Strict canonical constructive systems

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We define the notions of a canonical inference rule and a canonical constructive system in the framework of strict single-conclusion Gentzen-type systems (or, equivalently, natural deduction systems), and develop a corresponding general non-deterministic Kripke-style semantics. We show that every strict constructive canonical system induces a class of non-deterministic Kripke-style frames, for which it is strongly sound and complete. This non-deterministic semantics is used for proving a strong form of the cut-elimination theorem for such systems, and for providing a decision procedure for them. These results identify a large family of basic constructive connectives, including the standard intuitionistic connectives, together with many other independent connectives.

Original languageEnglish
Title of host publicationFields of Logic and Computation - Essays Dedicated to Yuri Gurevich on the Occasion of His 70th Birthday
PublisherSpringer Berlin Heidelberg
Pages75-94
Number of pages20
ISBN (Print)3642150241, 9783642150241
DOIs
StatePublished - 2010
Event35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010, and 19th EACSL Annual Conference on Computer Science Logic, CSL 2010 - Brno, Czech Republic
Duration: 22 Aug 201022 Aug 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6300 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010, and 19th EACSL Annual Conference on Computer Science Logic, CSL 2010
Country/TerritoryCzech Republic
CityBrno
Period22/08/1022/08/10

Keywords

  • Kripke semantics
  • cut-elimination
  • non-classical logics
  • non-deterministic semantics
  • sequent calculus

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