Mechanising first-order temporal resolution

  • Authors:

  • Boris Konev;Anatoli Degtyarev;Clare Dixon;Michael Fisher;Ullrich Hustadt

  • Affiliations:

  • Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, King's College London, Strand, London, UK;Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK

  • Venue:
  • Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
  • Year:
  • 2005

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Abstract

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. Although a complete and correct resolution-style calculus has already been suggested for this specific fragment, this calculus involves constructions too complex to be of practical value. In this paper, we develop a machine-oriented clausal resolution method which features radically simplified proof search. We first define a normal form for monodic formulae and then introduce a novel resolution calculus that can be applied to formulae in this normal form. By careful encoding, parts of the calculus can be implemented using classical first-order resolution and can, thus, be efficiently implemented. We prove correctness and completeness results for the calculus and illustrate it on a comprehensive example. An implementation of the method is briefly discussed.