$\{log\}$ (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.

Probabilistic Answer Set Programming under the credal semantics extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming. Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on performance. Sampling allows handling larger instances but sometimes requires an increasing amount of memory.

Advances in incremental Datalog evaluation strategies have made Datalog popular among use cases with constantly evolving inputs such as static analysis in continuous integration and deployment pipelines. As a result, new logic programming debugging techniques are needed to support these emerging use cases.

This paper introduces an incremental debugging technique for Datalog, which determines the failing changes for a rollback in an incremental setup. Our debugging technique leverages a novel incremental provenance method. We have implemented our technique using an incremental version of the Soufflé Datalog engine and evaluated its effectiveness on the DaCapo Java program benchmarks analyzed by the Doop static analysis library. Compared to state-of-the-art techniques, we can localize faults and suggest rollbacks with an overall speedup of over 26.9$\times$ while providing higher quality results.

Static analysis is an essential component of many modern software development tools. Unfortunately, the ever-increasing complexity of static analyzers makes their coding error-prone. Even analysis tools based on rigorous mathematical techniques, such as abstract interpretation, are not immune to bugs. Ensuring the correctness and reliability of software analyzers is critical if they are to be inserted in production compilers and development environments. While compiler validation has seen notable success, formal validation of static analysis tools remains relatively unexplored. In this paper we present checkification, a simple, automatic method for testing static analyzers. Broadly, it consists in checking, over a suite of benchmarks, that the properties inferred statically are satisfied dynamically. The main advantage of our approach lies in its simplicity, which stems directly from framing it within the Ciao assertion-based validation framework, and its blended static/dynamic assertion checking approach. We demonstrate that in this setting, the analysis can be tested with little effort by combining the following components already present in the framework: 1) the static analyzer, which outputs its results as the original program source with assertions interspersed; 2) the assertion run-time checking mechanism, which instruments a program to ensure that no assertion is violated at run time; 3) the random test case generator, which generates random test cases satisfying the properties present in assertion preconditions; and 4) the unit-test framework, which executes those test cases. We have applied our approach to the CiaoPP static analyzer, resulting in the identification of many bugs with reasonable overhead. Most of these bugs have been either fixed or confirmed, helping us detect a range of errors not only related to analysis soundness but also within other aspects of the framework.

Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, while possibly accounting for the uncertainty of the environment. In this paper, we introduce the possibility to encode decision theory problems with Probabilistic Answer Set Programming under the credal semantics via decision atoms and utility attributes. To solve the task, we propose an algorithm based on three layers of Algebraic Model Counting, that we test on several synthetic datasets against an algorithm that adopts answer set enumeration. Empirical results show that our algorithm can manage non-trivial instances of programs in a reasonable amount of time.

We study randomized generation of sequences of test inputs to a system using Prolog. Prolog is a natural fit to generate test sequences that have complex logical interdependent structure. To counter the problems posed by a large (or infinite) set of possible tests, randomization is a natural choice. We study the impact that randomization in conjunction with SLD resolution have on the test performance. To this end, this paper proposes two strategies to add randomization to a test-generating program. One strategy works on top of standard Prolog semantics, whereas the other alters the SLD selection function. We analyze the mean time to reach a test case and the mean number of generated test cases in the framework of Markov chains. Finally, we provide an additional empirical evaluation and comparison between both approaches.

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.

DLV2 is an AI tool for knowledge representation and reasoning that supports answer set programming (ASP) – a logic-based declarative formalism, successfully used in both academic and industrial applications. Given a logic program modeling a computational problem, an execution of DLV2 produces the so-called answer sets that correspond one-to-one to the solutions to the problem at hand. The computational process of DLV2 relies on the typical ground & solve approach, where the grounding step transforms the input program into a new, equivalent ground program, and the subsequent solving step applies propositional algorithms to search for the answer sets. Recently, emerging applications in contexts such as stream reasoning and event processing created a demand for multi-shot reasoning: here, the system is expected to be reactive while repeatedly executed over rapidly changing data. In this work, we present a new incremental reasoner obtained from the evolution of DLV2 toward iterated reasoning. Rather than restarting the computation from scratch, the system remains alive across repeated shots, and it incrementally handles the internal grounding process. At each shot, the system reuses previous computations for building and maintaining a large, more general ground program, from which a smaller yet equivalent portion is determined and used for computing answer sets. Notably, the incremental process is performed in a completely transparent fashion for the user. We describe the system, its usage, its applicability, and performance in some practically relevant domains.

We present plingo, an extension of the answer set programming (ASP) system clingo that incorporates various probabilistic reasoning modes. Plingo is based on $\textit{Lpmln}^{\pm }$, a simple variant of the probabilistic language Lpmln, which follows a weighted scheme derived from Markov logic. This choice is motivated by the fact that the main probabilistic reasoning modes can be mapped onto enumeration and optimization problems and that $\textit{Lpmln}^{\pm }$ may serve as a middle-ground formalism connecting to other probabilistic approaches. Plingo offers three alternative frontends, for Lpmln, P-log, and ProbLog. These input languages and reasoning modes are implemented by means of clingo’s multi-shot and theory-solving capabilities. In this way, the core of plingo is an implementation of $\textit{Lpmln}^{\pm }$ in terms of modern ASP technology. On top of that, plingo implements a new approximation technique based on a recent method for answer set enumeration in the order of optimality. Additionally, in this work, we introduce a novel translation from $\textit{Lpmln}^{\pm }$ to ProbLog. This leads to a new solving method in plingo where the input program is translated and a ProbLog solver is executed. Our empirical evaluation shows that the different solving approaches of plingo are complementary and that plingo performs similarly to other probabilistic reasoning systems.

