Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning

  • Authors:

  • Brandon Bennett;Anthony G. Cohn;Frank Wolter;Michael Zakharyaschev

  • Affiliations:

  • School of Computing, University of Leeds, LS2 9JT, UK. brandon@comp.leeds.ac.uk;School of Computing, University of Leeds, LS2 9JT, UK. agc@comp.leeds.ac.uk;Institut für Informatik, Universität Leipzig, Augustus-Platz 10-11, 04109 Leipzig, Germany. wolter@informatik.uni-leipzig.de;Department of Computer Science, King's College, Strand, London WC2R 2LS, UK. mz@dcs.kcl.ac.uk

  • Venue:
  • Applied Intelligence
  • Year:
  • 2002

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Abstract

In this paper we advocate the use of multi-dimensional modal logics as a framework for knowledge representation and, in particular, for representing spatio-temporal information. We construct a two-dimensional logic capable of describing topological relationships that change over time. This logic, called PSTL (Propositional Spatio-Temporal Logic) is the Cartesian product of the well-known temporal logic PTL and the modal logic S4u, which is the Lewis system S4 augmented with the universal modality. Although it is an open problem whether the full PSTL is decidable, we show that it contains decidable fragments into which various temporal extensions (both point-based and interval based) of the spatial logic RCC-8 can be embedded. We consider known decidability and complexity results that are relevant to computation with multi-dimensional formalisms and discuss possible directions for further research.