Canonical signed calculi, non-deterministic matrices and cut-elimination

Arnon Avron, Anna Zamansky

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

Abstract

Canonical propositional Gentzen-type calculi are a natural class of systems which in addition to the standard axioms and structural rules have only logical rules where exactly one occurrence of a connective is introduced and no other connective is mentioned. Cut-elimination in such systems is fully characterized by a syntactic constructive criterion of coherence. In this paper we extend the theory of canonical systems to the considerably more general class of signed calculi. We show that the extended criterion of coherence fully characterizes only analytic cutelimination in such calculi, while for characterizing strong and standard cut-elimination a stronger criterion of density is required. Modular semantics based on non-deterministic matrices are provided for every coherent canonical signed calculus.

Original languageEnglish
Title of host publicationLogical Foundations of Computer Science - International Symposium, LFCS 2009, Proceedings
Pages31-45
Number of pages15
DOIs
StatePublished - 2009
EventInternational Symposium on Logical Foundations of Computer Science, LFCS 2009 - Deerfield Beach, FL, United States
Duration: 3 Jan 20096 Mar 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5407 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Symposium on Logical Foundations of Computer Science, LFCS 2009
Country/TerritoryUnited States
CityDeerfield Beach, FL
Period3/01/096/03/09

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