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.

This is a preliminary abridged version of a forthcoming Technical Report, Computer Science Department, Stanford University.

This research was supported in part by the National Science Foundation under Grant MCS76-83655 and by the Advanced Research Projects Agency of the Department of Defense under Contract MDA903-76-C-0206.