License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2021.17
URN: urn:nbn:de:0030-drops-153723
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15372/
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Gu, Tao ; Zanasi, Fabio

Functorial Semantics as a Unifying Perspective on Logic Programming

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LIPIcs-CALCO-2021-17.pdf (0.9 MB)

Abstract

Logic programming and its variations are widely used for formal reasoning in various areas of Computer Science, most notably Artificial Intelligence. In this paper we develop a systematic and unifying perspective for (ground) classical, probabilistic, weighted logic programs, based on categorical algebra. Our departure point is a formal distinction between the syntax and the semantics of programs, now regarded as separate categories. Then, we are able to characterise the various variants of logic program as different models for the same syntax category, i.e. structure-preserving functors in the spirit of Lawvere’s functorial semantics.
As a first consequence of our approach, we showcase a series of semantic constructs for logic programming pictorially as certain string diagrams in the syntax category. Secondly, we describe the correspondence between probabilistic logic programs and Bayesian networks in terms of the associated models. Our analysis reveals that the correspondence can be phrased in purely syntactical terms, without resorting to the probabilistic domain of interpretation.

BibTeX - Entry

@InProceedings{gu_et_al:LIPIcs.CALCO.2021.17,
  author =	{Gu, Tao and Zanasi, Fabio},
  title =	{{Functorial Semantics as a Unifying Perspective on Logic Programming}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15372},
  URN =		{urn:nbn:de:0030-drops-153723},
  doi =		{10.4230/LIPIcs.CALCO.2021.17},
  annote =	{Keywords: string diagrams, functorial semantics, logic programming}
}

Keywords: string diagrams, functorial semantics, logic programming
Collection: 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)
Issue Date: 2021
Date of publication: 08.11.2021

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