Converse-PDL with regular inclusion axioms: a framework for MAS logics

摘要

In this paper we study automated reasoning in the modal logic CPDL_(reg) which is a combination of CPDL (Propositional Dynamic Logic with Converse) and REG~c (Regular Grammar Logic with Converse). The logic CPDL is widely used in many areas, including program verification, theory of action and change, and knowledge representation. On the other hand, the logic REG~c is applicable in reasoning about epistemic states and ontologies (via Description Logics). The modal logic CPDL_(reg) can serve as a technical foundation for reasoning about agency. Even very rich multi-agent logics can be embedded into CPDL_(reg) via a suitable translation. Therefore, CPDL_(reg) can serve as a test bed to implement and possibly verify new ideas without providing specific automated reasoning techniques for the logic in question. This process can to a large extent be automated. The idea of embedding various logics into CPDL_(reg) is illustrated on a rather advanced logic TeamLOG~K designed to specify teamwork in multi-agent systems. Apart from defining informational and motivational attitudes of groups of agents, TeamLOG~K allows for grading agents' beliefs, goals and intentions. The current paper is a companion to our paper (Dunin-Keplicz et al.,2010α). The main contribution are proofs of soundness and completeness of the tableau calculus for CPDL_(reg) provided in (Dunin-Keplicz et al., 2010α).