In this paper, we compare four different semantics for disjunction in Answer Set Programming that, unlike stable models, do not adhere to the principle of model minimality. Two of these approaches, Cabalar and Muñiz’ Justified Models and Doherty and Szalas’ Strongly Supported Models, directly provide an alternative non-minimal semantics for disjunction. The other two, Aguado et al’s Forks and Shen and Eiter’s Determining Inference (DI) semantics, actually introduce a new disjunction connective, but are compared here as if they constituted new semantics for the standard disjunction operator. We are able to prove that three of these approaches (Forks, Justified Models and a reasonable relaxation of the DI-semantics) actually coincide, constituting a common single approach under different definitions. Moreover, this common semantics always provides a superset of the stable models of a programme (in fact, modulo any context) and is strictly stronger than the fourth approach (Strongly Supported Models), that actually treats disjunctions as in classical logic.

We present ASP Chef Mustache, an extension of ASP Chef that enhances template-based rendering of answer set programming (ASP) solutions using a logic-less templating system inspired by Mustache. Our approach integrates data visualization frameworks such as Tabulator, Chart.js, and vis.js, enabling interactive representations of ASP interpretations as tables, charts, and graphs. Mustache queries in templates support advanced constructs for formatting, sorting, and multi-stage expansion, facilitating the generation of rich, structured outputs. We demonstrate the power of this framework through a series of use cases, including data analysis for the Italian VQR, visualization of blocking sets in graphs, and scheduling problems. The result is a versatile tool for bridging declarative problem solving and modern web-based visual analytics.

Novel utility computing paradigms rely upon the deployment of multi-service applications to pervasive and highly distributed cloud-edge infrastructure resources. Deciding onto which computational nodes to place services in cloud-edge networks, as per their functional and non-functional constraints, can be formulated as a combinatorial optimisation problem. Most existing solutions in this space are not able to deal with unsatisfiable problem instances, nor preferences, i.e., requirements that DevOps may agree to relax to obtain a solution. In this article, we exploit Answer Set Programming optimisation capabilities to tackle this problem. Experimental results in simulated settings show that our approach is effective on lifelike networks and applications.

Probabilistic Logic Programming (PLP) under the distribution semantics is a leading approach to practical reasoning under uncertainty. An advantage of the distribution semantics is its suitability for implementation as a Prolog or Python library, available through two well-maintained implementations, namely ProbLog and cplint/PITA. However, current formulations of the distribution semantics use point-probabilities, making it difficult to express epistemic uncertainty, such as arises from, for example, hierarchical classifications from computer vision models. Belief functions generalize probability measures as non-additive capacities and address epistemic uncertainty via interval probabilities. This paper introduces interval-based Capacity Logic Programs based on an extension of the distribution semantics to include belief functions and describes properties of the new framework that make it amenable to practical applications.

Product configuration is a successful application of answer set programming (ASP). However, challenges are still open for interactive systems to effectively guide users through the configuration process. The aim of our work is to provide an ASP-based solver for interactive configuration that can deal with large-scale industrial configuration problems and that supports intuitive user interfaces (UIs) via an application programming interface (API). In this paper, we focus on improving the performance of automatically completing a partial configuration. Our main contribution enhances the classical incremental approach for multi-shot solving by four different smart expansion functions. The core idea is to determine and add specific objects or associations to the partial configuration by exploiting cautious and brave consequences before checking for the existence of a complete configuration with the current objects in each iteration. This approach limits the number of costly unsatisfiability checks and reduces the search space, thereby improving solving performance. In addition, we present a UI that uses our API and is implemented in ASP.

