We introduce a multi-sorted stratified syllogistic, called 4LQS(R), 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 (4LQS(R))(h) of 4LQS(R), consisting of 4LQS(R)-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 (4LQS(R))(3)

On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic

CANTONE, Domenico;NICOLOSI ASMUNDO, MARIANNA
2013-01-01

Abstract

We introduce a multi-sorted stratified syllogistic, called 4LQS(R), 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 (4LQS(R))(h) of 4LQS(R), consisting of 4LQS(R)-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 (4LQS(R))(3)
2013
4-level; Modal logic; Model properties; NP Complete; Satisfiability problems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/35490
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