Nonmonotonic Reasoning

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Nonmonotonic reasoning models everyday and rule-based inference where defaults can be overridden—for example, birds normally fly, unless specific information says otherwise. Major approaches include preferential and ranking semantics such as KLM-style reasoning and rational or lexicographic closure, as well as answer set programming, stable models, well-founded semantics, and cumulative logics. These methods support applications ranging from knowledge bases and defeasible obligations to abduction, causal models, and reasoning with multiple viewpoints. A central challenge is balancing formal guarantees and tractable inference with reliable behavior in complex settings, including whether language models can consistently follow specified negation and exception semantics.

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17 papers0 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Not What You Meant: Can LLMs Follow a Specified Negation Semantics?
Sep 23, 2026Qiming Bao, Agnieszka Mensfelt, Michael J. Witbrock +1Nonmonotonic Reasoning Reasoning Consistency in Language Models
University of Auckland, New Zealand · Royal Holloway, University of London, United Kingdom
Stratified Negation in RDF Rules: A Correct Approach (Extended Version)
Jul 30, 2026Nils Küchenmeister, Alex Ivliev, Dörthe Arndt +1Nonmonotonic Reasoning Knowledge Representation
Knowledge-Based Systems Group, TU Dresden, Dresden, Germany · Computational Logic Group, TU Dresden / ScaDS.AI, Dresden/Leipzig, Germany
Hybrid MKNF with Classical Negation in the Rule Component
Jul 23, 2026Arun Raveendran Nair Sheela, Christophe Rey, Florence De GranceyLogical Reasoning Symbolic Reasoning
Université Clermont Auvergne, LIMOS Laboratory, Thales · Université Clermont Auvergne, LIMOS · France +3
Representative Sets in Propositional Abduction
Jul 23, 2026Johannes Schmidt, Mohamed Maizia, Victor Lagerkvist +1Abductive Reasoning Nonmonotonic Reasoning
Jönköping University · Jönköping University, Linköping University · Linköping University
DeFAb: A Dataset for Grounded Scientific Discovery through Defeasible Abduction
Jun 17, 2026Patrick Cooper, Avyay Sadhu, Alvaro VelasquezSymbolic Reasoning LLM Evaluation
University of Colorado Boulder
Standpoint Logics with Defeasible Beliefs
Jun 7, 2026Nicholas Leisegang, Thomas Meyer, Sebastian RudolphLogical Reasoning Nonmonotonic Reasoning
University of Cape Town and CAIR, South Africa · Technische Universität Dresden, Dresden, Germany · ScaDS.AI – Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig, Germany
Towards Non-Monotonic Entailment in Propositional Defeasible Standpoint Logic
Jun 2, 2026Nicholas Leisegang, Thomas Meyer, Ivan VarzniczakLogical Reasoning Nonmonotonic Reasoning
University of Cape Town and CAIR, South Africa · 2Université Sorbonne Paris Nord, Inserm, Sorbonne Université, Limics, 93017 Bobigny, France · 3ISTI-CNR, Pisa, Italy
ZX-Calculus:Trace-Indexed Dependent Types and Epistemic Semantics
Jun 2, 2026Peng ChenBelief Revision Logical Reasoning
School of Information Science, Beijing Language and Culture University Beijing 100081
On the Complexity of Entailment for Cumulative Propositional Dependence Logics
May 20, 2026Kai Sauerwald, Juha Kontinen, Arne MeierLogical Reasoning Nonmonotonic Reasoning
FernUniversität in Hagen, Hagen, Germany · University of Helsinki, Helsinki, Finland · Leibniz Universität Hannover, Hannover, Germany
Weighted Rules under the Stable Model Semantics
May 10, 2026Joohyung Lee, Yi WangLogic Programming Nonmonotonic Reasoning
School of Computing, Informatics and Decision Systems Engineering Arizona State University, Tempe, USA
LLMs as ASP Programmers: Self-Correction Enables Task-Agnostic Nonmonotonic Reasoning
Apr 30, 2026Adam Ishay, Joohyung LeeLLM Self-Correction Logical Reasoning
Arizona State University · Samsung Research
Defeasible Conditional Obligation in a Two-tiered Preference-based Semantics (Extended Version)
Apr 28, 2026Xavier ParentLogical Reasoning Nonmonotonic Reasoning
Institute of Logic and Computation, TU Wien, Vienna, Austria
Plausible Reasoning and First-Order Plausible Logic
Apr 21, 2026David BillingtonLogical Reasoning Nonmonotonic Reasoning
School of Information and Communication Technology, Nathan campus, Griffith University, Brisbane, Queensland 4111, Australia.
Broadening the Applicability of Conditional Syntax Splitting for Reasoning from Conditional Belief Bases
Apr 14, 2026Lars-Phillip Spiegel, Jonas Haldimann, Jesse Heyninck +2Inductive Inference Nonmonotonic Reasoning
FernUniversität in Hagen, Hagen, Germany · University of Cape Town and CAIR, Cape Town, South Africa · TU Wien, Vienna, Austria +2
Non-monotonic causal discovery with Kolmogorov-Arnold Fuzzy Cognitive Maps
Apr 6, 2026Jose L. SalmeronFuzzy Cognitive Maps Fuzzy Logic
School of Engineering, CUNEF Universidad, Madrid, Spain
NM-DEKL $^3_\infty$ : A Three-Layer Non-Monotone Evolving Dependent Type Logic
Mar 2, 2026Peng ChenNonmonotonic Reasoning Formal Verification
Representation Theorems for Cumulative Propositional Dependence Logics
Feb 24, 2026Juha Kontinen, Arne Meier, Kai SauerwaldLogical Reasoning Nonmonotonic Reasoning
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland · Theoretical Computer Science, Leibniz University Hannover, Hannover, Germany · Faculty of Mathematics and Computer Science, FernUniversität in Hagen, Hagen, Germany

Sep 23, 2026J/K move · Enter open · S save

Not What You Meant: Can LLMs Follow a Specified Negation Semantics?

Qiming Bao, Agnieszka Mensfelt, Michael J. Witbrock, Kostas Stathis

University of Auckland, New Zealand · Royal Holloway, University of London, United Kingdom

Nonmonotonic Reasoning Reasoning Consistency in Language Models LLM Evaluation Logic Programming

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Negation does not carry a uniform interpretation across domains. In legal, regulatory, and medical reasoning, the intended interpretation depends on the reading in force -- open- versus closed-world, two- versus three-valued, and credulous versus skeptical. We study which reading of negation large language models adopt by default and whether they can override that preference when a different reading is explicitly specified. To this end, we introduce NAFBench, a procedural generator of solver-certified instances spanning four semantic viewpoints: SLDNF, well-founded semantics (WFS), and credulous and skeptical reasoning under stable-model semantics. The generator emits ground normal logic programs with controlled depth, width, and cycle structure. Each program is solved under all four viewpoints using SWI-Prolog, a well-founded semantics solver, and clingo, yielding up to four divergent labels. The programs are then verbalized into natural language under multiple framings and rule orderings that leave the answer invariant. The results expose a consistent gap. Across open-source models, following a specified negation semantics remains unsolved: the strongest models score 59--74% across the four semantic viewpoints, while the weakest score 31--67%. All models are order-sensitive on more than half of logically identical rule shufflings, while the two weaker models frequently overcommit on well-founded "undefined." Two frontier models reach 100% on the main fixed-complexity evaluation set, and a third, o4-mini, is near-perfect, falling only to 81% on well-founded "undefined." Delegating reasoning to a solver, fine-tuning on certified traces, or forcing an explicit three-valued verdict each partly closes the gap.