The grounding bottleneck poses one of the key challenges that hinders the widespread adoption of answer set programming in industry. Hybrid grounding is a step in alleviating the bottleneck by combining the strength of standard bottom-up grounding with recently proposed techniques where rule bodies are decoupled during grounding. However, it has remained unclear when hybrid grounding shall use body-decoupled grounding (BDG) and when to use standard bottom-up grounding. In this paper, we address this issue by developing automated hybrid grounding: we introduce a splitting algorithm based on data-structural heuristics that detects when to use BDG and when standard grounding is beneficial. We base our heuristics on the structure of rules and an estimation procedure that incorporates the data of the instance. The experiments conducted on our prototypical implementation demonstrate promising results, which show an improvement on hard-to-ground scenarios, whereas on hard-to-solve instances, we approach state-of-the-art performance.

Answer Set Programming (ASP) is a successful method for solving a range of real-world applications. Despite the availability of fast ASP solvers, computing answer sets demands significant computational resources, since the problem tackled is on the second level of the polynomial hierarchy. Answer set computation can be accelerated if the program is split into two disjoint parts, bottom and top. Thus, the bottom part is evaluated independently of the top part, and the results of the bottom part evaluation are used to simplify the top part. Lifschitz and Turner have introduced the concept of a splitting set, that is, a set of atoms that defines the splitting.

In a previous paper, the notion of g-splitting set, which generalize the concept of splitting sets for disjunctive logic programs, was introduced. In this paper, we further investigate the topic of splitting sets and g-splitting sets. We show that the set inclusion problem for splitting sets can be reduced to a classic Search Problem and solved in polynomial time. We also show that the task of computing g-splitting sets with desirable properties is relatively easy and straightforward. Finally, we show that stable models can be decomposed to models of rules inspired by g-splitting sets and models of the rest of the program. This interesting property can assist in incremental computation of stable models.

In the design of integrated circuits, one critical metric is the maximum delay introduced by combinational modules within the circuit. This delay is crucial because it represents the time required to perform a computation: in an Arithmetic Logic Unit, it represents the maximum time taken by the circuit to perform an arithmetic operation. When such a circuit is part of a larger, synchronous system, like a CPU, the maximum delay directly impacts the maximum clock frequency of the entire system. Typically, hardware designers use static timing analysis to compute an upper bound of the maximum delay because it can be determined in polynomial time. However, relying on this upper bound can lead to suboptimal processor speeds, thereby missing performance opportunities. In this work, we tackle the challenging task of computing the actual maximum delay, rather than an approximate value. Since the problem is computationally hard, we model it in answer set programming (ASP), a logic language featuring extremely efficient solvers. We propose non-trivial encodings of the problem into ASP. Experimental results show that ASP is a viable solution to address complex problems in hardware design.

The multi-agent path finding (MAPF) problem aims to find plans for multiple agents in an environment within a given time, such that the agents do not collide with each other or obstacles. Motivated by the execution and monitoring of these plans, we study dynamic MAPF (D-MAPF) problem, which allows changes such as agents entering/leaving the environment or obstacles being removed/moved. Considering the requirements of real-world applications in warehouses with the presence of humans, we introduce (1) a general definition for D-MAPF (applicable to variations of D-MAPF), (2) a new framework to solve D-MAPF (utilizing multi-shot computation and allowing different methods to solve D-MAPF), and (3) a new answer set programming-based method to solve D-MAPF (combining advantages of replanning and repairing methods, with a novel concept of tunnels to specify where agents can move). We have illustrated the strengths and weaknesses of this method by experimental evaluations, from the perspectives of computational performance and quality of solutions.

The operating room scheduling (ORS) problem deals with the optimization of daily operating room surgery schedules. It is a challenging problem subject to many constraints, like to determine the starting time of different surgeries and allocating the required resources, including the availability of beds in different department units. Recently, solutions to this problem based on answer set programming (ASP) have been delivered. Such solutions are overall satisfying but, when applied to real data, they can currently only verify whether the encoding aligns with the actual data and, at most, suggest alternative schedules that could have been computed. As a consequence, it is not currently possible to generate provisional schedules. Furthermore, the resulting schedules are not always robust. In this paper, we integrate inductive and deductive techniques for solving these issues. We first employ machine learning algorithms to predict the surgery duration, from historical data, to compute provisional schedules. Then, we consider the confidence of such predictions as an additional input to our problem and update the encoding correspondingly in order to compute more robust schedules. Results on historical data from the ASL1 Liguria in Italy confirm the viability of our integration.

