PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relations

The paper introduces the Probabilistic Allen Algebra (PAA), a generative and complete extension of Allen’s interval algebra that assigns relation probabilities based on Gaussian distributions over interval boundaries rather than fixed scores. In PAA, time points, interval midpoints, and durations are modeled with Gaussian and truncated‑Gaussian distributions, allowing all thirteen base relations to be expressed as boundary‑ordering predicates within a single probability space. The framework incorporates tolerance bands for contact relations, preserves Allen’s taxonomy through hierarchical unions of relations, and is validated via Monte‑Carlo simulations, with the implementation released as an open, tested Python package.

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