Rewrite rule systems for modal propositional logic

  • Annie Foret
Submitted Papers
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 343)

Abstract

The aim of this paper is to explain our new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K,Q,T and S5.

These systems are presented as extensions of Hsiang's system for classical propositional calculus [7].

We have checked local confluence with the rewrite rule system K.B. developped by the Formel project at INRIA[2,4]. We prove that these systems are noetherian, and then infer their confluence from Newman's lemma.

Therefore each term rewriting system provides a new automated decision procedure and defines a canonical form for the corresponding logic. We also show how to characterize the canonical forms thus obtained.

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Copyright information

© Akademie-Verlag Berlin 1988

Authors and Affiliations

  • Annie Foret
    • 1
  1. 1.University Paris 6 and INRIA Domaine de Voluceau RocquencourtLe ChesnayFrance

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