Reasoning about dynamic systems with a fine-grained temporal and numeric resolution presents significant challenges for logic-based approaches like Answer Set Programming (ASP). To address this, we introduce and elaborate upon a novel temporal and constraint-based extension of the logic of Here-and-There and its nonmonotonic equilibrium extension, representing, to the best of our knowledge, the first approach to nonmonotonic temporal reasoning with constraints specifically tailored for ASP. This expressive system is achieved by a synergistic combination of two foundational ASP extensions: the linear-time logic of Here-and-There, providing robust nonmonotonic temporal reasoning capabilities, and the logic of Here-and-There with constraints, enabling the direct integration and manipulation of numeric constraints, among others. This work establishes the foundational logical framework for tackling complex dynamic systems with high resolution within the ASP paradigm.

We investigate the expressive power of Higher-Order $Datalog^\neg$ under both the well-founded and the stable model semantics, establishing tight connections with complexity classes. We prove that under the well-founded semantics, for all $k\geq 1$, $(k+1)$-Order $Datalog^\neg$ captures $k-\textsf {EXP}$, a result that holds without explicit ordering of the input database. The proof of this fact can be performed either by using the powerful existential predicate variables of the language or by using partially applied relations and relation enumeration. Furthermore, we demonstrate that this expressive power is retained within a stratified fragment of the language. Under the stable model semantics, we show that $(k+1)$-Order $Datalog^\neg$ captures $\textsf {co}-(k-\textsf {NEXP})$ using cautious reasoning and $k-\textsf {NEXP}$ using brave reasoning, again with analogous results for the stratified fragment augmented with choice rules. Our results establish a hierarchy of expressive power, highlighting an interesting trade-off between order and non-determinism in the context of higher-order logic programing: increasing the order of programs under the well-founded semantics can surpass the expressive power of lower-order programs under the stable model semantics.

Higher-order constructs enable more expressive and concise code by allowing procedures to be parameterized by other procedures. Assertions allow expressing partial program specifications, which can be verified either at compile time (statically) or run time (dynamically). In higher-order programs, assertions can also describe higher-order arguments. While in the context of (constraint) logic programming ((C)LP), run-time verification of higher-order assertions has received some attention, compile-time verification remains relatively unexplored. We propose a novel approach for statically verifying higher-order (C)LP programs with higher-order assertions. Although we use the Ciao assertion language for illustration, our approach is quite general, and we believe is applicable to similar contexts. Higher-order arguments are described using predicate properties – a special kind of property which exploits the (Ciao) assertion language. We refine the syntax and semantics of these properties and introduce an abstract criterion to determine conformance to a predicate property at compile time, based on a semantic order relation comparing the predicate property with the predicate assertions. We then show how to handle these properties using an abstract interpretation-based static analyzer for programs with first-order assertions by reducing predicate properties to first-order properties. Finally, we report on a prototype implementation and evaluate it through various examples within the Ciao system.

Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces all the answers required by the specifications. We also consider semi-completeness – completeness for those queries for which the program does not diverge. This paper presents an approach to systematically construct provably correct and semi-complete logic programs, for a given specification. Normal programs are considered, under Kunen’s 3-valued completion semantics (of negation as finite failure) and the well-founded semantics (of negation as possibly infinite failure). The approach is declarative, it abstracts from details of operational semantics, like, for example, the form of the selected literals (“procedure calls”) during the computation. The proposed method is simple and can be used (maybe informally) in actual everyday programming.

We present the solver asp-fzn for Constraint Answer Set Programming (CASP), which extends ASP with linear constraints. Our approach is based on translating CASP programs into the solver-independent FlatZinc language that supports several Constraint Programming and Integer Programming backend solvers. Our solver supports a rich language of linear constraints, including some common global constraints. As for evaluation, we show that asp-fzn is competitive with state-of-the-art ASP solvers on benchmarks taken from past ASP competitions. Furthermore, we evaluate it on several CASP problems from the literature and compare its performance with clingcon, which is a prominent CASP solver that supports most of the asp-fzn language. The performance of asp-fzn is very promising as it is already competitive on plain ASP and even outperforms clingcon on some CASP benchmarks.

