Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time

TL;DR

This paper introduces eight new maximal tractable subclasses of Allen's interval algebra that incorporate metric temporal constraints, advancing the understanding of efficient temporal reasoning with both qualitative and quantitative information.

Contribution

It presents eight novel maximal tractable subclasses of Allen's algebra that include metric temporal constraints, some extending previous tractable classes.

Findings

Eight new maximal tractable subclasses identified.

Some subclasses subsume previously known tractable algebras.

Two subclasses can express sequentiality with qualitative and metric time.

Abstract

This paper combines two important directions of research in temporal resoning: that of finding maximal tractable subclasses of Allen's interval algebra, and that of reasoning with metric temporal information. Eight new maximal tractable subclasses of Allen's interval algebra are presented, some of them subsuming previously reported tractable algebras. The algebras allow for metric temporal constraints on interval starting or ending points, using the recent framework of Horn DLRs. Two of the algebras can express the notion of sequentiality between intervals, being the first such algebras admitting both qualitative and metric time.