Logic Programming

Follow this topic Ask about this topic

Momentum

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

Jul 13Week of Sep 28

Latest papers 29

Sep 17, 2026cs.AI

Structured Four-Stage Legal Translation: From Natural-Language Traffic Rules to PROLOG

Traffic regulations are written for human interpretation and therefore rely on shared background knowledge and flexible phrasing, which inherently introduce ambiguity, context dependence, and semantic underspecification. These linguistic characteristics conflict with the precision required by computational reasoning engines such as Prolog, which demand explicit logical structure. This study evaluates two baseline translation approaches, Natural Language to Prolog (

NL\rightarrow Prolog

) and Logical English to Prolog (

LE\rightarrow Prolog

), and introduces a new reasoning-guided translation framework called Structured Four-Stage Legal Translation (

S4L\rightarrow Prolog

). The proposed S4L framework performs semantic role extraction, scene completion, logical mapping, and Prolog rule generation within a single guided prompt, enabling direct translation of raw traffic rules into executable logic without human intervention. A benchmark consisting of twenty real-world traffic rules was used to evaluate each approach in terms of syntactic validity, semantic correctness, and logical completeness.

S4L\rightarrow Prolog

achieves the highest accuracy, correctly formalizing 75 percent of the rules, while

NL\rightarrow Prolog

reaches 60 percent and

LE\rightarrow Prolog

reaches 55 percent. Qualitative analysis further shows that S4L captures implicit causal relations, deontic modality, and exception structure more reliably than the baselines. These results demonstrate that structured reasoning prompts can substantially improve the reliability of natural-language-to-logic translation for legal and safety-critical applications.

May Myo Zin, Wachara Fungwacharakorn, Ken Satoh +1

Center for Juris-Informatics, ROIS-DS, Tokyo, Japan

Logic Programming Legal NLP Legal Reasoning

Aug 13, 2026cs.AI

Foundations of MT-PDCL: Measure-Theoretic Probabilistic Definite Clause Logic

Standard probabilistic logic programming frameworks typically rely on grounding logic programs into discrete propositional representations. This operational requirement restricts exact inference to finite domains and discrete probability distributions. In this paper, we introduce Measure-Theoretic Probabilistic Definite Clause Logic (MT-PDCL), a generalized foundational framework that eliminates this finite-domain restriction. By explicitly defining stochastic variables over bounded index domains and equipping the interpretation space with standard Borel

σ

-algebras, MT-PDCL allows logical variables to operate natively over continuous measurable spaces. Building on Continuous Distribution Semantics, MT-PDCL models probabilistic rules as mutually independent causal events. However, rather than aggregating these derivations via finite boolean circuits, declarative entailment is formally defined through exact Lebesgue integration over the continuous measure space. We introduce a continuous immediate consequence operator that unifies the integration of continuous prior distributions with the evaluation of exact continuous observations. We demonstrate that this approach replaces the combinatorial bottleneck of discrete grounding with exact, algebraic, and structurally differentiable inference. While this transition trades discrete combinatorics for the geometric curse of dimensionality, it achieves the expressive power of continuous probabilistic models while preserving the pure declarative syntax of definite clause logic.

Costin Bădică, Amelia Bădică

Department of Computers and Information Technology University of Craiova Craiova, Romania · Department of Business Informatics University of Craiova Craiova, Romania

Probabilistic Logic Logic Programming Probabilistic Programming

Aug 3, 2026cs.CR

EntailLLM: Verifying LLM-Generated Vulnerability Discovery Paths with Domain Knowledge via Logic Programming

Large language models are increasingly used to reason about software vulnerabilities, but their outputs can silently violate domain knowledge, limiting their reliability in safety-critical settings such as medical devices. Prior work either treats that output as a prediction to be scored or constrains it to walks within a single knowledge graph; neither checks whether reasoning over a binary is consistent with an independent body of domain knowledge. We present EntailLLM, which validates each LLM-proposed analyst path by entailment: the path is a traversal of the binary's function call graph, the domain knowledge is represented in a separate graph, and verification aligns the two under temporal annotated logic. Across three CWE classes, four LLMs, three prompting strategies, and seven binaries varying in size from 405 to 12,696 function call-graph nodes, domain knowledge raises pooled entailment from 78% to 98%, with entailment decreasing in only 3% of the experiments. EntailLLM is deployed end-to-end on real medical-device binaries, reaching 98% pooled entailment without per-device tuning. Our system inherits the formal guarantees of generalized annotated logic, providing logical verification of LLM output that is both explainable and grounded in well-defined semantics.

