On the Computational Complexity of Spatio-Temporal Logics

Recently, a hierarchy of spatio-temporal languages based on the propositional temporal logic PTL and the spatial languages RCC-8, BRCC-8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open. In this paper, we solve these problems and provide a clear picture of the balance between expressiveness and ‘computational realisability’ within the hierarchy.

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