Canonical signed calculi, non-deterministic matrices and cut-elimination

Arnon Avron; Anna Zamansky

doi:10.1007/978-3-540-92687-0_3

Canonical signed calculi, non-deterministic matrices and cut-elimination

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

Abstract

Canonical propositional Gentzen-type calculi are a natural class of systems which in addition to the standard axioms and structural rules have only logical rules where exactly one occurrence of a connective is introduced and no other connective is mentioned. Cut-elimination in such systems is fully characterized by a syntactic constructive criterion of coherence. In this paper we extend the theory of canonical systems to the considerably more general class of signed calculi. We show that the extended criterion of coherence fully characterizes only analytic cutelimination in such calculi, while for characterizing strong and standard cut-elimination a stronger criterion of density is required. Modular semantics based on non-deterministic matrices are provided for every coherent canonical signed calculus.

Original language	English
Title of host publication	Logical Foundations of Computer Science - International Symposium, LFCS 2009, Proceedings
Pages	31-45
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-540-92687-0_3
State	Published - 2009
Externally published	Yes
Event	International Symposium on Logical Foundations of Computer Science, LFCS 2009 - Deerfield Beach, FL, United States Duration: 3 Jan 2009 → 6 Mar 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5407 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Symposium on Logical Foundations of Computer Science, LFCS 2009
Country/Territory	United States
City	Deerfield Beach, FL
Period	3/01/09 → 6/03/09

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-92687-0_3

Cite this

Avron, A., & Zamansky, A. (2009). Canonical signed calculi, non-deterministic matrices and cut-elimination. In Logical Foundations of Computer Science - International Symposium, LFCS 2009, Proceedings (pp. 31-45). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5407 LNCS). https://doi.org/10.1007/978-3-540-92687-0_3

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title = "Canonical signed calculi, non-deterministic matrices and cut-elimination",

abstract = "Canonical propositional Gentzen-type calculi are a natural class of systems which in addition to the standard axioms and structural rules have only logical rules where exactly one occurrence of a connective is introduced and no other connective is mentioned. Cut-elimination in such systems is fully characterized by a syntactic constructive criterion of coherence. In this paper we extend the theory of canonical systems to the considerably more general class of signed calculi. We show that the extended criterion of coherence fully characterizes only analytic cutelimination in such calculi, while for characterizing strong and standard cut-elimination a stronger criterion of density is required. Modular semantics based on non-deterministic matrices are provided for every coherent canonical signed calculus.",

author = "Arnon Avron and Anna Zamansky",

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

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Avron, A & Zamansky, A 2009, Canonical signed calculi, non-deterministic matrices and cut-elimination. in Logical Foundations of Computer Science - International Symposium, LFCS 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5407 LNCS, pp. 31-45, International Symposium on Logical Foundations of Computer Science, LFCS 2009, Deerfield Beach, FL, United States, 3/01/09. https://doi.org/10.1007/978-3-540-92687-0_3

Canonical signed calculi, non-deterministic matrices and cut-elimination. / Avron, Arnon; Zamansky, Anna.
Logical Foundations of Computer Science - International Symposium, LFCS 2009, Proceedings. 2009. p. 31-45 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5407 LNCS).

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

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Avron A, Zamansky A. Canonical signed calculi, non-deterministic matrices and cut-elimination. In Logical Foundations of Computer Science - International Symposium, LFCS 2009, Proceedings. 2009. p. 31-45. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-92687-0_3

Canonical signed calculi, non-deterministic matrices and cut-elimination

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