Kaustuv Mukherji, Jaikrishna Manojkumar Patil, Colton Payne +4

Syracuse University · HRL Laboratories

Logic Programming Software Vulnerability Detection Formal Verification LLM Reliability LLMs for Cybersecurity

Jul 30, 2026cs.AI

Distilling Answer Set Programming Theories from Large Language Models

Writing Answer Set Programming (ASP) theories from scratch is a difficult and time-consuming task. We take a neurosymbolic approach to study whether a model can distill complete and correct theories, given a fixed agent harness with the solver in the loop. The protocol is dataset-agnostic: with a single prompt and an empty file as the starting point the model is given a 1-hour time limit to derive a complete theory. We chose VQA as the application domain, three benchmarks (CLEVR, GQA, CLEVRER), as these are publicly available and non-trivial. In order to study the model scale required for solving this task we nine different models: four frontier (Claude Sonnet 4.6, Claude Opus 4.7, GPT-5, DeepSeek V4 Pro), two mid-tier (DeepSeek V4 Flash, gpt-oss-120b), and three open-weights (qwen3.6-27b, gpt-oss-20b, qwen3.5-9b). Three of four frontier models reach 100% on CLEVR and 92.8%-98.8% on GQA; on CLEVRER, Sonnet, Opus, DeepSeek V4 Pro score 92.7%-95.3%. GPT-5 reaches 98.7% on CLEVR but drops to 41.8% on GQA and to 86.7% on CLEVRER. Adding handwritten reference theories from other datasets moves the other three frontier models by at most +/-3.4 pp but reduces GPT-5's accuracy by 3-19 pp. We release the code, prompts, and theories distilled.

Nelson Higuera Ruiz, Markus Hofmarcher, Claudiu Leoveanu-Condrei

ExtensityAI, Vienna, Austria

Logic Programming LLM-Based Program Synthesis Answer Set Programming Neuro-Symbolic Reasoning Knowledge-Based VQA

Jul 26, 2026cs.LO

An Unofficial FastLAS Tutorial: A Programmer's Guide

FastLAS is a scalable system for Inductive Logic Programming (ILP): you give it some background knowledge, a language bias, and a set of examples, and it searches for a set of logic program rules (a hypothesis) that explains the examples. These notes are a hands-on introduction to writing FastLAS programs. They are organised as a programmer's guide: syntax first, then a ladder of worked, numbered examples of increasing difficulty. Every self-contained example here has been run against FastLAS 2.2.0 and shows the tool's actual output. We keep theory to the minimum needed to write correct programs; throughout, set-off notes flag where FastLAS differs from its sibling system ILASP, and where the two learning algorithms (--opl and --nopl) behave differently. The document is intended as an unofficial tutorial to FastLAS 2.2.0, not as an official language specification.

Fabio Aurelio D'Asaro

University of Verona, Italy · University College London, United Kingdom

Logic Programming Inductive Logic Programming

Jul 25, 2026cs.AI

Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming

Chain-of-thought (CoT) prompting enables large language models (LLMs) to tackle multi-step reasoning tasks, yet the generated intermediate steps are not guaranteed to be logically sound. We present Reason Popper-ly, a neurosymbolic framework that uses inductive logic programming (ILP) to learn relation composition rules from reasoning traces and deploys them as an online verifier for step-level correction. Given an LLM-generated trace, the method checks each inferred step against the learned rule table, diagnoses the violation type, rewrites incorrect steps with symbolically derived repairs, and regenerates the remaining suffix so that the model can produce its final answer conditioned on a verified trace. We evaluate on CLUTRR, a multi-hop kinship reasoning benchmark, using five language models over reasoning chains of 2 to 10 hops. Across all models, Reason Popper-ly consistently improves terminal accuracy over standard CoT, with gains of up to 48 percentage points for small models and 15 points for frontier models on the longest chains. Compared with a fully exogenous symbolic pipeline, our method performs better on harder instances by preserving the model's successful grounding while correcting only verifiable reasoning failures. In addition, step-level ILP verification yields a fine-grained error taxonomy that provides diagnostic insight beyond final-answer accuracy.

