Canonical calculi: Invertibility, axiom expansion and (non)-determinism

Arnon Avron, Agata Ciabattoni, Anna Zamansky

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

Abstract

We apply the semantic tool of non-deterministic matrices to characterize two important properties of canonical Gentzen-type calculi: invertibility of rules and axiom expansion. We show that in every canonical calculus G satisfying a natural condition, the following are equivalent: (i) the connectives of G admit axiom expansion, (ii) the rules of G are invertible, and (iii) G has a characteristic finite deterministic matrix.

Original languageEnglish
Title of host publicationComputer Science - Theory and Applications - 4th International Computer Science Symposium in Russia, CSR 2009, Proceedings
Pages26-37
Number of pages12
DOIs
StatePublished - 2009
Externally publishedYes
Event4th International Computer Science Symposium in Russia, CSR 2009 - Novosibirsk, Russian Federation
Duration: 18 Aug 200923 Aug 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5675 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Computer Science Symposium in Russia, CSR 2009
Country/TerritoryRussian Federation
CityNovosibirsk
Period18/08/0923/08/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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