Abstract

This paper is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the fundaments are laid for later results. These fundaments consist of a thorough treatment of a construction method to obtain modal models. This construction method is used to reprove some known results in the area of interpretability like the modal completeness of the logic IL. Next, the method is applied to obtain new results: the modal completeness of the logic ILMo, and modal completeness of ILW*