Executable Ontologies: A Declarative Paradigm

• Executable Ontologies are formal semantic models that merge ontological representation with executable rules, unifying declarative knowledge, data, and computation.
• They employ an event-driven, rule-based framework with explicit causal ordering, ensuring determinism, traceability, and model-based validation.
• Practical applications include workflow management, robotic control, digital twins, and blockchain orchestration, highlighting their value in complex system integration.

Executable Ontologies (EO) are formal semantic models in which ontological structures are not merely descriptive, but constitute the program executed by a computational engine. In contrast to passive ontologies that serve as knowledge bases for validation or reasoning, Executable Ontologies unify declarative knowledge, data, and computational process, directly controlling system evolution via rule-based, event-driven mechanisms. Core research in this area formalizes the combination of subject-event ontologies, explicit causal order, strong multiperspectivity, and model-based schema enforcement, realized in platforms such as boldsea and eXtended Formal Ontology (XFO). EO technology is applicable across workflow management, distributed systems, robotic control, business process execution, and dynamic digital twins, offering determinism, traceability, runtimable semantic models, and native temporal transparency (Boldachev, 20 Oct 2025, Allen et al., 2018, Boldachev, 11 Sep 2025, Boldachev, 19 Nov 2025, Singer, 2019).

1. Formal Foundations and Core Principles

The foundation of Executable Ontologies centers on an event-based, subject-driven causal framework. A formal subject-event ontology is defined by:

• A finite set of actors (subjects) $A$
• A finite set of models (conceptual templates) $M$
• A set of contexts $C$ (individuals/actions)
• Events $e \in \mathcal{E}$ structured as records $$e = (\mathit{id}(e),\,\mathit{actor}(e)\in A,\,\mathit{model}(e)\in M,\,\mathit{ctx}(e)\in C,\,\mathit{payload}(e),\, \mathrm{refs}(e)\subseteq H)$$
• A partition key $$\mathrm{key}(e) = (\mathit{model}(e),\,\mathit{ctx}(e)) \in K$$ where $K = M \times C$
• Causality defined by transitive closure of explicit references:

$$hb := \mathsf{tc}(\mathrm{refs}), \quad hb(e_1, e_2) \iff (e_1 \in \mathrm{refs}(e_2)) \vee (\exists\,e' : hb(e_1,e') \wedge hb(e', e_2))$$

This framework eliminates reliance on global time; all causal ordering is explicit and reconstructible from the “refs” graph (Boldachev, 20 Oct 2025, Boldachev, 11 Sep 2025). The underlying history $H$ is strictly monotonic; corrections are issued as new events, and deletions are prohibited.

Nine axioms (A1–A9) capture existence, constructive causality, explicit references (no hidden causes), multiperspectivity (conflicting events coexist), presumption of truth (instant availability), monotonic correction, last-write-wins semantics per actor/key, key-partitioned isolation, and model-based event validation.

2. Execution Semantics and Dataflow Architecture

EO systems employ a declarative, dataflow-oriented execution semantics, shifting control from imperative flow to event-driven propagation. In the boldsea engine and similar frameworks, execution proceeds in snapshot → batch → fixpoint cycles. Guards monitor the causal event graph for conditions; when satisfied, they emit new events, automatically maintaining causal invariants via “auto_chain” rules (e.g., always linking the new event to the unique prior maximal event per actor/key):

$$\mathrm{refs}_{\mathrm{auto}}(e) = \begin{cases} \{e_{\max}\}, & \text{if } e_{\max} = \max_{hb}\{e'\,|\,\mathrm{actor}(e')=a,\,\mathrm{key}(e')=k\} \ \varnothing, & \text{otherwise} \end{cases}$$

Batch update and stratified negation ensure determinism and finite fixed-point convergence (Boldachev, 20 Oct 2025). The engine architecture uses no global polling; instead, it indexes rules against their data dependencies, re-evaluating each only as relevant events are appended to $H$ (Boldachev, 19 Nov 2025, Boldachev, 11 Sep 2025).

3. Model-Based Validation and Schema Enforcement

Model-based validation is realized via three orthogonal layers per model $M$:

• Authorization: $\mathrm{actor}(e) \in \mathsf{Perms}(M)$
• Schema check: $\mathrm{payload}(e) \models \mathsf{Schema}(M)$
• Conditional dependencies: Each $\Exists(\phi) \in \mathsf{Cond}(M)$ requires a witness event $e'$ with $\mathrm{matches}(e',\phi)$ present in $\mathrm{refs}(e)$

Each event is admitted only if these constraints are satisfied. Reference computation is a union of explicit (for matching model conditions), auto (for total ordering), and base references (Boldachev, 20 Oct 2025). BSL (Boldsea Semantic Language) and similar DSLs provide concise constructs for expressing models, conditions, SetValue/SetDo rules, permissions, and UI bindings, integrating data and logic in a unified substrate (Boldachev, 11 Sep 2025).

