Ockhamist Propositional Dynamic Logic: A Natural Link between PDL and CTL*

Abstract

We present a new logic called Ockhamist Propositional Dynamic Logic, OPDL, which provides a natural link between PDL and CTL * . We show that both PDL and CTL * can be polynomially embedded into OPDL in a rather simple and direct way. More generally, the semantics on which OPDL is based provides a unifying framework for making the dynamic logic family and the temporal logic family converge in a single logical framework. Decidability of the satisfiability problem for OPDL is studied in the paper.

Decidability and Expressivity of Ockhamist Propositional Dynamic Logics

“…In [2] a new logic, called Ockhamist Propositional Dynamic Logic (OPDL) has been introduced. This logic connects the family of dynamic logics with the family of branching-time temporal logics, two families of logic that are traditionally used in artificial intelligence for the verification of programs and for modelling autonomous agents and multi-agent systems (MAS).…”

“…As shown in [2], OPDL offers the right "bridge" between these two families of logics, as it embeds in a natural and polynomial way both Propositional Dynamic Logic (PDL) [10] and Full Computation Tree Logic (CTL * ) [14]. Existing embeddings of both PDL and CTL * are rather complicated and unnatural.…”

“…The original semantics for OPDL given by [2] is based on the concept of OPDL Ockhamist model, which can be seen as an extension with a program component of Zanardo's Ockhamist model for branching-time temporal logics [20]. Specifically, in an OPDL Ockhamist model, temporal transitions between states are labelled with sets of atomic programs.…”

“…Specifically, in an OPDL Ockhamist model, temporal transitions between states are labelled with sets of atomic programs. A second variant of OPDL is studied by [2], called OPDL lts . Like PDL, OPDL lts is interpreted in labelled transition systems (LTS).…”

“…The OPDL Ockhamist semantics is proved to correspond to the fusion closure condition in the path semantics. Observing that OPDL lts studied by [2] lacks the conservative property, a new variant of OPDL, called OPDL lc , is devised by adding the limit closure property to the path semantics, thereby imitating the difference between the semantics for Bundled CTL * (BCTL * ) and the semantics for CTL * . We show that the satisfiability problems of OPDL and OPDL lts are both 2EXPTIME-complete, the same complexity as for CTL * .…”