Enhanced Propositional Dynamic Logic for Reasoning about Concurrent Actions

Introduction This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about ac tions Propositional Dynamic Logics PDL s are modal logics for describing and reasoning about system dynamics in terms of properties of states and actions modeled as relations between states see Kozen Tiuryn Harel Parikh for surveys on PDL s see also Stirling for a somewhat di erent account The language of PDL includes formulae built from the boolean combinations of atomic propositions that are interpreted as simple properties of states plus the construct hRi where is a formula and R is an action whose meaning is that it is possible to perform R and terminate in a state where is true The action R can be either an atomic action or a complex expres sion denoting sequential composition nondeterministic choice iteration or test PDL s have been originally developed in Theo retical Computer Science to reason about program schemas Fisher Ladner and their variants have been adopted to specify and verify properties of reactive processes e g Hennessy Milner Logic Hen nessy Milner Milner modal mu calculus Kozen Larsen Stirling They are also of interest in Philosophical Logic as a formal ism to capture procedural reasoning see for ex ample Van Benthem Bergstra Van Ben them Van Eijck Stebletsova de Rijke M Van Benthem In Arti cial Intelligence PDL s have been exten sively used in establishing decidability and computa tional complexity results of many formalisms for ex ample they have been used in investigating Common Knowledge Halpern Conditional Logics Fried man Halpern Description Logics Schild De Giacomo Lenzerini a c Features Log ics Blackburn Spaan However they have been only sparingly adopted for reasoning about ac tions main exceptions being Rosenschein Kautz but also Cohen Levesque