4. System Architectures and Execution Engines

EO platforms feature architectures where semantic models are first-class, mutable at runtime, and interpreted directly without compilation. The boldsea-engine illustrates this: model schemas and rules are stored and edited live; every interaction results in the addition of causally-typed reification events. The core engine components typically include:

• UI controllers generating data-entry forms from model events
• Semantic validators enforcing all model-driven restrictions
• Execution controllers orchestrating demand-driven dataflow propagation by subscribing to relevant parts of the event graph
• Cryptographically-chained, immutable event graphs for auditability and forensic analysis (Boldachev, 20 Oct 2025, Boldachev, 11 Sep 2025, Boldachev, 19 Nov 2025)

Platforms such as XFO implement similar integration, mapping ontological universals and particulars onto class/object hierarchies in OOP languages, providing constraint-checking, querying, and execution of state transitions (Allen et al., 2018).

5. Practical Applications and Exemplars

Executable Ontologies have been demonstrated in diverse application domains:

• Business process modeling and execution: BPMN models can be fully lifted into OWL ontologies, enabling model validation, pattern-based transformation (e.g., BPMN to S-BPM), and execution by microservice-based actor runtimes. Process state changes, user tasks, and gateway logic are enacted through ontology queries and event instantiation (Singer, 2019).
• Microservice and blockchain orchestration: Independent services publish events to a common log; cross-service causality is managed by explicit references, and audit via cryptographically-chained event IDs. This approach enables asynchronous, trust-by-fixation workflows and supports multiperspectivity (conflicting facts from different subjects) (Boldachev, 20 Oct 2025, Boldachev, 11 Sep 2025).
• Robot control and cyber-physical systems: In declarative EO robotics, complex behaviors are specified as the asynchronous evolution of a temporal event graph. Behavioral rules are fired purely by dataflow changes, enabling hot-reloadable models, fine-grained audit trails, and parallel execution—contrasting with the polling-based nature of Behavior Trees (Boldachev, 19 Nov 2025).
• Digital twins, manufacturing, and microworlds: EO frameworks support complex aggregated entities, stateful transitions (e.g., pottery workflows), and semantic simulation of both digital artifacts and physical processes (Allen et al., 2018).

6. Comparison to Alternative Paradigms

Unlike imperative control architectures (e.g., Behavior Trees, traditional BPM engines), EO eliminates the distinction between world model and program:

• The event graph constitutes both the system state and the executable history.
• Data, logic, and interface are unified at the ontological level (no separate code layers).
• Execution is triggered by changes in semantic relations, not by global tick or polling.
• Zero-downtime extension is feasible, as new models and rules can be loaded live; previous history remains available and auditable.

EO supports full domain traceability, native parallelism, and significantly reduces integration complexity, but requires a conceptual shift to declarative, event-driven modeling and sophisticated semantic tooling (Boldachev, 19 Nov 2025, Boldachev, 11 Sep 2025).

7. Limitations, Theorems, and Future Directions

The principal theoretical results include:

• Determinism and Uniqueness: For each actor/key, the causal chain is totally ordered, guaranteeing unique maxima and deterministic update.
• Acyclicity: The happens-before relation forms a strict partial order, ensuring no cycles.
• Fixed-point convergence: The batch operator is monotonic and converges to a least fixpoint under stratified negation.

Practical limitations include cognitive barriers for users accustomed to procedural programming, an immature ecosystem for large-scale deployments, and the need for high-quality ontological foundries for universal entities and model sharing. Future enhancements focus on integrating model-level knowledgebases, providing encapsulation mechanisms, embedding logic-based reasoners, and enabling deep integration with ML and NLG frameworks (Allen et al., 2018, Boldachev, 20 Oct 2025).

———

In summary, Executable Ontologies represent a formal, declarative computational paradigm where semantic models, events, and declarative rules directly govern system evolution. By replacing time-based control with causality graphs and model-based validation, EO achieves determinism, multiperspectivity, immutability, and runtime extensibility, establishing a foundation for traceable, semantically integrated distributed and dynamic systems across multiple technical domains (Boldachev, 20 Oct 2025, Boldachev, 11 Sep 2025, Boldachev, 19 Nov 2025, Allen et al., 2018, Singer, 2019).