Bialgebraic Semantics for Logic Programming

Filippo Bonchi; Fabio Zanasi

doi:10.2168/LMCS-11(1:14)2015

Filippo Bonchi ; Fabio Zanasi - Bialgebraic Semantics for Logic Programming

lmcs:1155 - Logical Methods in Computer Science, March 30, 2015, Volume 11, Issue 1 - https://doi.org/10.2168/LMCS-11(1:14)2015

Bialgebraic Semantics for Logic ProgrammingArticle

Authors: Filippo Bonchi ; Fabio Zanasi

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.

https://doi.org/10.2168/LMCS-11(1:14)2015

Source: arXiv.org:1502.06095

Volume: Volume 11, Issue 1

Secondary volumes: Selected Papers of the 5th Conference on Algebra and Coalgebra in Computer Science (CALCO 2013)

Published on: March 30, 2015

Imported on: February 28, 2014

Keywords: Computer Science - Logic in Computer Science

Licence: arXiv.org - Non-exclusive license to distribute

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

9 Documents citing this article

Alexander V. Gheorghiu;David J. Pym, 2025, Semantic Foundations of Reductive Reasoning, Topoi, 10.1007/s11245-025-10211-6, https://doi.org/10.1007/s11245-025-10211-6.

Alexander V. Gheorghiu;Simon Docherty;David J. Pym, 2023, Reductive Logic, Proof-Search, and Coalgebra: A Perspective from Resource Semantics, Outstanding contributions to logic, pp. 833-875, 10.1007/978-3-031-24117-8_23.

Roberto Bruni;Ugo Montanari;Giorgio Mossa, 2019, A Coalgebraic Approach to Unification Semantics of Logic Programming, CINECA IRIS Institutial research information system (University of Pisa), pp. 223-240, 10.1007/978-3-030-31175-9_13, http://hdl.handle.net/11568/1029374.

Bartek Klin;Julian Salamanca, 2018, Iterated Covariant Powerset is not a Monad, Electronic Notes in Theoretical Computer Science, 341, pp. 261-276, 10.1016/j.entcs.2018.11.013, https://doi.org/10.1016/j.entcs.2018.11.013.

Brendan Fong;Fabio Zanasi, 2018, Universal Constructions for (Co)Relations: categories, monoidal categories, and props, Logical Methods in Computer Science, Volume 14, Issue 3, Categorical models and logic, 10.23638/lmcs-14(3:14)2018, https://doi.org/10.23638/lmcs-14(3:14)2018.

Ekaterina Komendantskaya;John Power, 2018, Logic programming: Laxness and saturation, arXiv (Cornell University), 101, pp. 1-21, 10.1016/j.jlamp.2018.07.004, http://arxiv.org/abs/1608.07708.

John Power, 2017, Proceedings of the First Workshop on Coalgebra, Horn Clause Logic Programming and Types, Electronic Proceedings in Theoretical Computer Science, 258, pp. 74-75, 10.4204/eptcs.258.8, https://doi.org/10.4204/eptcs.258.8.

Ekaterina Komendantskaya;John Power, 2016, Category Theoretic Semantics for Theorem Proving in Logic Programming: Embracing the Laxness, Lecture notes in computer science, pp. 94-113, 10.1007/978-3-319-40370-0_7.

Gu, Tao;Zanasi, Fabio, 2013, Causal Theories: A Categorical Perspective on Bayesian Networks, arXiv (Cornell University), 10.4230/lipics.calco.2021.17, http://arxiv.org/abs/1301.6201.

Sources : OpenCitations, OpenAlex & Crossref

Share and export

Consultation statistics

This page has been seen 2281 times.

This article's PDF has been downloaded 801 times.