NONDET~IIi~ISTiC PROPOSITIONAL DYNAMIC LOGIC ~ITH II~T~Q~ECTION IS DECIDABLE

Propositional Dynamic Logic (PDL) of [FL] defines meaning of programs in terms of binary input-output relations. Basic regular operations on programs are interpreted as superposition, union, and reflexive-transitive closure of relations. The intersection, cf. [HI , is a binary program forming functor a~b with the meaning given by the set-theoretical intersection of relations corresponding to programs a and b. By adding intersection of programs to PDL we obtain a programming logic called PDL with intersection. Harel [H] has proved that the problem of whether or not a formula of PDL with intersection has a deterministic model is highly undecidable (~-hard). The present paper shows that in the general case (nondeterministic models allowed) the satisfiability problem for PDL with intersection is decidable in time double exponential in the length of the formula tested. In comparison with PDL with strong loop predicate ED] , this is more powerful and interesting example of a logic which is decidable in contrast to its deterministic case and despite the lack of finite and even tree model properties.