Reasoning on Interval and Point-based Disjunctive Metric Constraints in Temporal Contexts

TL;DR

This paper presents a novel temporal reasoning model for disjunctive metric constraints on intervals and points, incorporating labels, hierarchies, and non-binary constraints to handle complex temporal contexts.

Contribution

It introduces a labeled temporal algebra with reasoning algorithms capable of managing hierarchical, disjunctive, and non-binary temporal constraints in a unified framework.

Findings

Algorithms guarantee consistency and minimal networks.

Model handles context-dependent disjunctive constraints.

Proposed improvements mitigate exponential complexity.

Abstract

We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defines labeled disjunctive metric point-based constraints, where each disjunct in each input disjunctive constraint is univocally associated to a label. Reasoning algorithms manage labeled constraints, associated label lists, and sets of mutually inconsistent disjuncts. These algorithms guarantee consistency and obtain a minimal network. Additionally, constraints can be organized in a hierarchy of alternative temporal contexts. Therefore, we can reason on context-dependent disjunctive metric constraints on intervals and points. Moreover, the model is able to represent non-binary constraints, such that logical dependencies on disjuncts in constraints can be handled. The computational cost of reasoning algorithms is exponential in accordance with the underlying problem complexity, although some improvements are proposed.