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.
arXiv:2608. 13018v1 Announce Type: new Abstract: Standard probabilistic logic programming frameworks typically rely on grounding logic programs into discrete propositional representations.
By Costin B\u{a}dic\u{a}, Amelia B\u{a}dic\u{a}
arXiv:2606. 26418v1 Announce Type: new Abstract: A non-agentic "oracle" AI that estimates probabilities of future events faces a self-reference problem: once its answer is learned and acted upon, it can change the very probability it was asked to report.
By Jobst Heitzig
arXiv:2609.25388v1 Announce Type: cross
Abstract: A classical question in statistics is which observable quantities to condition on when drawing inferences about unobservable targets. For conformal p...
By Xuelin Yang, Baihe Huang, Yilong Hou, Guido Imbens, Michael I. Jordan
arXiv:2104. 11547v5 Announce Type: replace-cross Abstract: Statistical models contain variables that are not random: parameters, treatments, environments, design points.
By Patrick Forr\'e
The paper studies observational dominance among causal structures with latent variables, defining one structure as dominating another if it can realize all distributions that the other can over the same visible variables. It provides a full characterization of this dominance partial order for three visible variables and a partial one for four, and shows that many equivalence classes are distinguished by nontrivial inequality constraints similar to Bell or instrumental inequalities. The authors also demonstrate that constraint‑based causal discovery algorithms relying only on conditional independence are much less powerful than those incorporating nested Markov and inequality constraints.
By Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens