Canonical constructive systems

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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 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 to show that such a system always admits a strong form of the cut-elimination theorem, and for providing a decision procedure for such systems.

Original languageEnglish
Title of host publicationAutomated Reasoning with Analytic Tableaux and Related Methods - 18th International Conference, TABLEAUX 2009, Proceedings
Pages62-76
Number of pages15
DOIs
StatePublished - 2009
Event18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009 - Oslo, Norway
Duration: 6 Jul 200910 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5607 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009
Country/TerritoryNorway
CityOslo
Period6/07/0910/07/09

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