Subject-Event Ontology Without Global Time: Foundations and Execution Semantics

A formalization of a subject-event ontology is proposed for modeling complex dynamic systems without reliance on global time. Key principles: (1) event as an act of fixation - a subject discerns and fixes changes according to models (conceptual templates) available to them; (2) causal order via happens-before - the order of events is defined by explicit dependencies, not timestamps; (3) making the ontology executable via a declarative dataflow mechanism, ensuring determinism; (4) models as epistemic filters - a subject can only fix what falls under its known concepts and properties; (5) presumption of truth - the declarative content of an event is available for computation from the moment of fixation, without external verification. The formalization includes nine axioms (A1-A9), ensuring the correctness of executable ontologies: monotonicity of history (I1), acyclicity of causality (I2), traceability (I3). Special attention is given to the model-based approach (A9): event validation via schemas, actor authorization, automatic construction of causal chains (W3) without global time. Practical applicability is demonstrated on the boldsea system - a workflow engine for executable ontologies, where the theoretical constructs are implemented in BSL (Boldsea Semantic Language). The formalization is applicable to distributed systems, microservice architectures, DLT platforms, and multiperspectivity scenarios (conflicting facts from different subjects).