Zirong Chen, Meiyi Ma

Department of Computer Science, Vanderbilt University, USA

Logic Programming Reasoning Consistency in Language Models Structured Reasoning Neuro-Symbolic Reasoning Inductive Logic Programming Multi-Hop Reasoning+1

Jul 23, 2026cs.AI

Euclid-MCP: A Model Context Protocol Server for Deterministic Logical Reasoning via Prolog

Large Language Models (LLMs) excel at natural language understanding and generation but remain unreliable for multi-step logical reasoning, especially in safety-critical or compliance-sensitive domains. Recent neuro-symbolic approaches address this gap by coupling neural models with external symbolic engines, yet most integrations are bespoke and lack a standardized interface for tool-augmented agents. This paper presents Euclid-MCP, an open-source MCP server that provides deterministic logical reasoning via SWI-Prolog. Euclid-MCP introduces Euclid-IR, an engine-agnostic intermediate representation for Horn-clause logic that is human-readable, easy for LLMs to generate, and straightforward to compile into Prolog or alternative backends. The server exposes a compact tool interface that supports a translate-run-inspect-repair loop, enabling LLM clients to delegate inference while retaining full access to proof traces and derivation logs. We evaluate Euclid-MCP on a realistic IT security and compliance use case. Results show that while LLMs alone are sufficient on small knowledge bases, they hallucinate systematically on larger problems, whereas Euclid-MCP delivers exact answers with lower latency and more compact outputs. We argue that semantic RAG is fundamentally unsuited for rule enforcement, and that Euclid-MCP can serve as a stable, shared reasoning substrate for both RAG-based assistants and agentic systems.

Bartolomeo Bogliolo

Logic Programming LLM Reliability Model Context Protocol Neuro-Symbolic Reasoning LLM Reasoning

Jul 23, 2026cs.AI

Logic Programming Semantics for Causal Processes

Motivated by challenging modelling issues in the life sciences, we investigate the relationship between logic programming semantics and the eventual states of causal processes compatible with those logic programs. More precisely, we show that while stable models of positive logic programs correspond to the eventual states of processes commencing from a neutral state and continuing undisturbed indefinitely, supported models describe the eventual states reachable from arbitrary starting points. This also contributes to the discussion of the appropriate semantics for logic programming as a causal rule language, adding a temporal perspective to recent interpretations of the stable and supported model semantics from an explanatory viewpoint of causality.

Felix Weitkämper

German University Of Digital Science Potsdam, Germany

Logic Programming Causal Reasoning

Jul 23, 2026cs.AI

How Rules Represent Causal Knowledge: Causal Modeling with Probabilistic Logic Programming

Pearl famously argues that causal knowledge enables the prediction of intervention effects. By contrast, purely descriptive knowledge supports only conclusions drawn from observations. His theory of causality, however, is developed exclusively within Bayesian networks and causal models. Consequently, it is largely restricted to acyclic causal relationships, and transferring its ideas to other formalisms risks misinterpretation or inconsistency. This paper brings Pearl's approach to causality into probabilistic logic programming (PLP). To this end, such programs are aligned with philosophical foundations established in prior work that do not rely on temporal notions; that is, all relevant events are assumed to occur simultaneously. A formal causal semantics for these programs, together with a notion of intervention and an implementation, is proposed. It is shown that this semantics coincides with the P-log semantics for stratified ProbLog programs, while the two may differ in the non-stratified case and for other PLP formalisms.

Kilian Rueckschloss, Felix Weitkaemper

Eberhard Karls Universitaet Tuebingen · University of Tübingen Tübingen, Germany · German University of Digital Science +1

Probabilistic Logic Logic Programming Causal Reasoning Probabilistic Programming Causal Intervention

Jul 23, 2026cs.AI

A New Well-Supported Semantics for Description Logic Programs

Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies. Most popular semantics for logic programming have this property of well-supportedness. We recognize two limitations of the current well-supported semantics for DL programs: its increased computational complexity for the consistency problem and its lack of a reduct transformation characterization. In this work, we present a new semantics which evaluates ontological atoms more strictly than the current semantics. This keeps the complexity of its consistency problem NP-complete, rather than increasing it to the second level of the polynomial hierarchy. Additionally, we identify a syntactic class of description logic programs for which our new semantics is equivalent to the current semantics. We characterize our semantics using a fixpoint operator and a reduct-based transformation. Our new semantics is a strict subset of the current well-supported semantics, so it maintains the prior notion of well-supportedness while inducing its own stricter notion. We prefer our new notion of well-supportedness due to its similarities with logic programming.

