On the Satisfiability Problem for a 4-level Quantified Syllogistic and Some Applications to Modal Logic

Authors:
Domenico Cantone;Marianna Nicolosi Asmundo
Affiliations:
Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, I-95125 Catania, Italy. cantone@dmi.unict.it;Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, I-95125 Catania, Italy. nicolosi@dmi.unict.it
Venue:
Fundamenta Informaticae - Special Issue on the Italian Conference on Computational Logic: CILC 2011
Year:
2013

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Abstract

We introduce a multi-sorted stratified syllogistic, called 4LQSR, admitting variables of four sorts and a restricted form of quantification over variables of the first three sorts, and prove that it has a solvable satisfiability problem by showing that it enjoys a small model property. Then, we consider the fragments 4LQSRh of 4LQSR, consisting of 4LQSR-formulae whose quantifier prefixes have length bounded by h ≥ 2 and satisfying certain additional syntactical constraints, and prove that each of them has an NP-complete satisfiability problem. Finally we show that the modal logic K45 can be expressed in 4LQSR3.