannKnowledge Graph Question Answering LLM Answer Verification
Brandenburg University of Applied Sciences, Brandenburg a.d.H., Germany
Improving O-RADS Risk Stratification from Ultrasound Reports: A Comparative Evaluation of Hybrid versus End-to-End LLM Reasoning Strategies
Aug 24, 2026Xiaotong Tan, Chunli Qiu, Xin Liu +11Medical LLMs Clinical Decision Support
National-Regional Key Technology Engineering Laboratory for Medical Ultrasound, Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, School of Biomedical Engineering, Shenzhen University Medical School, Shenzhen University, Shenzhen 518055, China · Marshall Laboratory of Biomedical Engineering, Shenzhen University, Shenzhen 518055, China · Department of Ultrasound, Qilu Hospital of Shandong University, Jinan 250012, China +9
Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits
Aug 18, 2026Olga Mashkova, Asaad Mohammedsaleh, Fernando Zhapa-Camacho +1Neurosymbolic Learning Logical Reasoning
Computer Science Program, Computer, Electrical, and Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
Structure-Internalized Rule Language Model for Faithful Knowledge Graph Reasoning
Aug 18, 2026Xingrui Zhuo, Jiapu Wang, Manzong Huang +2LLM Reasoning with Graphs Logical Reasoning
Key Laboratory of Knowledge Engineering with Big Data (Hefei University of Technology), Ministry of Education, China · School of Computer Science and Information Engineering, Hefei University of Technology, China · Nanjing University of Science and Technology, China

Oct 29, 2026J/K move · Enter open · S save

Non-Zero Radius: The Missing Component of Neural Networks

Tiansi Dong, Mateja Jamnik, Pietro Liò

Computer Lab, The University of Cambridge · The Alan Turing Institute

Logical Reasoning Neuro-Symbolic Reasoning Neural Representation Geometry Hyperspherical Representation Learning

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Inspired by the analogy between the all-or-none activation of biological neurons and the true-false of logic circuits, McCulloch and Pitts proposed a mathematical model of the biological neuron in 1943 with the aim of simulating logical reasoning. Although Norbert Wiener considered the model overly simplistic at the time, it later became a building block of modern neural networks, including large language models. Despite their remarkable empirical success, however, conventional neural networks remain largely black-box systems and struggle with reliable symbolic reasoning. Viewing vectors as spheres of zero radius, we relax the zero-radius constraint and represent concepts as spheres with non-zero radii. We argue that sphere-based representations can capture additional features of biological cognition, including representing spatial concepts as regions and reasoning through model construction and inspection. Building on sphere embeddings, we introduce Sphere Neural Networks (SphNNs), which use a transition map to achieve symbolic-level Aristotelian syllogistic reasoning without training data, thereby taking an initial step toward the original goal of McCulloch and Pitts. We suggest that the zero-radius constraint may reflect an aspect of the oversimplification identified by Wiener and may limit conventional neural networks' capacity for symbolic-level logical reasoning.