Implication algebras and implication semigroups of binary relations

Andrew Lewis-Smith, Jaš Šemrl*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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Abstract

Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary) relations and present a Stone-style representation theorem. We then show that the (finite) representation decision problem is undecidable for implication semigroups, in stark contrast with implication algebras.
Original languageEnglish
Title of host publicationRelational and Algebraic Methods in Computer Science. RAMiCS 2023.
EditorsR. Glück, L. Santocanale, M. Winter
PublisherSpringer Cham
Pages194-207
Number of pages14
ISBN (Electronic)9783031280832
ISBN (Print)9783031280825
DOIs
Publication statusPublished - 8 Mar 2023
Externally publishedYes

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume13896
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • implication algebras
  • implication semigroups
  • representability as binary relations

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