Generalized non-deterministic matrices and (n,k)-ary quantifiers

Arnon Avron, Anna Zamansky

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


An (n, k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical Gentzen-type systems with (n, k)-ary quantifiers are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of an (n, k)-ary quantifier is introduced. The semantics of such systems for the case of k ∈{0,1} are provided in [16] using two-valued non-deterministic matrices (2Nmatrices). A constructive syntactic coherence criterion for the existence of a 2Nmatrix for which a canonical system is strongly sound and complete, is formulated there. In this paper we extend these results from the case of k ∈ {0,1} to the general case of k > 0. We show that the interpretation of quantifiers in the framework of Nmatrices is not sufficient for the case of k > 1 and introduce generalized Nmatrices which allow for a more complex treatment of quantifiers. Then we show that (i) a canonical calculus G is coherent iff there is a 2GNmatrix, for which G is strongly sound and complete, and (ii) any coherent canonical calculus admits cut-elimination.

Original languageEnglish
Title of host publicationLogical Foundations of Computer Science - International Symposium, LFCS 2007, Proceedings
PublisherSpringer Verlag
Number of pages15
ISBN (Print)3540727329, 9783540727323
StatePublished - 2007
Externally publishedYes
EventInternational Symposium on Logical Foundations of Computer Science, LFCS 2007 - New York, NY, United States
Duration: 4 Jun 20077 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4514 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Symposium on Logical Foundations of Computer Science, LFCS 2007
Country/TerritoryUnited States
CityNew York, NY

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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