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.

Neurosymbolic AI combines neural networks with symbolic programs to create robust and explainable predictions. One such framework is NeurASP, which trains a neural network to predict concepts and reasons over them using rules written in answer set programming (ASP) to solve downstream tasks. Crucially, labels are only provided for the downstream prediction produced by the symbolic rules, not for the latent concepts themselves. Backpropagation through the non-differentiable ASP component requires expensive probability and gradient calculations, which has hindered scalability to more sophisticated tasks. In this paper, we address the current limitations of NeurASP by improving its computational performance through vectorization, batch processing, and caching of intermediate computations during training. We compare computation speeds between the original and our new implementation of NeurASP and report speedups of multiple orders of magnitude for larger tasks. To this end, we propose a new dataset of difficult tasks involving playing cards, which we use to test the capabilities of NeurASP’s enhanced learning function.

Generating accurate and executable code using Large Language Models (LLMs) remains a significant challenge for underrepresented programming languages, such as Prolog and Lisp, due to the scarcity of public training data compared to high-resource languages like Python. This paper introduces a generalizable Reinforcement Learning (RL) approach that combines small-scale versions of the Qwen2.5-Coder model with Group Relative Policy Optimization (GRPO) to enable effective code generation through reasoning. To address the limitations of sparse datasets, we integrate execution-driven feedback directly into the RL loop, utilizing a reward system that exploits both logical correctness and structural formatting. Experimental results on GSM8K dataset demonstrate significant improvements in reasoning quality and code accuracy across underrepresented languages. These findings underscore the potential of our approach to benefit a wide range of programming languages lacking extensive training resources by leveraging symbolic reasoning and interpreter-based feedback.

When large language models (LLMs) are used for semantic data extraction from unstructured text, producing candidate relational facts from natural language, they may remain unreliable for tasks requiring complex combinatorial reasoning and global consistency. This paper proposes a logic-guided data extraction framework combining LLM-based extraction with answer set programming (ASP). The LLM produces candidate facts, whereas ASP performs validation, inference, consistency checking, and control. Unlike existing pipelines that query the LLM independently for all target predicates, the proposed approach uses ASP reasoning to identify which predicates are logically admissible at each stage and to guide extraction queries. By interleaving LLM calls with ASP derivation, the framework infers logically implied facts without further extraction and detects inconsistencies early. We formalize the pipeline and prove that, under mild assumptions, it is equivalent to the baseline approach with respect to the final extracted facts, while requiring fewer LLM calls. We also introduce a caching mechanism for logic-based control queries, exploiting monotonicity of conjunctive queries over incrementally constructed fact sets to reduce solver invocations. Experiments on ASP-derived benchmarks show that the framework reduces LLM calls and improves extraction quality by mitigating spurious outputs, demonstrating the value of non-monotonic logic programming for controlled semantic extraction.

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 Prologue, CARCASS leverages domain knowledge to create powerful abstractions. We explore Answer-Set Programming (ASP), which is a rich and, contrary to Prologue, 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 (our implementation is available at https://github.com/rbankosegger/RLASP-core. Further material (data, encodings, extended documentation) can be found here: https://www.bankosegger.at/iclp26/).

Prolog is a well-known declarative programming language commonly used in introductory courses on logic and reasoning. However, many students find Prolog challenging because it lacks the familiar debugging mechanisms found in imperative languages. In large classes, this difficulty is exacerbated by the challenge of providing timely and personalized feedback to students. In this work, we introduce ProDebug, the first tool to combine large language models (LLMs) with spectrum-based and mutation-based techniques for automated debugging of Prolog assignments. ProDebug automatically identifies faults and proposes bug repairs for student Git submissions. Faults are detected using three approaches – spectrum-based, mutation-based, and LLM reasoning – while repairs are generated using mutation-based techniques and LLMs. Our evaluation on 1499 buggy student submissions from a bachelor’s level programming class demonstrates the potential of automated, LLM-augmented feedback systems to scale support for declarative programming education.

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$^w$(Q). 2-ASP$^w$(Q) is a practically relevant fragment of ASP(Q) that is expressive enough to capture optimization problems up to the class $\Delta ^P_3$. On the theoretical side, we provide a complete complexity characterization of the main computational tasks for 2-ASP$^w$(Q) 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.

