Algebraic Properties of Qualitative Spatio-Temporal Calculi
This work addresses foundational issues in qualitative spatial and temporal reasoning, which is incremental in clarifying algebraic properties for representation and reasoning.
The paper identifies minimal requirements for binary spatio-temporal calculi and analyzes existing qualitative calculi, providing a classification based on relation algebra notions.
Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.