Enhanced Propositional Dynamic Logic for Reasoning about Concurrent Actions (Extended Abstract)

modeled as relations between states (see (Kozen Tiuryn 1990; Harel 1984; Parikh 1981) for surveys on PDL’s, see also (Stifling 1992) for a somewhat different 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 (R/¢, 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 expression denoting sequential composition, nondeterministic choice, iteration, or test. PDL’s have been originally developed in Theoretical Computer Science to reason about program schemas (Fisher & Ladner 1979), and their variants have been adopted to specify and verify properties of reactive processes (e.g., Hennessy Milner Logic (Hennessy & Milner 1985; Milner 1989), modal mu-calculus (Kozen 1983; Larsen 1990; Stirling 1992)). They also of interest in Philosophical Logic as a formalism to capture "procedural reasoning" (see, for example, (Van Benthem ~z Bergstra 1993; Van Benthem, Van Eijck, & Stebletsova 1993; de Rijke.M 1992; Van Benthem 1991)). In Artificial Intelligence, PDL’s have been extensively used in establishing decidability and computational complexity results of many formalisms: for example they have been used in investigating Common Knowledge (Halpern 1992), Conditional Logics (Friedman & Halpern 1994), Description Logics (Schild 1991; De Giacomo & Lenzerini 1994a; 1994c), Features Logics (Blackburn & Spaan 1993). However they have been only sparingly adopted for reasoning about actions, main exceptions being (Rosenschein 1991; Kautz 1980) (but also (Cohen & Levesque 1990)).