Minimal Semantics for Action Specifications in First-order Dynamic Logic

In this paper we investigate minimal semantics for First Order Dynamic Logic formulas. The goal is to be able to write action specifications in a declarative pre/post-condition style. The declarative specification of actions comes with some well known problems: the frame problem, the qualification problem and the ramification problem. We incorporate the assumptions that are inherent to both the frame and qualification problem into the semantics of Dynamic Logic by defining orderings over Dynamic Logic models. These orderings allow us to identify for each declarative Dynamic Logic action specification a unique intended model. This unique model represents the system that must be associated with the specification given the prefential semantics that is defined by the orderings.