A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae

  • Renate A. Schmidt
  • Ullrich Hustadt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2741)


In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity, Euclideanness and functionality, to decidable logics. The goal of the axiomatic translation principle is to find simplified theories, which capture the inference problems in the original theory, but in a way that is more amenable to automation and easier to deal with by existing theorem provers. The principle of the axiomatic translation is conceptually very simple and can be largely automated. Soundness is automatic under reasonable assumptions, and termination of ordered resolution is easily achieved, but the non-trivial part of the approach is proving completeness.


Modal Logic Description Logic Kripke Model Axiom Schema Modal Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Renate A. Schmidt
    • 1
    • 2
  • Ullrich Hustadt
    • 3
  1. 1.University of Manchester 
  2. 2.Max Planck Institute for Computer ScienceSaarbrücken
  3. 3.University of Liverpool 

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