Spencer Killen, Jia-Huai You

University of Alberta Alberta, Canada

Logic Programming Answer Set Programming Description Logic

Jul 23, 2026cs.LO

Case study: solving P-99 with LPTP and an LLM

Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises. We solved the first thirty three just by prompting an LLM (Large Language Model). We used Claude from Anthropic. By solved we mean: generate the Prolog code and a test file, run the tests and check whether they pass, then formally prove types, groundness, termination, uniqueness, existence and also sometimes functional correctness with LPTP (Logic Program Theorem Prover). Hence our approach is an experiment in vibe-coding/vericoding of P-99. It is a vibe-coding experiment because we started from informal specifications written in English and let Claude generate the Prolog code. It also fits within vericoding because the LLM proved reliability guarantees on the generated Prolog code. Claude wrote 58 logic procedures, 508 tests, 257 lemmas for a total of 11800 proof lines. We manually checked each file generated by the LLM. We checked the Prolog code, ran the tests, examined the logical statements generated by Claude and proof-checked Claude's proofs with LPTP. This paper describes this experiment and provides the main details so that it can be reproduced by the interested reader.

Fred Mesnard, Thierry Marianne, Étienne Payet +1

LIM, université de La Réunion, France · Université de Namur, Belgium

Logic Programming LLM-Based Program Synthesis Program Synthesis

Jul 23, 2026cs.LO

Chess_db: A framework for working with large chess game datasets

Chess is a two player strategic game that is embedded in classical AI culture as it was once the frontier for intelligent behaviour. There was the silent assumption that the advent of computer engines that play better than the best humans will extinguish interest in the game. However, the opposite has come to pass, with a growing following for the game. A lot of the computational resources are now centered around training of players, where the engine output is just one aspect. Access to past games is also an essential part, both in knowing what games a specific player has played previously, and also which continuations at a certain position have led to victory more often for each of the two colour players. We present Chess_db a suite of logic programming tools that can effectively manipulate games both in memory and via creating back end databases. In particular, we provide versatile code that creates databases from PGN (portable game notation) game files and explore the suitability of open source key-value databases for storing position tables that provide near-instant access to information pertaining to substantially large number of games.

Nicos Angelopoulos, Jan Wielemaker

University College & Imperial College, London UK · University College & Imperial College London, UK · SWI-Prolog solutions +1

Logic Programming Chess

Jul 23, 2026cs.LO

Animation, Verification and Visualisation of Prolog Transition Systems with ProB

ProB is a Prolog-based model checker, animator and constraint solver for high-level formal specifications. One can also use ProB to animate transition systems defined by Prolog predicates, allowing the application of its various validation techniques. In this work, we present the existing features of ProB's Prolog animation mode and its recent extensions. The extended capabilities include simulation for statistical checks, more reliable trace replay, transitions with user input and improved state visualisation. We apply the new features to case studies, particularly for evaluating different strategies in game play, such as Connect Four. The features are useful for many other applications, especially for ProB's new sequent prover for Event-B proof obligations, as well as for demonstration models for teaching in combination with interactive visualisation.

Jan Gruteser, Michael Leuschel, Katharina Engels +1

Heinrich Heine University Düsseldorf · Faculty of Mathematics and Natural Science, Institute of Computer Science, Heinrich Heine University Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf

Logic Programming Formal Verification

Jul 23, 2026cs.PL

GLP: A Grassroots, Multiagent, Concurrent, Logic Programming Language for AI

A grassroots platform is a multiagent distributed system in which multiple independent instances can form and operate independently of each other and of any global resource, yet may coalesce into ever larger instances, possibly resulting in a single global instance. Grassroots platforms aim to offer an egalitarian/democratic alternative to centralised/autocratic and decentralised/plutocratic global platforms. Here, we present Grassroots Logic Programs (GLP), a multiagent concurrent logic programming language designed for the implementation of grassroots platforms: we recall the standard operational semantics of logic programs; introduce the concurrent operational semantics of GLP as its restriction; recall multiagent atomic transactions; use them to introduce a multiagent operational semantics of GLP; and prove multiagent GLP to be grassroots. The grassroots social graphâthe foundational grassroots platform on which all others are basedâserves as a GLP programming example.

