---
title: "Path Consistency in a Network of Non-Convex Intervals"
authors:
  - "Robert A. Morris"
  - "William D. Shoaff"
  - "Lina Khatib"
doi: ""
url: "https://ijcai.org/proceedings/1993/92"
pdf: "https://ijcai.org/proceedings/1993/0092.pdf"
venue: "Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence"
year: 1993
pages: "655-660"
track: "Knowledge Representation"
keywords:
---

# Path Consistency in a Network of Non-Convex Intervals

Robert A. Morris, William D. Shoaff, Lina Khatib

*Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence*, pages 655-660.

## Abstract

Reasoning about time often involves incomplete information about periods and their relationships. Varieties of incompleteness include uncertainty about the number of objects involved, the distribution of a set of temporal relations among these objects, and what can be called the participation of a set of objects in a temporal relation. A solution to the problem of representing and reasoning about incomplete temporal information of these kinds is forthcoming if a restricted class of non-convex intervals (called n-intervals) is added to the temporal domain of discourse. Ann-interval corresponds to the common sense notion of a recurring period of time with a (possibly) unspecified number of occurrences. In this paper, we formalize a representation for temporal reasoning problems using n-intervals. The language of the framework is restricted in such a way that tractable techniques from constraint satisfaction can be applied. Specifically, it is demonstrated how the problem of determining path-consistency in a network of binary n-interval relations can be solved.