Canonical constructive systems

Arnon Avron; Ori Lahav

doi:10.1007/978-3-642-02716-1_6

Canonical constructive systems

Arnon Avron^*, Ori Lahav

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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 language	English
Title of host publication	Automated Reasoning with Analytic Tableaux and Related Methods - 18th International Conference, TABLEAUX 2009, Proceedings
Pages	62-76
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-642-02716-1_6
State	Published - 2009
Event	18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009 - Oslo, Norway Duration: 6 Jul 2009 → 10 Jul 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5607 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009
Country/Territory	Norway
City	Oslo
Period	6/07/09 → 10/07/09

Funding

Funders	Funder number
Israel Science Foundation	809-06

Access to Document

10.1007/978-3-642-02716-1_6

Cite this

Avron, A., & Lahav, O. (2009). Canonical constructive systems. In Automated Reasoning with Analytic Tableaux and Related Methods - 18th International Conference, TABLEAUX 2009, Proceedings (pp. 62-76). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5607 LNAI). https://doi.org/10.1007/978-3-642-02716-1_6

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title = "Canonical constructive systems",

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.",

author = "Arnon Avron and Ori Lahav",

note = "Funding Information: This research was supported by THE ISRAEL SCIENCE FOUNDATION (grant No 809-06).; 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009 ; Conference date: 06-07-2009 Through 10-07-2009",

year = "2009",

doi = "10.1007/978-3-642-02716-1_6",

language = "אנגלית",

isbn = "3642027156",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "62--76",

booktitle = "Automated Reasoning with Analytic Tableaux and Related Methods - 18th International Conference, TABLEAUX 2009, Proceedings",

}

Avron, A & Lahav, O 2009, Canonical constructive systems. in Automated Reasoning with Analytic Tableaux and Related Methods - 18th International Conference, TABLEAUX 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5607 LNAI, pp. 62-76, 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2009, Oslo, Norway, 6/07/09. https://doi.org/10.1007/978-3-642-02716-1_6

Canonical constructive systems. / Avron, Arnon ; Lahav, Ori.
Automated Reasoning with Analytic Tableaux and Related Methods - 18th International Conference, TABLEAUX 2009, Proceedings. 2009. p. 62-76 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5607 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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.

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Canonical constructive systems

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