Allen's Interval Algebra Makes the Difference

TL;DR

This paper introduces a new encoding of Allen's Interval Algebra using answer-set programming with difference constraints, demonstrating its potential for improved reasoning in temporal applications.

Contribution

The paper presents a novel ASP(DL) encoding for Allen's Interval Algebra, enabling efficient reasoning and suggesting applicability to other point-based calculi.

Findings

Preliminary experiments show promising performance of the ASP(DL) encoding.

The encoding facilitates reasoning tasks in planning, scheduling, and temporal databases.

Potential for extending the approach to other temporal calculi.

Abstract

Allen's Interval Algebra constitutes a framework for reasoning about temporal information in a qualitative manner. In particular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions, events, or tasks, and binary relations such as precedes and overlaps to encode the possible configurations between those entities. Allen's calculus has found its way in many academic and industrial applications that involve, most commonly, planning and scheduling, temporal databases, and healthcare. In this paper, we present a novel encoding of Interval Algebra using answer-set programming (ASP) extended by difference constraints, i.e., the fragment abbreviated as ASP(DL), and demonstrate its performance via a preliminary experimental evaluation. Although our ASP encoding is presented in the case of Allen's calculus for the sake of clarity, we suggest that analogous encodings can be devised for other point-based calculi, too.