Ehud Shapiro

London School of Economics · London School of Economics and Weizmann Institute of Science

Logic Programming Multi-Agent Systems

Jul 2, 2026cs.LO

ADVENT: LLM-Driven Automatic Predicate Invention for ILP

Predicate invention (PI), the creation of new predicates to extend the hypothesis space, remains a critical bottleneck in Inductive Logic Programming (ILP). Existing methods rely on domain expertise and produce semantically opaque predicates, hindering adaptation to unfamiliar domains and cross-task reuse. We present ADVENT, an LLM-driven PI mechanism for ILP. ADVENT pairs LLM abductive generation with Prolog deductive verification, forming an iterative loop in which concrete execution results guide the LLM to refine candidate predicates. The mechanism leverages Large Language Models to identify implicit patterns in structured relational data and invent auxiliary predicates with meaningful names and definitions. Invented predicates and learned rules accumulate in a knowledge pool for cross-task reuse. Experiments on nine poker-hand concepts across seven LLMs show that LLM-driven PI achieves 58% success rate where ILP alone fails entirely, formal verification raises this to 80%, and the knowledge pool yields gains up to +31 percentage points, while producing human-interpretable rules. These results suggest that ADVENT offers a promising direction for automating predicate invention and enabling cross-task knowledge reuse in ILP.

Tingting Yu, Pei-Cing Huang, Chan Hsu +2

Department of Information Management National Sun Yat-Sen University Kaohsiung, Taiwan

Logic Programming Inductive Logic Programming

Jun 14, 2026cs.LO

The algebra of Krom logic programs

This paper investigates the algebraic structure of Krom logic programs, consisting only of facts and rules with at most one body atom. We show that sequential composition endows the class of Krom programs with a natural monoid structure and that this structure admits rich algebraic extensions to Krom seminearrings, Krom quemirings, Krom-Conway seminearrings, and Krom-Conway omegaseminearrings. Furthermore, we establish explicit generating sets and canonical decompositions, study the associated

{}^ω

-operator, characterize the Kleene star in graph-theoretic terms, and relate finite Krom monoids to transformation monoids and finite-state automata. These results provide new connections between logic programming, algebraic automata theory, and algebraic graph theory.

Christian Antić

Vienna University of Technology Vienna, Austria

Logic Programming

Jun 12, 2026cs.AI

PrologMCP: A Standardized Prolog Tool Interface for LLM Agents

Frontier reasoning-tuned language models still fail on deductive tasks at depth, and the cost of improved performance through extended internal reasoning scales poorly. Symbolic delegation offers a complementary route: a language model translates the problem, while a solver performs the inference. However, current autoformalization pipelines for logic programming are typically bespoke integrations tied to particular tasks or agents. We introduce PrologMCP, a task-agnostic, open-source server that exposes Prolog as a stateful tool through the Model Context Protocol (MCP). Its compact tool interface, structured error reporting, and per-session isolation make the translate-run-inspect-repair loop a reusable primitive for MCP-capable agents. We evaluate a formalizer agent enhanced with PrologMCP against standard and reasoning LLMs (Claude Sonnet 4.6, GPT-4.1, and o4-mini) on two subsets of PARARULE-Plus: a general-purpose sample and a more challenging one targeting a specific failure mode of natural-language reasoning. On the general sample, the formalizer matches or exceeds reasoning LLMs (accuracy 1.00 vs.\ 1.00 / 0.998), with the largest gains over standard models (0.762 for GPT-4.1). On the challenging subset, the formalizer remains near-perfect (1.00 / 0.99) while reasoning LLMs drop to 0.95 / 0.94. These results suggest that delegating inference to Prolog via MCP is a robust and inspectable alternative to extended natural-language reasoning.

Agnieszka Mensfelt, Adarsh Prabhakaran, Adrian Haret +2

Department of Computer Science, Royal Holloway, University of London, UK

Logic Programming Symbolic Reasoning Agentic Reasoning Neuro-Symbolic Reasoning Autoformalization LLM Reasoning

May 26, 2026cs.AI

2-ASP(Q) programs with weak constraints: Complexity and efficient implementation

ASP(Q) extends Answer Set Programming (ASP) with Quantifiers over answer sets. In this paper we focus on the class of ASP(Q) programs with two quantifiers and weak constraints, denoted as 2-ASP(Q)^w. 2-ASP(Q)^w is a practically relevant fragment of ASP(Q) that is expressive enough to capture optimization problems up to the class Delta_3^P. On the theoretical side, we provide a complete complexity characterization of the main computational tasks for 2-ASP(Q)^w programs, including tight completeness results and the analysis of nontrivial cases that have not been addressed in previous works. On the practical side, we introduce novel strategies for computing (optimal) quantified answer sets in the Casper system, that rely on a Counterexample-Guided Abstraction Refinement (CEGAR) technique tailored to ASP(Q). An experimental evaluation on hard benchmarks from different application domains shows that the proposed techniques are effective in practice.

