Answer Set Programming (ASP) is a declarative formalism widely used in knowledge representation and reasoning for modeling and solving combinatorial problems, yet current Large Language Models (LLMs) often struggle to generate correct programs from natural language specifications. This difficulty stems both from the limited presence of ASP in training corpora and from the strict syntactic and semantic constraints imposed by stable model semantics. We introduce ALM–ASP (Agentic Loop for Modeling in ASP), a multi-agent architecture for automatic ASP modeling grounded in a functional model of language agents equipped with tools and persistent state. ALM–ASP instantiates this model via two interacting agents: a Modeler, which incrementally constructs candidate ASP programs, and a Validator, which assesses their alignment with the original specification and provides feedback for refinement. The agents interact through a shared ASP execution environment backed by the CLINGO engine, yielding an iterative construct–validate loop. An empirical evaluation on a challenging subset of CP–Bench and on problems from recent LP/CP Programming Contests shows that ALM–ASP significantly improves both syntactic validity and end-to-end correctness over general-purpose LLM baselines, and also achieves improved instance coverage compared to the closest agentic alternative, CP–Agent.

Languages for Knowledge Representation and Reasoning, such as ASP, CP, and SMT, excel at solving some complex problems, but encoding them into a higher-level language may be more profitable, leaving these formalisms as targets for solving. Recent studies aim to convert controlled natural languages into formal representations, yet these solutions are often tailored to specific languages and require significant effort. This paper introduces a general framework that generates grammars for target representation languages, enabling the translation of problems stated in CNL into formal representations. The related system, CNLWizard, offers a flexible, high-level approach to defining desired grammars, significantly reducing the time and effort needed to create custom grammars. Finally, we demonstrate the system's effectiveness through an experimental analysis.

Abstract In the context of urban traffic control, traffic signal optimisation is the problem of determining the optimal green length for each signal in a set of traffic signals. The literature has effectively tackled such a problem, mostly with automated planning techniques leveraging the PDDL + language and solvers. However, such language has limitations when it comes to specifying optimisation statements and computing optimal plans. In this paper, we provide an alternative solution to the traffic signal optimisation problem based on Constraint Answer Set Programming (CASP). We devise an encoding in a CASP language, which is then solved by means of clingcon 3 , a system extending the well-known ASP solver clingo . We performed experiments on real historical data from the town of Huddersfield in the UK, comparing our approach to the PDDL+ model that obtained the best results for the considered benchmark. The results showed the potential of our approach for tackling the traffic signal optimisation problem and improving the solution quality of the PDDL + plans.

The ability to efficiently solve hard combinatorial optimization problems is a key prerequisite to various applications of declarative programming paradigms. Symmetries in solution candidates pose a significant challenge to modern optimization algorithms since the enumeration of such candidates might substantially reduce their performance. This paper proposes a novel approach using Inductive Logic Programming (ILP) to lift symmetry-breaking constraints for optimization problems modeled in Answer Set Programming (ASP). Given an ASP encoding with optimization statements and a set of small representative instances, our method augments ground ASP programs with auxiliary normal rules enabling the identification of symmetries using existing tools, like SBASS. Then, the obtained symmetries are lifted to first-order constraints with ILP. We prove the correctness of our method and evaluate it on real-world optimization problems from the domain of automated configuration. Our experiments show significant improvements of optimization performance due to the learned first-order constraints.

Writing correct models for combinatorial problems is relatively straightforward; however, they must be efficient to be usable with instances producing many solution candidates. In this work, we aim to automatically generalise the discarding of symmetric solutions of Answer Set Programming instances, improving the efficiency of the programs with first-order constraints derived from propositional symmetry-breaking constraints.

Abstract Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic since the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. As a result, a time-consuming recomputation of SBCs must be done before every invocation of a solver. To overcome these limitations, we introduce a new model-oriented approach for Answer Set Programming that lifts the SBCs of small problem instances into a set of interpretable first-order constraints using the Inductive Logic Programming paradigm. Experiments demonstrate the ability of our framework to learn general constraints from instance-specific SBCs for a collection of combinatorial problems. The obtained results indicate that our approach significantly outperforms a state-of-the-art instance-specific method as well as the direct application of a solver.

Abstract Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based approaches for symmetry breaking are limited to problems for which a set of representative and easily solvable instances is available, which is often not the case in practical applications. This work extends the learning framework and implementation of a model-based approach for Answer Set Programming to overcome these limitations and address challenging problems, such as the Partner Units Problem. In particular, we incorporate a new conflict analysis algorithm in the Inductive Logic Programming system ILASP, redefine the learning task, and suggest a new example generation method to scale up the approach. The experiments conducted for different kinds of Partner Units Problem instances demonstrate the applicability of our approach and the computational benefits due to the first-order constraints learned.

Efficient omission of symmetric solution candidates is essential for combinatorial problem solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic. Moreover, the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. To overcome these limitations, we introduce a new model-oriented approach for Answer Set Programming that lifts the SBCs of small problem instances into a set of interpretable first-order constraints using the Inductive Logic Programming paradigm. Experiments demonstrate the ability of our framework to learn general constraints from instance-specific SBCs for a collection of combinatorial problems. The obtained results indicate that our approach significantly outperforms a state-of-the-art instance-specific method as well as the direct application of a solver.

The main goal of this work is to propose a tool-chain capable of analyzing a data collection of temporally qualified (genetic) mutation profiles, i.e., a collection of DNA-sequences (genes) that present variations with respect to their “healthy” versions. We implemented a system consisting of a front-end, a reasoning core, and a post-processor: the first transforms the input data retrieved from medical databases into a set of logical facts, while the last displays the computation results as graphs. Concerning the reasoning core, we employed the Answer Set Programming paradigm, which is capable of deducing complex information from data. However, since the system is modular, this component can be replaced by any logic programming tool for different kinds of data analysis. Indeed, we tested the use of a probabilistic inductive logic programming core.