The modal logic of programs

  • Zohar Manna
  • Amir Pnueli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)


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.


Modal Logic Critical Section Accessibility Relation Mutual Exclusion Proper Part 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Zohar Manna
    • 1
  • Amir Pnueli
    • 2
  1. 1.Stanford University and Weizmann InstituteUSA
  2. 2.Tel-Aviv UniversityIsrael

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