# Allen's Interval Algebra Makes the Difference

arXiv: https://arxiv.org/abs/1909.01128 · HTML: https://mlsanity.com/paper/1909.01128/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [ChronoSense: Exploring Temporal Understanding in Large Language Models with Time Intervals of Events](https://mlsanity.com/paper/2501.03040/) (2025)
- [Neuro-Symbolic Spatio-Temporal Reasoning](https://mlsanity.com/paper/2211.15566/) (2022)
- [PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relations](https://mlsanity.com/paper/2609.20634/) (2026)
- [APTree: Extended Behavior Trees for Adaptive and Scalable Automated Robotic Task Planning in Construction](https://mlsanity.com/paper/2610.18523/) (2026)

## Abstract (arXiv)

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.