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

arXiv: https://arxiv.org/abs/1606.00133 · HTML: https://mlsanity.com/paper/1606.00133/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2016.

## Built on by (most cited first, 3 of 3)

- [Formalizing and Evaluating Requirements of Perception Systems for Automated Vehicles using Spatio-Temporal Perception Logic](https://mlsanity.com/paper/2206.14372/) (2022)
- [Explainable Scene Understanding with Qualitative Representations and Graph Neural Networks](https://mlsanity.com/paper/2504.12817/) (2025)
- [QSTRBench: a New Benchmark to Evaluate the Ability of Language Models to Reason with Qualitative Spatial and Temporal Calculi](https://mlsanity.com/paper/2605.18380/) (2026)

## Abstract (arXiv)

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.