Bialgebraic Semantics for Logic Programming

Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic programs as reactive systems and exploit abstract techniques developed in that setting. First we use saturation to model the operational semantics of logic programs as coalgebrae on presheaves. Then, we make explicit the underlying algebraic structure by using bialgebrae on presheaves. The resulting semantics turns out to be compositional with respect to conjunction and term substitution. Also, it encodes a parallel model of computation, whose soundness is guaranteed by a built-in notion of synchronisation between different threads

Enhancing Regular Corecursion

Nowadays, data structures which are conceptually infinite, such as streams or infinite trees, are very common in computer science. When it comes to their manipulation, one major problem to face is how to finitely represent and deal with them without incurring in non-terminating behaviours. Regular corecursion is a solution relying on finite representation of regular data structures, and detection of cyclic calls. The topics in the thesis revolve around two enhancements of regular corecursion in different directions. In the first part, we present Corecursive Featherweight Java (coFJ), an object-oriented calculus which supports flexible regular corecursion, that is, allows the programmer to specify the behaviour when a cyclic call is found. In the second part, instead, we extend regular corecursion beyond regular terms, focusing on the significant case of stream definitions

Logic-based Technologies for Intelligent Systems: State of the Art and Perspectives

Together with the disruptive development of modern sub-symbolic approaches to artificial intelligence (AI), symbolic approaches to classical AI are re-gaining momentum, as more and more researchers exploit their potential to make AI more comprehensible, explainable, and therefore trustworthy. Since logic-based approaches lay at the core of symbolic AI, summarizing their state of the art is of paramount importance now more than ever, in order to identify trends, benefits, key features, gaps, and limitations of the techniques proposed so far, as well as to identify promising research perspectives. Along this line, this paper provides an overview of logic-based approaches and technologies by sketching their evolution and pointing out their main application areas. Future perspectives for exploitation of logic-based technologies are discussed as well, in order to identify those research fields that deserve more attention, considering the areas that already exploit logic-based approaches as well as those that are more likely to adopt logic-based approaches in the future

Proceedings of the Workshop on the lambda-Prolog Programming Language

The expressiveness of logic programs can be greatly increased over first-order Horn clauses through a stronger emphasis on logical connectives and by admitting various forms of higher-order quantification. The logic of hereditary Harrop formulas and the notion of uniform proof have been developed to provide a foundation for more expressive logic programming languages. The λ-Prolog language is actively being developed on top of these foundational considerations. The rich logical foundations of λ-Prolog provides it with declarative approaches to modular programming, hypothetical reasoning, higher-order programming, polymorphic typing, and meta-programming. These aspects of λ-Prolog have made it valuable as a higher-level language for the specification and implementation of programs in numerous areas, including natural language, automated reasoning, program transformation, and databases

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

A proof-theoretic approach to coinduction in Horn clause logic

The thesis is on coinduction in Horn clauses. Specifically, it considers productive corecursion, and presents a framework called Coinductive Uniform Proof as a principled approach to coinduction in first-order Horn clause logic. It addresses the challenges of 1) discovering sufficient conditions for logic programs to be productive, 2) providing an explanation of why unification (without occur-check) between goals in a SLD derivation can be exploited to capture productive corecursion, and 3) identifying the principle that unifies the diverse approaches to Horn clause coinduction which are scattered across the literature. The thesis advances the state of the art by 1) providing a sufficient condition for productive corecursion which requires that a logic program does not admit perpetual term-rewriting steps nor existential variables, 2) showing that the goal-unification technique can be used to capture productive corecursion if a goal is no less general than some previous goal to which it unifies, and 3) defining a coinductively sound proof construction method for Horn clauses where a Horn clause to be proved is first asserted as an assumption and then used for its own proof