Auxiliary Modal Operators and the Characterization of Modal Frames

In modal logics we are interested in classes of frames which determine the logic under consideration. Such classes are usually distinguished by their respective frame properties, often also called the modal logic's background theory. In general these characterizations are not unique and it is desireable (and that not only from a theorem prover's perspective) to nd a strongest possible. In this paper an approach is presented which helps in this respect. It allows us to transform a given background theory into one which is more general and which modal logics cannot distinguish from the former because of their syntactic and semantic restrictions. The underlying technique is based on the idea to nd conservative extensions (of a given logic) whose determining properties serve as a starting point from which it is possible to extract signi cantly stronger characterizations of the original logic.