One of the most significant achievements of equilibrium logic was the characterization of strong equivalence, a property crucial for program transformation and optimization in answer set programming (ASP). While ASP has recently been extended to a higher-order setting to enhance its expressive power, the lack of a comparable purely logical foundation has made verifying strong equivalence for higher-order programs or even proving the correctness of simple program transformations, a difficult challenge. This paper addresses this gap by developing a logical semantics for higher-order ASP by extending the equilibrium logic framework. Within this extended framework, we demonstrate that every stratified higher-order logic program possesses a unique equilibrium model. Moreover, we establish definability results demonstrating that the syntax of our higher-order language is sufficiently expressive to capture its semantic domains. Finally, and most importantly, we generalize the classical theorem of strong equivalence to the higher-order setting: we prove that two programs are strongly equivalent if and only if they share the same higher-order models.

We consider a fragment of Higher-Order Datalog with negation and argue that it generalizes the familiar and important fragment of Linear Datalog. We investigate the expressive power of this fragment, establishing a tight connection with the hierarchy of space complexity classes. In particular, we demonstrate that for all $k \ge 1$, the $(k+1)$-order fragment of Stratified Linear Higher-Order Datalog$^\neg$ captures $(k-1)-\textsf {EXPSPACE}$. This result suggests that restricting programs to linear recursion shifts the expressive power of the corresponding fragments from time to space, generalizing the classical result that (Stratified) Linear Datalog captures NL. Unlike the first-order setting where an ordering assumption is required to capture $\mathsf{NL}$, our results hold without any such assumption on the input database. The proof relies on simulating space-bounded Turing machines using Stratified Linear Higher-Order Datalog$^\neg$ programs and providing a space-efficient evaluation of the query program. We argue that identifying such computationally well-behaved fragments is a crucial step toward paving the way for practical implementations of Higher-Order Datalog.

In this paper, we propose using Learning from Answer Sets to approximate black-box models, such as Neural Networks (NN), in the specific case of learning user preferences. We specifically explore the use of ILASP (Inductive Learning of Answer Set Programs) to approximate preference learning systems through weak constraints. We have created a dataset on user preferences over a set of recipes, which is used to train the NNs that we aim to approximate with ILASP. Our experiments investigate ILASP both as a global and a local approximator of the NNs. These experiments address the challenge of approximating NNs working on increasingly high-dimensional feature spaces while achieving appropriate fidelity on the target model and limiting the increase in computational time. To handle this challenge, we propose a preprocessing step that exploits Principal Component Analysis to reduce the dataset’s dimensionality while keeping our explanations transparent.

Under consideration for publication in Theory and Practice of Logic Programming (TPLP).

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.

Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an application. This is supported by appropriate evaluation strategies. Demand-driven evaluation from functional programming is amalgamated with non-determinism from logic programming so that solutions or values are computed whenever they exist. This frees the programmer from considering the influence of an operational strategy on the success of a computation, but it is a challenge to the language implementer. A non-deterministic demand-driven strategy might duplicate unevaluated choices of an expression, which could duplicate the computational effort. In recent implementations, this problem has been tackled by adding a kind of memoization of non-deterministic choices to the expression under evaluation. Since this has been implemented in imperative target languages, it was unclear whether this could also be supported in a functional programming environment like Haskell. This paper presents a solution to this challenge by transforming functional logic programs into a monadic representation. Although this transformation is not new, we present an implementation of the monadic interface which supports memoization in non-deterministic branches. Additionally, we include more advanced features of functional logic languages, namely functional patterns and encapsulated search, in our approach. By optimizing our implementation for purely functional computations with both a static and dynamic approach, we are able to achieve a promising performance that outperforms current compilers for Curry.

The relationship between intuitionistic or intermediate logics and logic programming has been extensively studied, prominently featuring Pearce’s equilibrium logic and Osorio’s safe beliefs. Equilibrium logic admits a fixpoint characterization based on the logic of here-and-there, akin to theory completion in default and autoepistemic logics. Safe beliefs are similarly defined via a fixpoint operator, albeit under the semantics of intuitionistic or other intermediate logics. In this paper, we investigate the logical foundations of Temporal Answer Set Programming through the lens of Temporal Equilibrium Logic, a formalism combining equilibrium logic with linear-time temporal operators. We lift the seminal approaches of Pearce and Osorio to the temporal setting, establishing a formal correspondence between temporal intuitionistic logic and temporal logic programming. Our results deepen the theoretical underpinnings of Temporal Answer Set Programming and provide new avenues for research in temporal reasoning.

