Algebraic Properties of Qualitative Spatio-Temporal Calculi

TL;DR

This paper investigates the algebraic properties of qualitative spatio-temporal calculi, clarifies their minimal requirements, and analyzes how existing calculi meet these algebraic criteria, impacting reasoning algorithms.

Contribution

It identifies minimal algebraic requirements for binary spatio-temporal calculi and evaluates existing calculi against these criteria, linking algebraic properties to reasoning effectiveness.

Findings

Established minimal algebraic requirements for calculi

Analyzed existing calculi for algebraic properties

Classified calculi based on relation algebra notions

Abstract

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.