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.

In this paper, we delve into Notation3 Logic (N3), an extension of Resource Description Framework (RDF), which empowers users to craft rules introducing fresh blank nodes to RDF graphs. This capability is pivotal in various applications such as ontology mapping, given the ubiquitous presence of blank nodes directly or in auxiliary constructs across the Web. However, the availability of fast N3 reasoners fully supporting blank node introduction remains limited. Conversely, engines like VLog or Nemo, though not explicitly designed for Semantic Web rule formats, cater to analogous constructs, namely existential rules.

We investigate the correlation between N3 rules featuring blank nodes in their heads and existential rules. We pinpoint a subset of N3 that seamlessly translates to existential rules and establish a mapping preserving the equivalence of N3 formulae. To showcase the potential benefits of this translation in N3 reasoning, we implement this mapping and compare the performance of N3 reasoners like EYE and cwm against VLog and Nemo, both on native N3 rules and their translated counterparts. Our findings reveal that existential rule reasoners excel in scenarios with abundant facts, while the EYE reasoner demonstrates exceptional speed in managing a high volume of dependent rules.

Additionally to the original conference version of this paper, we include all proofs of the theorems and introduce a new section dedicated to N3 lists featuring built-in functions and how they are implemented in existential rules. Adding lists to our translation/framework gives interesting insights on related design decisions influencing the standardization of N3.

This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Bondarenko, Dung, Kowalski and Toni, and of Caminada and Schulz, by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs under the stable model semantics. For this, we consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect, and show the correspondence to the handling of disjunctions in the heads of the logic programs’ rules.

In the wake of the recent resurgence of the Datalog language of databases, together with its extensions for ontological reasoning settings, this work aims to bridge the gap between the theoretical studies of DatalogMTL (Datalog extended with metric temporal logic) and the development of production-ready reasoning systems. In particular, we lay out the functional and architectural desiderata of a modern reasoner and propose our system, Temporal Vadalog. Leveraging the vast amount of experience from the database community, we go beyond the typical chase-based implementations of reasoners, and propose a set of novel techniques and a system that adopts a modern data pipeline architecture. We discuss crucial architectural choices, such as how to guarantee termination when infinitely many time intervals are possibly generated, how to merge intervals, and how to sustain a limited memory footprint. We discuss advanced features of the system, such as the support for time series, and present an extensive experimental evaluation. This paper is a substantially extended version of “The Temporal Vadalog System” as presented at RuleML+RR ’22.

Catamorphisms are functions that are recursively defined on list and trees and, in general, on algebraic data types (ADTs), and are often used to compute suitable abstractions of programs that manipulate ADTs. Examples of catamorphisms include functions that compute size of lists, orderedness of lists, and height of trees. It is well known that program properties specified through catamorphisms can be proved by showing the satisfiability of suitable sets of constrained Horn clauses (CHCs). We address the problem of checking the satisfiability of those sets of CHCs, and we propose a method for transforming sets of CHCs into equisatisfiable sets where catamorphisms are no longer present. As a consequence, clauses with catamorphisms can be handled without extending the satisfiability algorithms used by existing CHC solvers. Through an experimental evaluation on a nontrivial benchmark consisting of many list and tree processing algorithms expressed as sets of CHCs, we show that our technique is indeed effective and significantly enhances the performance of state-of-the-art CHC solvers.

We introduce the framework FreeCHR which formalizes the embedding of Constraint Handling Rules (CHR) into a host language, using the concept of initial algebra semantics from category theory. We hereby establish a high-level implementation scheme for CHR as well as a common formalization for both theory and practice. We propose a lifting of the syntax of CHR via an endofunctor in the category Set and a lifting of the very abstract operational semantics of CHR into FreeCHR, using the free algebra, generated by the endofunctor. We give proofs for soundness and completeness with its original definition. We also propose a first abstract execution algorithm and prove correctness with the operational semantics. Finally, we show the practicability of our approach by giving two possible implementations of this algorithm in Haskell and Python. Under consideration in Theory and Practice of Logic Programming.

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.

Answer set programming (ASP), a well-known declarative logic programming paradigm, has recently found practical application in Process Mining. In particular, ASP has been used to model tasks involving declarative specifications of business processes. In this area, Declare stands out as the most widely adopted declarative process modeling language, offering a means to model processes through sets of constraints valid traces must satisfy, that can be expressed in linear temporal logic over finite traces (LTL$_{\text {f}}$). Existing ASP-based solutions encode Declare constraints by modeling the corresponding LTL$_{\text {f}}$ formula or its equivalent automaton which can be obtained using established techniques. In this paper, we introduce a novel encoding for Declare constraints that directly models their semantics as ASP rules, eliminating the need for intermediate representations. We assess the effectiveness of this novel approach on two Process Mining tasks by comparing it with alternative ASP encodings and a Python library for Declare.