Canonical Gentzen-type calculi with (n,k)-ary quantifiers

Anna Zamansky, Arnon Avron

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

Abstract

Propositional canonical Gentzen-type systems, introduced in [1], are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a connective is introduced and no other connective is mentioned. [1] provides a constructive coherence criterion for the non-triviality of such systems and shows that a system of this kind admits cut-elimination iff it is coherent. The semantics of such systems is provided using two-valued nondeterministic matrices (2Nmatrices). [14] extends these results to systems with unary quantifiers of a very restricted form. In this paper we substantially extend the characterization of canonical systems to (n, kc)-ary quantifiers, which bind k distinct variables and connect n formulas. We show that the coherence criterion remains constructive for such systems, and that for the case of k ε {0, 1}: (i) a canonical system is coherent iff it has a strongly characteristic 2Nmatrix, and (ii) if a canonical system is coherent, then it admits cut-elimination.

Original languageEnglish
Title of host publicationAutomated Reasoning - Third International Joint Conference, IJCAR 2006, Proceedings
PublisherSpringer Verlag
Pages251-265
Number of pages15
ISBN (Print)3540371877, 9783540371878
DOIs
StatePublished - 2006
EventThird International Joint Conference on Automated Reasoning, IJCAR 2006 - Seattle, WA, United States
Duration: 17 Aug 200620 Aug 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4130 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceThird International Joint Conference on Automated Reasoning, IJCAR 2006
Country/TerritoryUnited States
CitySeattle, WA
Period17/08/0620/08/06

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