Journal of Logic and Computation

Dovier, Agostino; Formisano, Andrea

doi: 10.1093/logcom/exae035pmid: N/A

Bistarelli, Stefano; David, Victor; Santini, Francesco; Taticchi, Carlo

doi: 10.1093/logcom/exae039pmid: N/A

The study of Dung-style Argumentation Frameworks in recent years has focused on incorporating time. For example, availability intervals have been added to arguments and relations, resulting in different outputs of Dung semantics over time. This paper examines the probability distribution of arguments over time intervals. Using this temporal probabilistic model, the study explores how these frameworks can be transformed into a probabilistic argumentation according to the constellation approach and how they can be interpreted within the epistemic approach. The epistemic approach relies on the notion of defeat to select significant conflicts based on probability distributions. The study also introduces the temporal acceptability of arguments based on the concept of defence, allowing for more precise results over time. Finally, the models (constellation and epistemic) are extended to account for events that have a duration, i.e. that can occur for several consecutive instants of time.

Gliozzi, Valentina; Pozzato, Gian Luca; Tessore, Gabriele; Valese, Alberto

doi: 10.1093/logcom/exae037pmid: N/A

In this paper we present our final solution to the problem of designing an efficient theorem prover for Conditional Logics with the selection function semantics. Conditional Logics recently have received a renewed attention and have found several applications in knowledge representation and artificial intelligence. In order to provide an efficient theorem prover for Conditional Logics, we introduce labelled sequent calculi for the logics characterized by well-established axioms systems including the axiom of strong centering CS, the axiom of conditional identity ID, the axiom of conditional modus ponens MP, as well as the conditional third excluded middle CEM, rejected by Lewis but endorsed by Stalnaker, as well as for the whole cube of extensions. The proposed calculi revise and improve the calculi SeqS introduced in Olivetti et al. (2007, ACM Trans. Comput. Logics, 8). We also present an implementation of these calculi in SWI Prolog, including a graphical interface in Python as well as standard heuristics and refinements that allow us to obtain an efficient theorem prover for the logics under consideration. Moreover, we present some statistics about the performances of the theorem prover, which are promising and significantly better than those of its predecessor CondLean, an implementation of the calculi SeqS.

Alviano, Mario; Giordano, Laura; Theseider Dupré, Daniele

doi: 10.1093/logcom/exae038pmid: N/A

Weighted knowledge bases for description logics with typicality under a ‘concept-wise’ multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a $\varPi ^{p}_{2}$ upper bound on the complexity of the problem, nonetheless leaving unknown the exact complexity and only providing a proof-of-concept implementation. This paper fulfills the lack by providing a ${P^{NP[log]}}$-completeness result and new ASP encodings that deal with both acyclic and cyclic weighted knowledge bases with large search spaces, as assessed empirically on synthetic test cases. The encodings are used to empower a reasoner for computing solutions and answering queries, possibly interacting with ASP Chef for obtaining an interactive visualization.

Alviano, Mario; Ly Trieu, Ly; Cao Son, Tran; Balduccini, Marcello

doi: 10.1093/logcom/exae036pmid: N/A

Explainable artificial intelligence (XAI) aims at addressing complex problems by coupling solutions with reasons that justify the provided answer. In the context of Answer Set Programming (ASP) the user may be interested in linking the presence or absence of an atom in an answer set to the logic rules involved in the inference of the atom. Such explanations can be given in terms of directed acyclic graphs (DAGs). This article reports on the advancements in the development of the XAI system xASP by revising the main foundational notions and by introducing new ASP encodings to compute minimal assumption sets, explanation sequences, and explanation DAGs. DAGs are shown to the user in an interactive form via the xASP navigator application, also introduced in this work.

Della Schiava, Alex; Piazza, Carla; Romanello, Riccardo

doi: 10.1093/logcom/exae040pmid: N/A

The lack of purely Quantum Programming Languages constitutes a hurdle in the general description of quantum computational processes; the implementation is heavily dependent on the considered quantum computational model. To bypass the obstacle, this paper pursues a new direction, investigating the compilation of classical programming paradigms over different quantum computational models: Gate-Based, Measurement-Based and Adiabatic Quantum Computation. Since graphs can be exploited to describe both classical and quantum computations, the problem of graph encoding on quantum hardware is tightly connected to our purposes. As such, it holds a major relevance in our quest for quantum compilation. While studying these topics through the lenses of Graph Theory, declarative programming emerges as the ideal candidate for such endeavour. In this paper we consider some existing quantum computational models and for each of them we identify the main subtleties in the compilation of classical languages. In turn, we break these complexities down into easier problems to stimulate further developments in this area of research. As it turns out, the observations for each model differ widely. Nevertheless, as for the tasks here considered, no model seems to claim supremacy over the others. In contrast, declarative programming maintains the spot as the ideal candidate for quantum compilation, independently of the model.

Dodaro, Carmine; Galatà, Giuseppe; Gebser, Martin; Maratea, Marco; Marte, Cinzia; Mochi, Marco; Scanu, Marco

doi: 10.1093/logcom/exae041pmid: N/A

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 units. In the past years, Answer Set Programming (ASP) has been successfully employed for addressing and solving the ORS problem. Despite its importance, due to the inherent difficulty of retrieving real data, all the analyses on ORS ASP encodings have been performed on synthetic data so far. In this paper, first we present a new, improved ASP encoding for the ORS problem. Then, we deal with the real case of ASL1 Liguria, an Italian health authority operating through three hospitals, and present adaptations of the ASP encodings to deal with the real-world data. Further, we analyse the resulting encodings on hospital scheduling data by ASL1 Liguria. Results on some scenarios show that the ASP solutions produce satisfying schedules also when applied to such challenging, real data.1

Bertagnon, Alessandro; Gavanelli, Marco

doi: 10.1093/logcom/exae042pmid: N/A

Logic programming is a declarative programming paradigm that finds extensive use in the field of Artificial Intelligence (AI). As a result, it has become a valuable tool used in university courses for teaching students AI techniques. Besides Prolog language, the more recent Answer Set Programming (ASP) language turns out to be a powerful tool for developing advanced applications due to the expressiveness of the language and the availability of efficient solving systems. Unfortunately, the output of ASP solvers can be difficult to interpret, since it is a set of atoms, often long and verbose. This is most true in the case of students learning the language or in the case of experts developing applications for complex real-world problems. For these reasons, the ability to produce, when possible, a graphical representation of the solver output becomes useful to ensure easier interpretation of the results. In this paper we present ASPECT, a sub-language of ASP in which the user can directly define, in an intuitive and declarative way, a graphical representation of the answer set. The ASPECT atoms can be converted into the popular LaTeX markup language to produce vector graphics. The documents produced by ASPECT are easy to embed in documents such as scientific articles, course handouts and presentations. Also, the development of user-friendly interfaces is critical for wider use of similar technologies in the industrial sector as well. Moreover, ASPECT is also extended to deal with temporal information, and provide graphical animations of answer sets that enclose the temporal dimension, such as in planning problems. Finally, we advocate the use of ASPECT to create complex and animated presentations starting from a declarative specification.