Andrea Cuteri, Giuseppe Mazzotta, Francesco Ricca

University of Calabria, Rende, Italy

Logic Programming Counterexample-Guided Refinement Answer Set Programming

May 21, 2026cs.AI

Parametric Modular Answer Set Programs Made Declarative

In this paper, we explore the concept of modularity in first-order answer set programming (ASP). We introduce a new formalism called parametric modular logic programs, which allows defining subprograms with parameters and intensionality statements. We demonstrate how this formalism can capture the semantics of clingo-programs with collective control, a feature that enables structuring and instantiating subprograms. We provide theoretical foundations for modular ASP, illustrate its usefulness, and connect to traditional non-modular ASP.

Jorge Fandinno, Yuliya Lierler, Torsten Schaub

University of Nebraska Omaha, USA · University of Potsdam, Germany

Logic Programming Answer Set Programming

May 14, 2026cs.AI

On Strong Equivalence Notions in Logic Programming and Abstract Argumentation

Strong equivalence between knowledge bases ensures the possibility of replacing one with the other without affecting reasoning outcomes, in any given context. This makes it a crucial property in nonmonotonic formalisms. In particular, the fields of logic programming and abstract argumentation provide primary examples in which this property has been subject to vast investigations. However, while (classes of) logic programs and abstract argumentation frameworks are known to be semantically equivalent in static settings, this alignment breaks in dynamic contexts due to differing notions of update. As a result, strong equivalence does not always carry over from one formalism to the other. In this paper, we carefully investigate this discrepancy and introduce a new notion of strong equivalence for logic programs. Our approach preserves strong equivalence under translation between certain classes of logic programs and both Dung-style and claim-augmented argumentation frameworks, thus restoring compatibility across these formalisms.

Giovanni Buraglio, Wolfgang Dvorak, Stefan Woltran

TU Wien, Austria

Logic Programming Computational Argumentation

May 10, 2026cs.AI

Cplus2ASP: Computing Action Language C+ in Answer Set Programming

We present Version 2 of system Cplus2ASP, which implements the definite fragment of action language C+. Its input language is fully compatible with the language of the Causal Calculator Version 2, but the new system is significantly faster thanks to modern answer set solving techniques. The translation implemented in the system is a composition of several recent theoretical results. The system orchestrates a tool chain, consisting of f2lp, clingo, iclingo, and as2transition. Under the incremental execution mode, the system translates a C+ description into the input language of iclingo, exploiting its incremental grounding mechanism. The correctness of this execution is justified by the module theorem extended to programs with nested expressions. In addition, the input language of the system has many useful features, such as external atoms by means of Lua calls and the user interactive mode. The system supports extensible multi-modal translations for other action languages, such as B and BC, as well.

Joseph Babb, Joohyung Lee

School of Computing, Informatics, and Decision Systems Engineering Arizona State University, Tempe, USA

Logic Programming Code Translation Symbolic Planning Answer Set Programming

May 10, 2026cs.AI

Weighted Rules under the Stable Model Semantics

We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

Joohyung Lee, Yi Wang

School of Computing, Informatics and Decision Systems Engineering Arizona State University, Tempe, USA

