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    Combining spatial and temporal logics: expressiveness vs. complexity

    Gabelaia, D. and Kontchakov, Roman and Kurucz, A. and Wolter, F. and Zakharyaschev, Michael (2005) Combining spatial and temporal logics: expressiveness vs. complexity. Journal of Artificial Intelligence Research 23 , pp. 167-243. ISSN 1076-9757.

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    Abstract

    In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.

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