Propositional Dynamic Logic in Two- and More Dimensions

Abstract

The Propositional Dynamic Logic PDL extends the Kripke modal logic with the intension to frame the behavior and formalize the properties of computer programs. A program α(as a rule non-deterministic) and a property A are interpreted respectively as a binary relation R(α) and a subset V(A) of some presupposed universe U={u, v, …}. Its elements are refered to as possible worlds or memory states and are traditionally regarded as some indivisible units. The aim of this paper is to suggest a reliable framework and to establish some basic results for that case, where the memory states have themselves been divided and granted the structure of ordered pairs (or generally, ordered N-tuples). In this case, formally R(α) and V(A) will be quaternary and binary relations, respectively. Informally this corresponds to the case of computation with two-cell memory device.