Logic Programming Nonmonotonic Reasoning Answer Set Programming

May 5, 2026cs.AI

ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming

Inductive Logic Programming (ILP) aims to learn interpretable first-order rules from data, but existing symbolic and neuro-symbolic approaches struggle to scale to noisy and probabilistic settings. Classical ILP relies on discrete combinatorial rule search and is brittle under uncertainty, while differentiable ILP methods typically depend on predefined rule templates or inaccurate fuzzy operators that suffer from vanishing gradients or poor approximation of logical structure when reasoning over probabilistic predicate valuations. This paper proposes an Attention-based Neuro-symbolic Differentiable Rule Extractor (ANDRE), a novel ILP framework that learns first-order logic programs by optimizing over a continuous rule space with attention-based logical operators. ANDRE replaces both rule templates and logical operators with fully differentiable, attention-driven conjunction and disjunction operators that approximate logical min-max semantics, enabling accurate, stable, and interpretable reasoning over probabilistic data. By softly selecting, negating, or excluding predicates within each rule, ANDRE supports flexible rule induction while preserving symbolic structure. Extensive experiments on classical ILP benchmarks, large-scale knowledge bases, and synthetic datasets with probabilistic predicates and noisy supervision demonstrate that ANDRE achieves competitive or superior predictive performance while reliably recovering correct symbolic rules under uncertainty. In particular, ANDRE remains robust to moderate label noise, substantially outperforming existing differentiable ILP methods in both rule extraction quality and stability.

Iman Sharifi, Peng Wei, Saber Fallah

Dept. of Mechanical and Aerospace Engineering, George Washington University, USA · Dept. of Mechanical Engineering Sciences, University of Surrey, UK

Logic Programming Differentiable Programming Neuro-Symbolic Reasoning Inductive Logic Programming

Apr 24, 2026cs.LO

BLAST: Benchmarking LLMs with ASP-based Structured Testing

Large Language Models (LLMs) have demonstrated remarkable performance across a broad spectrum of tasks, including natural language understanding, dialogue systems, and code generation. Despite evident progress, less attention has been paid to their effectiveness in handling declarative paradigms such as Answer Set Programming (ASP), to date. In this paper we introduce BLAST: The first dedicated benchmarking methodology and associated dataset for evaluating the accuracy of LLMs in generating ASP code. BLAST provides a structured evaluation framework featuring two novel semantic metrics tailored to ASP code generation. The paper presents the results of an empirical evaluation involving ten well-established graph-related problems from the ASP literature and a diverse set of eight state-of-the-art LLMs.

Manuel Alejandro Borroto Santana, Erica Coppolillo, Francesco Calimeri +3

University of Calabria, Rende, Italy · ICAR-CNR, Rende, Italy · Artificial Intelligence LAB, DeMaCS, University of Calabria, Rende, Italy +1

Logic Programming LLM Evaluation Language Model Generation Evaluation Answer Set Programming Code Generation Evaluation Code Generation Benchmarks+1

Apr 23, 2026cs.AI

Inferring High-Level Events from Timestamped Data: Complexity and Medical Applications

In this paper, we develop a novel logic-based approach to detecting high-level temporally extended events from timestamped data and background knowledge. Our framework employs logical rules to capture existence and termination conditions for simple temporal events and to combine these into meta-events. In the medical domain, for example, disease episodes and therapies are inferred from timestamped clinical observations, such as diagnoses and drug administrations stored in patient records, and can be further combined into higher-level disease events. As some incorrect events might be inferred, we use constraints to identify incompatible combinations of events and propose a repair mechanism to select preferred consistent sets of events. While reasoning in the full framework is intractable, we identify relevant restrictions that ensure polynomial-time data complexity. Our prototype system implements core components of the approach using answer set programming. An evaluation on a lung cancer use case supports the interest of the approach, both in terms of computational feasibility and positive alignment of our results with medical expert opinions. While strongly motivated by the needs of the healthcare domain, our framework is purposely generic, enabling its reuse in other areas.

Yvon K. Awuklu, Meghyn Bienvenu, Katsumi Inoue +2

1Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400, Talence, France · 2CHU de Bordeaux, Service d’Information M´edicale, F-33000, Bordeaux, France · 3Univ. Bordeaux, INSERM, BPH, U1219, F-33000, Bordeaux, France +1

Logic Programming Healthcare Temporal Reasoning

Apr 21, 2026cs.LO

Streamliners for Answer Set Programming

Streamliner constraints reduce the search space of combinatorial problems by ruling out portions of the solution space. We adapt the StreamLLM approach, which uses Large Language Models (LLMs) to generate streamliners for Constraint Programming, to Answer Set Programming (ASP). Given an ASP encoding and a few small training instances, we prompt multiple LLMs to propose candidate constraints. Candidates that cause syntax errors, render satisfiable instances unsatisfiable, or degrade performance on all training instances are discarded. The surviving streamliners are evaluated together with the original encoding, and we report results for a virtual best encoding (VBE) that, for each instance, selects the fastest among the original encoding and its streamlined variants. On three ASP Competition benchmarks (Partner Units Problem, Sokoban, Towers of Hanoi), the VBE achieves speedups of up to 4--5x over the original encoding. Different LLMs produce semantically diverse constraints, not mere syntactic variations, indicating that the approach captures genuine problem structure.

