Alternative axiomatics and complexity of deliberative STIT theories

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of the Chellas STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and the Chellas' STIT.Comment: Submitted to the Journal of Philosophical Logic; 13 pages excluding anne

Products, or how to create modal logics of high complexity

The aim of this paper is to exemplify the complexity of the satisfiability problem of products of modal logics. Our main goal is to arouse interest for the main open problem in this area: a tight complexity bound for the satisfiability problem of the product K x K. At present, only non-elementary decision procedures for this problem are known. Our modest contribution is two-fold. We show that the problem of deciding K x K-satisfiability of formulas of modal depth two is already hard for nondeterministic exponential time, and provide a matching upper bound. For the full language, a new proof for decidability is given which combines filtration and selective generation techniques from modal logic. We put products of modal logics into an historic perspective and review the most important results

Products, or How to Create Modal Logics of High Complexity

Abstract The aim of this paper is to exemplify the complexity of the satisfiability problem of products of modal logics. Our main goal is to arouse interest for the main open problem in this area: a tight complexity bound for the satisfiability problem of the product K\Theta K. At present, only non-elementary decision procedures for this problem are known. Our modest contribution is two-fold. We show that the problem of deciding K\Theta K-satisfiability of formulas of modal depth two is already hard for nondeterministic exponential time, and provide a matching upper bound. For the full language, a new proof for decidability is given which combines filtration and selective generation techniques from modal logic. We put products of modal logics into an historic perspective and review the most important results