Tableaux for type PDL

We give a deterministic exponential, sound and complete tableau-based satisfiability algorithm for the system of Type PDL (τPDL) [9, 8], by extending the algorithm of Goré and Widmann [6] that has been given for the case of the CPDL. The system of τPDL has been introduced to reason about types of actions and while the type semantics have been adopted in [9], here, we follow the standard relational semantics as they have been presented in [8]. We introduce an appropriate tableau calculus for the satisfiability algorithm and in relation with the case of the CPDL, the algorithm that we present for τPDL, handles the backwards possibility operator instead of the converse operator, as well as capabilities statements and abstract processes which are defined as pairs of preconditions and effects, written as φ ⇒ ψ.

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