Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

TL;DR

This paper explores a hierarchy of combined spatio-temporal logics, analyzing how different combinations affect expressiveness and computational complexity, revealing a spectrum from decidable to undecidable systems.

Contribution

It systematically investigates the expressiveness and complexity trade-offs in combined spatio-temporal logics derived from various propositional spatial and temporal logics.

Findings

Different combining principles lead to a range of complexities from NP to undecidable.

The hierarchy demonstrates how component logics' complexity influences the combined system.

Results include the identification of conditions under which combined logics are decidable or undecidable.

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.