Lahav O., Zohar Y. (2014) On the Construction of Analytic Sequent Calculi for Sub-classical Logics. In: Kohlenbach U., Barceló P., de Queiroz R. (eds) Logic, Language, Information, and Computation. WoLLIC 2014. Lecture Notes in Computer Science, vol 8652. Springer, Berlin, Heidelberg
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.