ANTHEM 2.0 is a tool to aid in the verification of logic programs written in an expressive fragment of CLINGO ’s input language named MINI-GRINGO, which includes arithmetic operations and simple choice rules but not aggregates. It can translate logic programs into formula representations in the logic of here-and-there and analyze properties of logic programs such as tightness. Most importantly, ANTHEM 2.0 can support program verification by invoking first-order theorem provers to confirm that a program adheres to a first-order specification or to establish strong and external equivalence of programs. This paper serves as an overview of the system’s capabilities. We demonstrate how to use ANTHEM 2.0 effectively and interpret its results.

The Stable Roommates problems are characterized by the preferences of agents over other agents as roommates. A solution is a partition of the agents into pairs that are acceptable to each other (i.e., they are in the preference lists of each other), and the matching is stable (i.e., there do not exist any two agents who prefer each other to their roommates and thus block the matching). Motivated by real-world applications, and considering that stable roommates problems do not always have solutions, we continue our studies to compute “good-enough” matchings. In addition to the agents’ habits and habitual preferences, we consider their networks of preferred friends and introduce a method to generate personalized solutions to stable roommates problems. We illustrate the usefulness of our method with examples and empirical evaluations.

Answer Set Programming (ASP) provides a powerful declarative paradigm for knowledge representation and reasoning. Recently, counting answer sets has emerged as an important computational problem with applications in probabilistic reasoning, network reliability analysis, and other domains. This has motivated significant research into designing efficient ASP counters. While substantial progress has been made for normal logic programs, the development of practical counters for disjunctive logic programs remains challenging. We present $\mathsf{sharpASP}$-$\mathcal{SR}$, a novel framework for counting answer sets of disjunctive logic programs based on subtractive reduction to projected propositional model counting. Our approach introduces an alternative characterization of answer sets that enables efficient reduction while ensuring the intermediate representations remain polynomial in size. This allows $\mathsf{sharpASP}$-$\mathcal{SR}$ to leverage recent advances in projected model counting technology. Through extensive experimental evaluation on diverse benchmarks, we demonstrate that $\mathsf{sharpASP}$-$\mathcal{SR}$ significantly outperforms existing counters on instances with large answer set counts. Building on these results, we develop a hybrid counting approach that combines enumeration techniques with $\mathsf{sharpASP}$-$\mathcal{SR}$ to achieve state-of-the-art performance across the full spectrum of disjunctive programs. The extended version of the paper is available at: https://arxiv.org/abs/2507.11655.

Recentneuro-symbolic approaches have successfully extracted symbolic rule-sets from Convolutional Neural Network-based models to enhance interpretability. However, applying similar techniques to Vision Transformers (ViTs) remains challenging due to their lack of modular concept detectors and reliance on global self-attention mechanisms. We propose a framework for symbolic rule extraction from ViTs by introducing a sparse concept layer inspired by Sparse Autoencoders (SAEs). This linear layer operates on attention-weighted patch representations and learns a disentangled, binarized representation in which individual neurons activate for high-level visual concepts. To encourage interpretability, we apply a combination of L1 sparsity, entropy minimization, and supervised contrastive loss. These binarized concept activations are used as input to the FOLD-SE-M algorithm, which generates a rule-set in the form of a logic program. Our method achieves a better classification accuracy than the standard ViT while enabling symbolic reasoning. Crucially, the extracted rule-set is not merely post-hoc but acts as a logic-based decision layer that operates directly on the sparse concept representations. The resulting programs are concise and semantically meaningful. This work is the first to extract executable logic programs from ViTs using sparse symbolic representations, providing a step forward in interpretable and verifiable neuro-symbolic AI.