Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

Details Combining Spatial and Temporal Logics: Expressiveness vs. Complexity Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

2011-10-12

arxiv.org/abs/1110.2726v1

Journal Of Artificial Intelligence Research, Volume 23, pages 167-243, 2005

Computer Science

Artificial Intelligence

Scientific paper

10.1613/jair.1537

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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