Connecting Qualitative Spatial and Temporal Representations by Propositional Closure

This paper establishes new relationships between existing qualitative spatial and temporal representations. Qualitative spatial and temporal representation (QSTR) is concerned with abstractions of infinite spatial and temporal domains, which represent configurations of objects using a finite vocabulary of relations, also called a qualitative calculus. Classically, reasoning in QSTR is based on constraints. An important task is to identify decision procedures that are able to handle constraints from a single calculus or from several calculi. In particular the latter aspect is a longstanding challenge due to the multitude of calculi proposed. In this paper we consider propositional closures of qualitative constraints which enable progress with respect to the longstanding challenge. Propositional closure allows one to establish several translations between distinct calculi. This enables joint reasoning and provides new insights into computational complexity of individual calculi. We conclude that the study of propositional languages instead of previously considered purely relational languages is a viable research direction for QSTR leading to expressive formalisms and practical algorithms.