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.
|Title of host publication||Logic, Language, Information, and Computation - 21st International Workshop, WoLLIC 2014, Proceedings|
|Number of pages||15|
|State||Published - 2014|
|Event||21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014 - Valparaiso, Chile|
Duration: 1 Sep 2014 → 4 Sep 2014
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||21st International Workshop on Logic, Language, Information, and Computation, WoLLIC 2014|
|Period||1/09/14 → 4/09/14|
Bibliographical noteFunding Information:
This research was supported by The Israel Science Foundation (grant no. 280-10).