The modal logic of programs

Abstract

We explore the general framework of Modal Logic and its applicability to program reasoning. We relate the basic concepts of Modal Logic to the programming environment: the concept of “world” corresponds to a program state, and the concept of “accessibility relation” corresponds to the relation of derivability between states during execution. Thus we adopt the Temporal interpretation of Modal Logic. The variety of program properties expressible within the modal formalism is demonstrated. The first axiomatic system studied, the sometime system, is adequate for proving total correctness and ‘eventuality’ properties. However, it is inadequate for proving invariance properties. The stronger nexttime system obtained by adding the next operator is shown to be adequate for invariances as well.