On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic (extended version)
Logic in Computer Science
2012-09-11 v1
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 (4LQSR)^h of 4LQSR, consisting of 4LQSR-formulae whose quantifier prefixes have length bounded by h > 1 and satisfying certain syntactic 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 4LQSR^3.
Keywords
Cite
@article{arxiv.1209.1943,
title = {On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic (extended version)},
author = {Domenico Cantone and Marianna Nicolosi Asmundo},
journal= {arXiv preprint arXiv:1209.1943},
year = {2012}
}
Comments
Extended version of a paper to be published in Fundamenta Informaticae