On the Construction of Analytic Sequent Calculi for Sub-classical Logics
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.
Unable to display preview. Download preview PDF.
- 1.Anderson, A.R., Belnap, N.D.: Entailment: The Logic of Relevance and Neccessity, vol. I. Princeton University Press (1975)Google Scholar
- 3.Avron, A., Konikowska, B., Zamansky, A.: Modular construction of cut-free sequent calculi for paraconsistent logics. In: Proceedings of the 27th Annual IEEE Symposium on Logic in Computer science (LICS), pp. 85–94 (2012)Google Scholar
- 7.Cotrini, C., Gurevich, Y.: Basic primal infon logic. Journal of Logic and Computation (2013)Google Scholar
- 10.Lahav, O., Zohar, Y.: Sat-based decision procedure for analytic pure sequent calculi. To appear in Proceedings of the 7th International Joint Conference on Automated Reasoning, IJCAR (2014)Google Scholar