Answer Set Programming

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.

Existing approaches to multi-agent belief combination have established mature foundations for combining uncertain beliefs under common assumptions: consensus methods use iterative averaging, logic-based methods resolve conflicting knowledge bases, and epistemic logic analyzes agents' information states. Typically, these approaches assume that the structure determining what each agent can represent remains fixed. However, in many scenarios, agents gain or lose observational capacity during execution, and what was once admissible may become structurally impossible. This paper presents a formal framework for handling such runtime changes in epistemic partitions over continuous belief profiles. A hybrid approach exploits the advantages of answer set programming in elaboration tolerance, declarative integrity constraints, and explanations, with the numerical flexibility of Python. The framework applies to domains where agents operate at heterogeneous and possibly changing levels of resolution, and provides formal guarantees of admissibility preservation under refinement, unique mass-preserving repair under coarsening, and explanation completeness. Evaluation across 100 randomly generated topology changes confirms complete violation detection and explanation coverage.

In the field of Artificial Intelligence, an agent is a system which is able to autonomously make decisions in order to reach a desired goal. As these systems grow more prevalent in our day-to-day lives, there has been an increased need to add explainability features which can provide an account for an agent's behavior. We therefore propose a framework that outlines how to produce comprehensible explanations for policy-aware agents, or agents which have rule-enforcing policies incorporated in their decision-making framework. This framework is designed using insights from the social sciences on how to produce good explanations. It is implemented in the Answer Set Programming language while using Python to assist with information extraction and natural-language translation. Because these agents incur penalties when violating policies, we are able to leverage these penalties to detect undesirable events in scenarios that are counterfactual to the agents' original actions. This lends itself to creating contrastive explanations (e.g., "the agent performed this action because, had it not, undesirable event X would have occurred."), which formulate the core component for our explainability framework. The framework is evaluated using a survey wherein human participants provide feedback on our program-generated explanations.

While the integration of linear constraints has significantly expanded the reach of Answer Set Programming (ASP), existing hybrid solvers often rely on disparate semantic underpinnings that lack a unified logical foundation. We address this gap by introducing a many-sorted variant of the Bound-founded Logic of Here-and-There (HTb), providing a versatile framework capable of characterizing equilibrium models across a wide spectrum of alternative semantics for extensions of ASP with linear constraints. We apply this framework to the setting of difference constraints, focusing on the semantic characterization of clingo[DL]. Central to our approach is the formalization of foundedness for numeric variables. By investigating how different hybrid systems - such as clingo[DL], clingcon, and flingo - justify constraint atoms, we uncover the semantic roots of their varying behaviors. This investigation results in a single, consistent framework that not only formalizes the foundations of current systems like clingo[DL] but also facilitates the rigorous study of program simplifications and the future integration of diverse semantic principles.

The growing demand for Urban Air Mobility (UAM) introduces significant challenges in airspace management, particularly within densely populated metropolitan regions. As the number of aerial vehicles-such as drones, air taxis, and helicopters-continues to rise, so does the risk of mid-air collisions and conflicts with existing air traffic and obstacles. Ensuring safe and efficient UAM operations requires robust strategic deconfliction mechanisms. We propose an Answer Set Programming (ASP) based approach for strategic deconfliction, focusing on time synchronization and route optimization for conflict-free flight plans. The solution is benchmarked against Constraint Programming (CP), emphasizing scalability and resource use. Results show that ASP offers faster execution and better scalability for small to medium cases, while CP maintains stable memory but degrades with complexity.

We present a general neurosymbolic reasoning and learning methodology based on a modular integration of answer set programming with an energy based model substrate. Key contributions are: (1) supporting joint optimisation in the continuous latent space through explicit ASP-based declarative semantics fully incorporating background knowledge, constraints, non-monotonic inference; and (2) advancing recent works at the interface of answer sets, probabilistic logic, and answer set modulo theories by providing a generalised model and practical platform for ASP-centric robust, end-to-end training for applications in dynamic domains (e.g., involving perception and interaction). We provide a practical implementation, and demonstrate basic use and application (with MNIST), and evaluate with the visual question-answering benchmark Clevr and the multi-object tracking benchmark MOT.

Human reasoning often operates through qualitative concepts expressed by linguistic labels such as high, low, expensive, or cheap, whose interpretation depends on context and is usually vague, despite being rooted in numerical data. This paper explores a novel fuzzy-logic-based qualitative extension of Answer Set Programming (ASP) to bridge numerical information and qualitative reasoning. The underlying language, formally introduced in a separate work, provides a principled framework that avoids rigid thresholds and supports robust reasoning under vagueness. Focusing on a representative use case, we illustrate how the framework integrates numerically grounded inputs (such as outputs of machine learning models) with symbolic reasoning over qualitative labels. Key features, including learning-based membership functions and semantically enriched predicates, enable the combination of expert knowledge, contextual factors, and subjective interpretations within a unified declarative setting.

We present a general answer set programming based hybrid quantitative-qualitative method for computing constrained branching trajectory modes for moving objects in real-world settings. The method performs constrained traversal of an environment graph, enumerating geometrically admissible motion behaviours as stable models, each constituting a distinct trajectory mode characterised by both domain-dependent and independent factors such as derived event sequence, map topology, and domain norms. The hybrid trajectory computation method is generally applicable across motion characteristics typically encountered in diverse dynamic domains with moving objects, e.g., autonomous driving. We demonstrate applicability and highlight how computed trajectories are traceable to their underlying stable model, thereby affording verifiable interpretability that purely learned approaches cannot provide. We also perform an empirical evaluation with Argoverse 2, a large-scale real-world autonomous driving benchmark representative of the class of dynamic domains within the scope of the proposed method.

This paper studies the expressive power of ASPIC$^+$ argumentation frameworks with uncertain preference profiles by comparing them with several abstract formalisms with uncertain defeats. Most of our results are negative (and some of them are theoretically unexpected). We also conjecture a positive, non-trivial threshold for the expressivity of uncertain preferences, and prove some essential preliminary steps toward the confirmation of this conjecture.

Operational Air Traffic Flow and Capacity Management (ATFCM) balances flight demand with available sector capacity, to ensure safe and efficient operations. Mathematical models enhance operational ATFCM performance by framing demand-capacity balancing as an optimization problem, maximizing efficiency while adhering to safety constraints. However, SOTA research optimizes the aircraft trajectories (called ATFM) or the sector configuration (called DAC) separately. This leaves a research gap of whether joint optimization of ATFM and DAC can bring benefits. We partially address this limitation by introducing a joint ATFCM model with an encoding in Answer Set Programming (ASP). The ASP implementation is evaluated against two baselines applied to our joint model: a SOTA Mixed Integer Programming (MIP) model and an iterative CASA-based heuristic. Computational experiments utilize an instance generator fitted to historical OpenSky Network flight data. Our results indicate that the ASP model outperforms the MIP model, while ASP remains competitive against heuristics on small instances. Furthermore, while DAC has the largest improvement on solving performance compared to rerouting and delaying, unrestricted variants of DAC or rerouting lead to search space thrashing.

Technical-standard compliance reasoning may involve incomplete evidence, inconsistent observations, exceptions, and derived normative outputs. This paper presents \textsc{Monir}, a four-valued normative intermediate representation for ASP-oriented compliance workflows. \textsc{Monir} separates factual support from normative outputs: facts are represented by positive and negative support bits, while deontic labels are rule-generated output constructors interpreted by aggregation policies. Its core semantics is a staged transition system over support configurations. We define the language, rule-state interface, diagnostics, and policy-parametric reporting; characterize admissible staged evaluation by a dependency graph; prove deterministic polynomial-time evaluation for fixed evidence; and give NP/coNP upper bounds, with matching hardness for representative completion-based verdict queries.

Visual Question Answering (VQA) is the task of answering questions about images, requiring the integration of multimodal input and reasoning. Modular approaches that incorporate logic-based representations into the reasoning component offer clear advantages over end-to-end trained systems, particularly in terms of interpretability. However, adapting or extending these representations when task requirements change can place a significant burden on developers. To address this challenge, we present an approach for distilling rules from Large Language Models (LLMs). Our method prompts an LLM to extend an initial VQA reasoning theory, expressed as an answer-set program, to meet new requirements of the task. Examples from VQA datasets guide the LLM, validate the results, and help correct erroneous rules by leveraging feedback from the ASP solver. We demonstrate that our approach is effective across diverse VQA datasets. Notably, only a few examples are needed to elicit correct rules from LLMs. Our experiments suggest that rule distillation from LLMs is a promising alternative to traditional data-driven rule learning approaches. Under consideration in Theory and Practice of Logic Programming (TPLP).

