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). Version 1.2 corrects four findings from an external mathematical review (errata E-4–E-7): the sign in P(precedes), the distributional assumption of the probabilistic Allen relations, the second unit indicator of the contact duration, and the notation of counterfactual queries. In addition: a formal m-nearest-neighbour definition of the matching operator, heuristic labelling of the Shapley back-propagation, and an NP-hardness note on sufficient explanations. Lizenz: Dieses Dokument steht unter AGPL-3.0-only. Alternativ ist eine kommerzielle Lizenzierung durch die ISCaD GmbH auf Anfrage über licensing@iscad-it.de verfügbar. Version 1.3: Lizenz-Restfundstellen (nun durchgängig AGPL-3.0-only) und Software-URL (fm2-project/cairn → iscad/aion) korrigiert, Erratum E-8. Keine inhaltliche Änderung.

Dual-licenced: AGPL-3.0-only OR Commercial (ISCaD GmbH). Commercial licence: licensing@iscad-it.de. NOT a medical device (EU MDR 2017/745).