AION — Algebraic Interval Ontology for Clinical Networks (FM-3)

AION (Algebraic Interval Ontology for Clinical Networks) is a fully general formal mathematical model of clinical information systems, containing FM-1 as a special case and extending it in all dimensions. Extensions include: a type system with type hierarchy and schema inheritance for arbitrary clinical event types; a universal event model covering examinations, therapies, diagnoses, and observations as typed, attributed time-interval events; a complete temporal relation algebra (all 13 Allen relations); a hierarchical process model with directed acyclic graphs (DAGs); an extended formal query language with temporal quantifiers, cohort combination and multi-patient relations; a causal model with do-operator and counterfactual queries; FHIR mapping as a structural homomorphism; a formal AI layer model; and federation with Differential Privacy guarantees. The reference implementation is available as the Python package aion-clinical on PyPI. NOT a medical device (EU MDR 2017/745 / MPDG).