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

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Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning (2000)

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by Brandon Bennett , Anthony G. Cohn , Frank Wolter , Michael Zakharyaschev

Venue:	APPLIED INTELLIGENCE
Citations:	53 - 6 self

BibTeX

@ARTICLE{Bennett00multi-dimensionalmodal,
    author = {Brandon Bennett and Anthony G. Cohn and Frank Wolter and Michael Zakharyaschev},
    title = {Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning},
    journal = {APPLIED INTELLIGENCE},
    year = {2000},
    volume = {17},
    pages = {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 spatiotemporal 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 muli-dimensional formalisms and discuss possible directions for further research.

Keyphrases

multi-dimensional modal logic spatio-temporal reasoning modal logic s4u cartesian product muli-dimensional formalism various temporal extension decidable fragment propositional spatio-temporal logic topological relationship universal modality two-dimensional logic full pstl spatial logic rcc-8 knowledge representation possible direction open problem spatiotemporal information complexity result lewis system s4 well-known temporal logic ptl

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