---
title: "An Algebra of Granular Temporal Relations for Qualitative Reasoning"
authors:
  - "Quentin Cohen-Solal"
  - "Maroua Bouzid"
  - "Alexandre Niveau"
doi: ""
url: "https://ijcai.org/proceedings/2015/406"
pdf: "https://ijcai.org/proceedings/2015/0406.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "2869-2874"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

# An Algebra of Granular Temporal Relations for Qualitative Reasoning

Quentin Cohen-Solal, Maroua Bouzid, Alexandre Niveau

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 2869-2874.

## Abstract

In this paper, we propose a qualitative formalism for representing and reasoning about time at different scales. It extends the algebra of Euzenat and overcomes its major limitations, allowing one to reason about relations between points and intervals. Our approach is more expressive than the other algebras of temporal relations: for instance, some relations are more relaxed than those in Allen's algebra, while others are stricter. In particular, it enables the modeling of imprecise, gradual, or intuitive relations, such as just before or almost meet. In addition, we give several results about how a relation changes when considered at different granularities. Finally, we provide an algorithm to compute the algebraic closure of a temporal constraint network in our formalism, which can be used to check its consistency.