A triple correspondence in canonical calculi: Strong cut-elimination, coherence, and non-deterministic semantics

Arnon Avron, Anna Zamansky

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

Abstract

An (n,k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n,k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence to characterize strong cut-elimination in such systems. We show that the following properties of a canonical system G with arbitrary (n,k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix.

Original languageEnglish
Title of host publicationComputer Science - Theory and Applications - Third International Computer Science Symposium in Russia, CSR 2008, Proceedings
PublisherSpringer Verlag
Pages52-63
Number of pages12
ISBN (Print)3540797084, 9783540797081
DOIs
StatePublished - 2008
Externally publishedYes
Event3rd International Computer Science Symposium in Russia, CSR 2008 - Moscow, Russian Federation
Duration: 7 Jun 200812 Jun 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5010 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Computer Science Symposium in Russia, CSR 2008
Country/TerritoryRussian Federation
CityMoscow
Period7/06/0812/06/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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