Converse, Local Determinism, and Graded Nondeterminism in Propositional Dynamic Logics Converse, Local Determinism, and Graded Nondeterminism in Propositional Dynamic Logics

Recent work on Knowledge Representation has brought new interest to Propositional Dynamic Logics PDL s by pointing out a tight correspondence between these logics and logics for representing structured knowledge Description Logics TerminologicalLanguages Nevertheless this work has also made apparent the lack in the known PDL s of certain constructs needed to fully exploit the correspondence These are constructs to locally wrt single states constrain the running of an atomic program or its converse the running of the atomic program backward to be deterministic or to have a speci ed amount of nondeterminism only In fact we believe that PDL s can take advantage of this kind of constructs to model many interesting properties of actual computations In this paper we extend Converse PDL rst by including a construct for local determinism of simple programs either an atomic program or the converse of an atomic program and then by including constructs for graded nondeterminism of simple programs The latter locally constrain the nondeterminism of simple programs by limiting the minimum and the maximum number of states satisfying a speci ed property that are reachable by the running of a simple program from a certain state The main result of the paper is that both the resulting logics are strictly more expressive than Converse Deterministic PDL Converse PDL where all atomic programs are interpreted as partial functions but still decidable in deterministic exponential time