Reinforcement Learning (RL) enables autonomous agents to learn policies from experience, but realistic problems often involve enormous state spaces, making learning and generalisation challenging. Abstraction and approximation are therefore essential. Relational Reinforcement Learning (RRL) offers a way to reason about objects and their relations, and the CARCASS framework by Martijn van Otterlo demonstrates how logical representations can model Markov Decision Processes (MDPs) in first-order domains. Originally implemented in Prolog, CARCASS leverages domain knowledge to create powerful abstractions. We explore Answer-Set Programming (ASP), which is a rich and, contrary to Prolog, fully declarative modelling language, to realise CARCASS abstractions. We evaluate our ASP-based implementation in case studies of two domains, viz. Blocks World and Minigrid. Our results indicate that CARCASS with ASP provides a promising approach to constructing abstractions for RL, especially when domain knowledge is available.

The development of temporal extensions of Answer Set Programming (ASP) has led to the emergence of non-monotonic linear-time (TEL), dynamic (DEL), and metric (MEL) temporal equilibrium logics. However, the inherent rigidity of highly optimized ASP systems often hinders the rapid exploration and implementation of alternative logical designs. In this work, we propose a flexible meta-programming framework that operationalizes the semantics of varied temporal logics through a unified, declarative framework. Our approach extends standard ASP meta-programming by augmenting clingo's theory grammar with formal type specifications and nesting capabilities. To ensure semantic correctness, we introduce a transformation pipeline that protects nested modalities from stable-model-based simplifications during grounding. We demonstrate the extensibility of our framework by implementing meta-encodings for TEL, MEL, and DEL. We provide a comprehensive account of TEL and highlight the key features for managing the interval constraints of MEL and the Fischer-Ladner closure in DEL. Finally, we introduce the metasp system, a versatile tool that encapsulates this workflow.

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.

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.

The Power grid is a critical infrastructure underpinning all aspects of modern society and its services. Maintaining its effectiveness requires continuous adaptations. In particular, addressing sustainability targets, demand patterns, and urbanisation trends requires implementing changes to the network. Actual developments can potentially span over a decade, with supply continuity and service quality that must be preserved throughout by ensuring conformance to several topological and combinatorial invariants. Long-term power grid planning deals with the above process, and although planning languages could be a natural choice, the kind of properties and invariants needed are cumbersome to express in such languages; on the contrary, they can be elegantly and succinctly encoded in Answer Set Programming (ASP). In this paper, we propose the first approach to automate and optimise the long-term power grid planning process using ASP. Experimental evaluations conducted on synthetic and real-world grid data confirm the expressive power of the proposed ASP-based approach and demonstrate its effectiveness.

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.

Recently there has been an increasing interest in incorporating intensional'' functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being pre-defined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of Answer Set Programming Modulo Theories (ASPMT)'' -- a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that ``tight'' ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.

Integration of Answer Set Programming (ASP) with neural networks has emerged as a promising tool in Neuro-symbolic AI. While existing approaches extend the capabilities of ASP to real world domains, their reasoning pipelines depend on classical solvers, which is a bottleneck for scalability. To tackle this problem, we propose a new method to compute stable models, called decision-propagation (DProp), which alternates falsity decisions and truth propagations. Successful DProp computations are shown to capture the stable model semantics. We then develop Neural DProp (NDProp), a differentiable extension of DProp with neural computation for decisions and fuzzy evaluation for propagations. We evaluate the capabilities of NDProp for learning decision heuristics as well as neuro-symbolic integration, and compare it with existing neuro-symbolic approaches. The results show that NDProp can learn to efficiently compute stable models, and it improves accuracy and scalability on neuro-symbolic benchmarks.

