TY - GEN
T1 - On the construction of analytic sequent calculi for sub-classical logics
AU - Lahav, Ori
AU - Zohar, Yoni
N1 - Funding Information:
This research was supported by The Israel Science Foundation (grant no. 280-10).
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84906872143
U2 - 10.1007/978-3-662-44145-9_15
DO - 10.1007/978-3-662-44145-9_15
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AN - SCOPUS:84906872143
SN - 9783662441442
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 206
EP - 220
BT - Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings
PB - Springer Verlag
T2 - 21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014
Y2 - 1 September 2014 through 4 September 2014
ER -