A Survey of Qualitative Spatial and Temporal Calculi -- Algebraic and Computational Properties

TL;DR

This survey comprehensively reviews all existing qualitative spatial and temporal calculi, focusing on their algebraic and computational properties to facilitate efficient reasoning and cognitive modeling.

Contribution

It provides the first complete overview and classification of qualitative calculi, including generalized definitions and analysis of their algebraic and computational features.

Findings

All existing qualitative calculi are classified by algebraic properties.

Generalized definitions unify the understanding of qualitative calculi.

Computational properties are analyzed to improve reasoning efficiency.

Abstract

Qualitative Spatial and Temporal Reasoning (QSTR) is concerned with symbolic knowledge representation, typically over infinite domains. The motivations for employing QSTR techniques range from exploiting computational properties that allow efficient reasoning to capture human cognitive concepts in a computational framework. The notion of a qualitative calculus is one of the most prominent QSTR formalisms. This article presents the first overview of all qualitative calculi developed to date and their computational properties, together with generalized definitions of the fundamental concepts and methods, which now encompass all existing calculi. Moreover, we provide a classification of calculi according to their algebraic properties.