In this paper, we introduce the action language C-MT (Mind Transition Language), built on top of answer set programs and transition systems to represent how human mental states evolve in response to sequences of observable actions. Drawing on well-established psychological theories, such as the Appraisal Theory of Emotion, we formalize mental states, such as emotions, as multi-dimensional configurations. To enable controlled agent behavior and limit undesirable effects such as undue psychological influence, we introduce a novel causal rule, forbids to cause, together with constructs tailored to mental state dynamics. These allow the specification of valid transitions as constraints and invariance properties, which are rigorously evaluated over trajectories in transition systems. The framework supports reasoning about and comparing different dynamics of mental change under varying constraints. We apply the action language to design models for emotion verification.

$\{log\}$ (read ‘setlog’) was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, $\{log\}$ is a constraint satisfiability solver implementing decision procedures for several fragments of set theory. Hence, $\{log\}$ can be used as a declarative, set, logic programming language and as an automated theorem prover for set theory. Over time $\{log\}$ has been extended with some components integrated to the satisfiability solver thus providing a formal verification environment. In this paper we make a comprehensive presentation of this environment which includes a language for the description of state machines based on set theory, an interactive environment for the execution of functional scenarios over state machines, a generator of verification conditions for state machines, automated verification of state machines, and test case generation. State machines are both, programs and specifications; exactly the same code works as a program and as its specification. In this way, with a few additions, a CLP language turned into a seamlessly integrated programming and automated proof system.

We address the challenge of product configuration in the context of increasing customer demand for diverse and complex products. We propose a solution through a curated selection of product model benchmarks formulated in the Coom language, divided into three fragments of increasing complexity. Each fragment is accompanied by a corresponding example on bike configuration, and additional scalable product models are included in the CoomSuite, along with relevant resources. We outline an ASP-based workflow for solving Coom-based configuration problems, highlighting its adaptability to different paradigms and alternative ASP solutions. The CoomSuite aims to provide a comprehensive, accessible, and representative set of examples that can serve as a common ground for stakeholders in the field of product configuration.

We present a new use of Answer Set Programming (ASP) to discover the molecular structure of chemical samples based on the relative abundance of elements and structural fragments, as measured in mass spectrometry. To constrain the exponential search space for this combinatorial problem, we develop canonical representations of molecular structures and an ASP implementation that uses these definitions. We evaluate the correctness of our implementation over a large set of known molecular structures, and we compare its quality and performance to other ASP symmetry-breaking methods and to a commercial tool from analytical chemistry.

This paper presents a logic programming-based framework for policy-aware autonomous agents that can reason about potential penalties for noncompliance and act accordingly. While prior work has primarily focused on ensuring compliance, our approach considers scenarios where deviating from policies may be necessary to achieve high-stakes goals. Additionally, modeling noncompliant behavior can assist policymakers by simulating realistic human decision-making. Our framework extends Gelfond and Lobo’s Authorization and Obligation Policy Language ($\mathscr{AOPL}$) to incorporate penalties and integrates Answer Set Programming (ASP) for reasoning. Compared to previous approaches, our method ensures well-formed policies, accounts for policy priorities, and enhances explainability by explicitly identifying rule violations and their consequences. Building on the work of Harders and Inclezan, we introduce penalty-based reasoning to distinguish between noncompliant plans, prioritizing those with minimal repercussions. To support this, we develop an automated translation from the extended $\mathscr{AOPL}$ into ASP and refine ASP-based planning algorithms to account for incurred penalties. Experiments in two domains demonstrate that our framework generates higher-quality plans that avoid harmful actions while, in some cases, also improving computational efficiency. These findings underscore its potential for enhancing autonomous decision-making and informing policy refinement.

In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of the other in an appropriate deductive system. This paper shows how to extend this method of proving strong equivalence to programs containing the counting aggregate.

Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming. While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive reasoning has not been investigated yet. This paper presents an approach to extracting poss-programs from a background program and examples (parts of intended possibilistic stable models). To this end, the notion of induction tasks is first formally defined, its properties are investigated and two algorithms ilpsm and ilpsmmin for computing induction solutions are presented. An implementation of ilpsmmin is also provided and experimental results show that when inputs are ordinary logic programs, the prototype outperforms a major inductive learning system for normal logic programs from stable models on the datasets that are randomly generated.