Recent large language models (LLMs) have achieved impressive reasoning milestones but continue to struggle with high computational costs, logical inconsistencies, and sharp performance degradation on high-complexity problems. While neuro-symbolic methods attempt to mitigate these issues by coupling LLMs with symbolic reasoners, existing approaches typically rely on monotonic logics (e.g., SMT) that cannot represent defeasible reasoning -- essential components of human cognition. We present "LLM+ASP," a framework that translates natural language into Answer Set Programming (ASP), a nonmonotonic formalism based on stable model semantics. Unlike prior "LLM+ASP" approaches that require manually authored knowledge modules, domain-specific prompts, or evaluation restricted to single problem classes, our framework operates without any per-task engineering and applies uniformly across diverse reasoning tasks. Our system utilizes an automated self-correction loop where structured feedback from the ASP solver enables iterative refinement. Evaluating across six diverse benchmarks, we demonstrate that: (1) stable model semantics allow LLMs to naturally express default rules and exceptions, outperforming SMT-based alternatives by significant margins on nonmonotonic tasks; (2) iterative self-correction is the primary driver of performance, effectively replacing the need for handcrafted domain knowledge; (3) compact in-context reference guides substantially outperform verbose documentation, revealing a "context rot" phenomenon where excessive context hinders constraint adherence.

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.

We explore the use of answer set programming (ASP) and its extension with quantifiers, ASP(Q), for inconsistency-tolerant querying of prioritized data, where a priority relation between conflicting facts is exploited to define three notions of optimal repairs (Pareto-, globally- and completion-optimal). We consider the variants of three well-known semantics (AR, brave and IAR) that use these optimal repairs, and for which query answering is in the first or second level of the polynomial hierarchy for a large class of logical theories. Notably, this paper presents the first implementation of globally-optimal repair-based semantics, as well as the first implementation of the grounded semantics, which is a tractable under-approximation of all these optimal repair-based semantics. Our experimental evaluation sheds light on the feasibility of computing answers under globally-optimal repair semantics and the impact of adopting different semantics, approximations, and encodings.

ASPIC-style structured argumentation frameworks provide a formal basis for reasoning in artificial intelligence by combining internal argument structure with abstract argumentation semantics. A key challenge in these frameworks is ensuring compliance with five critical rationality postulates: closure, direct consistency, indirect consistency, non-interference, and crash-resistance. Recent approaches, including ASPIC$^{\ominus}$ and Deductive ASPIC$-$, have made significant progress but fall short of meeting all postulates simultaneously under a credulous semantics (e.g. preferred) in the presence of undercuts. This paper introduces Deductive ASPIC$^{\ominus}$, a novel framework that integrates gen-rebuttals from ASPIC$^{\ominus}$ with the Joint Support Bipolar Argumentation Frameworks (JSBAFs) of Deductive ASPIC$-$, incorporating preferences. We show that Deductive ASPIC$^{\ominus}$ satisfies all five rationality postulates under a version of preferred semantics. This work opens new avenues for further research on robust and logically sound structured argumentation systems.

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.

We develop a computational approach to Metric Answer Set Programming (ASP) to allow for expressing quantitative temporal constraints, like durations and deadlines. A central challenge is to maintain scalability when dealing with fine-grained timing constraints, which can significantly exacerbate ASP's grounding bottleneck. To address this issue, we leverage extensions of ASP with difference constraints, a simplified form of linear constraints, to handle time-related aspects externally. Our approach effectively decouples metric ASP from the granularity of time, resulting in a solution that is unaffected by time precision.

Large Language Models (LLMs) possess extensive foundational knowledge and moderate reasoning abilities, making them suitable for general task planning in open-world scenarios. However, it is challenging to ground a LLM-generated plan to be executable for the specified robot with certain restrictions. This paper introduces CLMASP, an approach that couples LLMs with Answer Set Programming (ASP) to overcome the limitations, where ASP is a non-monotonic logic programming formalism renowned for its capacity to represent and reason about a robot's action knowledge. CLMASP initiates with a LLM generating a basic skeleton plan, which is subsequently tailored to the specific scenario using a vector database. This plan is then refined by an ASP program with a robot's action knowledge, which integrates implementation details into the skeleton, grounding the LLM's abstract outputs in practical robot contexts. Our experiments conducted on the VirtualHome platform demonstrate CLMASP's efficacy. Compared to the baseline executable rate of under 2% with LLM approaches, CLMASP significantly improves this to over 90%.