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arXiv · 1110.2726

Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

D. Gabelaia·R. Kontchakov·A. Kurucz·F. Wolter·M. Zakharyaschev
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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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D. Gabelaia, R. Kontchakov, A. Kurucz, F. Wolter, M. Zakharyaschev. 2011-10-12. Combining Spatial and Temporal Logics: Expressiveness vs. Complexity. https://doi.org/10.1613/jair.1537

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