On the construction of analytic sequent calculi for sub-classical logics

Ori Lahav; Yoni Zohar

doi:10.1007/978-3-662-44145-9_15

On the construction of analytic sequent calculi for sub-classical logics

Ori Lahav, Yoni Zohar

Tel Aviv University

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

7 Scopus citations

Abstract

We study the question of when a given set of derivable rules in some basic analytic propositional sequent calculus forms itself an analytic calculus. First, a general syntactic criterion for analyticity in the family of pure sequent calculi is presented. Next, given a basic calculus admitting this criterion, we provide a method to construct weaker pure calculi by collecting simple derivable rules of the basic calculus. The obtained calculi are analytic-by-construction. While the criterion and the method are completely syntactic, our proofs are semantic, based on interpretation of sequent calculi via non-deterministic valuation functions. In particular, this method captures calculi for a wide variety of paraconsistent logics, as well as some extensions of Gurevich and Neeman's primal infon logic.

Original language	English
Title of host publication	Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings
Publisher	Springer Verlag
Pages	206-220
Number of pages	15
ISBN (Print)	9783662441442
DOIs	https://doi.org/10.1007/978-3-662-44145-9_15
State	Published - 2014
Externally published	Yes
Event	21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014 - Valparaiso, Chile Duration: 1 Sep 2014 → 4 Sep 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8652 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014
Country/Territory	Chile
City	Valparaiso
Period	1/09/14 → 4/09/14

Bibliographical note

Funding Information:
This research was supported by The Israel Science Foundation (grant no. 280-10).

Funding

This research was supported by The Israel Science Foundation (grant no. 280-10).

Funders	Funder number
Israel Science Foundation	280-10

Access to Document

10.1007/978-3-662-44145-9_15

Cite this

Lahav, O., & Zohar, Y. (2014). On the construction of analytic sequent calculi for sub-classical logics. In Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings (pp. 206-220). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8652 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-662-44145-9_15

Lahav, Ori ; Zohar, Yoni. / On the construction of analytic sequent calculi for sub-classical logics. Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings. Springer Verlag, 2014. pp. 206-220 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We study the question of when a given set of derivable rules in some basic analytic propositional sequent calculus forms itself an analytic calculus. First, a general syntactic criterion for analyticity in the family of pure sequent calculi is presented. Next, given a basic calculus admitting this criterion, we provide a method to construct weaker pure calculi by collecting simple derivable rules of the basic calculus. The obtained calculi are analytic-by-construction. While the criterion and the method are completely syntactic, our proofs are semantic, based on interpretation of sequent calculi via non-deterministic valuation functions. In particular, this method captures calculi for a wide variety of paraconsistent logics, as well as some extensions of Gurevich and Neeman's primal infon logic.",

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Lahav, O & Zohar, Y 2014, On the construction of analytic sequent calculi for sub-classical logics. in Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8652 LNCS, Springer Verlag, pp. 206-220, 21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014, Valparaiso, Chile, 1/09/14. https://doi.org/10.1007/978-3-662-44145-9_15

On the construction of analytic sequent calculi for sub-classical logics. / Lahav, Ori; Zohar, Yoni.
Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings. Springer Verlag, 2014. p. 206-220 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8652 LNCS).

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

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Lahav O, Zohar Y. On the construction of analytic sequent calculi for sub-classical logics. In Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings. Springer Verlag. 2014. p. 206-220. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-44145-9_15

On the construction of analytic sequent calculi for sub-classical logics

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