Florentina Voboril, Martin Gebser, Stefan Szeider +1

TU Wien Vienna, Austria · University of Klagenfurt Klagenfurt, Austria

Logic Programming Large Language Model-Guided Optimization LLM-Based Program Synthesis Answer Set Programming

Feb 6, 2026cs.PL

Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI (Full Version)

Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its paired reader, and may contain additional readers and/or writers. This enables the concise expression of rich multidirectional communication modalities. The language was introduced together with concurrent (cGLP) and multiagent (maGLP) operational semantics. Here, we derive from these (1) dGLP, a deterministic counterpart of cGLP, and (2) madGLP, a counterpart of maGLP in which deterministic agents communicate solely by asynchronous message passing, and prove them correct against their abstract counterparts. maGLP shared variable pairs spanning agents can be implemented by two local variable pairs joined by a \emph{global link}, with correctness following from disjoint substitution commutativity (a consequence of GLP's single-occurrence invariant). We further prove that madGLP is grassroots. Both dGLP and madGLP serve as formal specifications for an AI-driven implementation discipline (math

\to

informal spec

\to

Dart) employed and described here: from dGLP, AI (Claude) developed a workstation-based GLP implementation in Dart, and from madGLP it is developing a smartphone-based multiagent one.

Ehud Shapiro

London School of Economics and Weizmann Institute of Science

Logic Programming Multi-Agent Systems Multi-Agent Communication

Oct 17, 2025cs.PL

GLP: A Grassroots, Multiagent, Concurrent, Logic Programming Language for AI (Full Version)

A grassroots platform is a multiagent distributed system in which multiple independent instances can form and operate independently of each other and of any global resource, yet may coalesce into ever larger instances, possibly resulting in a single global instance. Grassroots platforms aim to offer an egalitarian/democratic alternative to centralised/autocratic and decentralised/plutocratic global platforms. Here, we present Grassroots Logic Programs (GLP), a multiagent concurrent logic programming language designed for the implementation of grassroots platforms: we recall the standard operational semantics of logic programs; introduce the concurrent operational semantics of GLP as its restriction; recall multiagent atomic transactions; use them to introduce a multiagent operational semantics of GLP; and prove multiagent GLP to be grassroots. The grassroots social graph -- the foundational grassroots platform on which all others are based -- serves as a GLP programming example. These mathematical foundations are being used by AI to implement GLP as well as to program in GLP: a workstation-based implementation of concurrent GLP in Dart was derived from the concurrent operational semantics of GLP; a multiagent smartphone-based implementation of GLP in Dart/Flutter is being developed based on the multiagent operational semantics of GLP; a moded type system for GLP was designed (and implemented by AI in Dart) to facilitate collaborative human-AI development of GLP programs, where AI derives working GLP programs from human-approved type definitions and declarations; GLP implementations of grassroots platforms for the social graph, social networks, currencies and bonds, and more, have been derived by AI from mathematical specifications written as volitional multiagent atomic transactions.

Ehud Shapiro

London School of Economics and Weizmann Institute of Science

Logic Programming Multi-Agent Systems

Dec 10, 2024cs.AI

Goal-Driven Reasoning in DatalogMTL with Magic Sets

DatalogMTL is a powerful rule-based language for temporal reasoning. Due to its high expressive power and flexible modeling capabilities, it is suitable for a wide range of applications, including tasks from industrial and financial sectors. However, due to its high computational complexity, practical reasoning in DatalogMTL is highly challenging. To address this difficulty, we introduce a new reasoning method for DatalogMTL which exploits the magic sets technique -- a rewriting approach developed for (non-temporal) Datalog to simulate top-down evaluation with bottom-up reasoning. We have implemented this approach and evaluated it on publicly available benchmarks, showing that the proposed approach significantly and consistently outperformed state-of-the-art reasoning techniques.

Shaoyu Wang, Kaiyue Zhao, Dongliang Wei +4

School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, China · Department of Computer Science, University of Oxford, UK · School of Electronic Engineering and Computer Science, Queen Mary University of London, UK

Logic Programming Logical Reasoning Temporal Reasoning