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

Ori Lahav, Yoni Zohar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationLogic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings
PublisherSpringer Verlag
Pages206-220
Number of pages15
ISBN (Print)9783662441442
DOIs
StatePublished - 2014
Event21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014 - Valparaiso, Chile
Duration: 1 Sep 20144 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8652 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014
Country/TerritoryChile
CityValparaiso
Period1/09/144/09/14

Funding

FundersFunder number
Israel Science Foundation280-10

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