Biological System Ontology

FLOW ALGEBRA
TITLE: Biological System Ontology
DOMAIN: Foundations of Biological Entities
VERSION: 1.0
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/biological-entities/foundations-of-biological-entities/biological-system-ontology-2.html
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; definitions and rules require domain-specific validation.

1. PURPOSE
Represent biological systems as bounded, interacting collections of biological components, processes and environments, with explicit scale, context and evidence. Support typed graph queries, conservative inference, provenance tracking and change management.

2. TYPE SYSTEM
TYPE Entity = {id: IRI, label: String, kind: EntityKind}
TYPE EntityKind = BiologicalSystem | Component | BiologicalProcess | Organism | Tissue | Organ | Cell | Molecule | Environment | Observation | Model
TYPE BiologicalSystem <: Entity = {
  boundary: Boundary,
  scale: Scale,
  components: Set[Entity],
  processes: Set[BiologicalProcess],
  environment: Optional[Environment],
  context: Context,
  temporal_extent: Optional[Interval]
}
TYPE Boundary = {criterion: String, spatial_extent: Optional[Region], temporal_extent: Optional[Interval]}
TYPE Scale = Molecular | Cellular | Tissue | Organ | Organismal | Population | Community | Ecosystem
TYPE Context = {taxon: Optional[IRI], conditions: Map[String,Value], model_assumptions: Set[String]}
TYPE Evidence = {source: IRI, method: String, date: Optional[Date], limitations: Set[String]}
TYPE Assertion = {subject: IRI, predicate: Relation, object: IRI, evidence: Set[Evidence], status: Status}
TYPE Status = Proposed | Supported | Contested | Refuted | Unknown
TYPE Confidence = {value: Real[0,1], basis: String, calibration: Optional[String]}

3. RELATIONSHIP VOCABULARY
RELATION has_component(BiologicalSystem, Entity)
RELATION part_of(Entity, BiologicalSystem)
RELATION has_process(BiologicalSystem, BiologicalProcess)
RELATION participates_in(Entity, BiologicalProcess)
RELATION interacts_with(Entity, Entity)
RELATION regulates(Entity, BiologicalProcess)
RELATION exchanges_with(BiologicalSystem, Environment)
RELATION located_in(Entity, Entity)
RELATION depends_on(BiologicalProcess, Entity)
RELATION observed_by(Entity, Observation)
RELATION represented_by(BiologicalSystem, Model)
RELATION has_subsystem(BiologicalSystem, BiologicalSystem)
RELATION occurs_during(BiologicalProcess, Interval)
RELATION supported_by(Assertion, Evidence)

4. GRAPH CONSTRUCTION
INPUT: source_records: Set[SourceRecord]
NORMALISE identifiers, labels, units, scale and temporal context.
CREATE typed nodes for systems, components, processes and environments.
CREATE typed edges only where supported by records or explicitly tagged inference.
ATTACH source, method, conditions, timestamp and confidence basis to each assertion.
REJECT dangling references and malformed identifiers.
OUTPUT: G = (V, E, Attributes, Provenance).

5. STRUCTURAL RULES
RULE R01: has_component(S,C) => part_of(C,S), with the same contextual scope.
RULE R02: has_subsystem(S,T) => has_component(S,T), when the ontology models subsystems as components.
RULE R03: has_process(S,P) AND participates_in(C,P) does NOT imply has_component(S,C) without evidence of membership.
RULE R04: interacts_with(A,B) is not assumed symmetric unless the interaction relation is explicitly declared symmetric.
RULE R05: part_of(A,B) AND part_of(B,C) => part_of(A,C) ONLY for compatible transitive mereological scopes; do not apply to arbitrary membership.
RULE R06: Different boundaries or temporal contexts may yield different valid decompositions of the same system.
RULE R07: Functional similarity alone does not establish biological identity or homology.
RULE R08: An observed correlation does not by itself establish regulation or causation.

6. SYSTEM DYNAMICS
STATE S(t) = {component_states, process_states, environmental_conditions}.
TRANSITION S(t+dt) = F(S(t), inputs(t), parameters, dt) where F is a declared model.
REQUIRE explicit assumptions for F, measurement units, temporal resolution and validity range.
IF a component is removed or altered THEN recompute only dependencies justified by the declared model.
DISTINGUISH observed dynamics from predicted or simulated dynamics.

7. INFERENCE AND REASONING
INFER candidate system membership from explicit composition records.
INFER candidate dependencies from validated process models, never solely from co-occurrence.
CHECK taxonomic, spatial, temporal and scale compatibility before graph joins.
MAINTAIN inference lineage: derived_assertion -> rule -> premise_assertions.
MARK all non-deductive conclusions as hypotheses with uncertainty.
STOP recursive traversal at visited (node, relation, context) states to prevent cycles.

8. SEMANTIC_EQUIVALENCE
EQUIVALENCE candidate(A,B) requires compatible identity criteria, boundaries, scale, taxon and time.
SYNONYM labels may map to the same entity only after disambiguation.
ANALOGY(A,B) is not identity(A,B).
HOMOLOGY(A,B) is not functional equivalence(A,B).
SUBSYSTEM_OF is not EQUIVALENT_TO.
RECORD mapping_type = exact | close | broader | narrower | related | incompatible.
REQUIRE evidence and context for every asserted equivalence.

9. VALIDATION
V01: Each BiologicalSystem has a stable identifier and a declared boundary.
V02: Each relation respects domain/range typing.
V03: Each quantitative observation carries units and measurement context.
V04: Each process is connected to a biological context or system.
V05: Each inference records premises, rule identifier and provenance.
V06: Conflicting assertions remain distinguishable; never silently overwrite.
V07: Time-dependent relationships specify applicable interval where available.
V08: Cross-scale relationships identify aggregation or mechanistic assumptions.
V09: Absence of evidence is not automatically evidence of absence.
V10: Validation status distinguishes syntactic, structural, semantic and empirical checks.

10. CONFIDENCE
CONFIDENCE(assertion) = calibrated assessment derived from evidence quality, independence,
method suitability, consistency and applicability to context; no universal numerical formula assumed.
RULE: Deductive certainty applies only conditional on accepted premises and valid rules.
RULE: Aggregating dependent sources must not double-count evidence.
RULE: Conflicting or out-of-scope evidence triggers reassessment rather than automatic averaging.
STORE confidence.value, confidence.basis, method and calibration information.

11. PROVENANCE
FOR EACH assertion STORE origin, author or issuing organisation, observation/model method,
source identifier, version, date, licence if known, and transformation history.
DISTINGUISH primary observation, literature assertion, model output and AI inference.
PRESERVE original records and track derived records without destructive replacement.

12. FLOW_HASH
CANONICALISE typed nodes, relations, scope, assertions, provenance identifiers and version.
FLOW_HASH = SHA256(UTF8(canonical_serialisation)).
NOTE: Hash establishes content integrity/identity, not scientific correctness.
EXCLUDE volatile rendering metadata from canonical content where appropriate.

13. UPDATE_MODEL
ON new evidence or revision:
  validate input;
  identify affected nodes, edges and derived conclusions;
  version assertions rather than overwrite history;
  recompute dependent inferences;
  refresh confidence and conflict markers;
  regenerate canonical hash;
  publish change log and rollback reference.

14. AI_CONSUMPTION
INPUT: question, biological context, graph snapshot, permitted inference rules.
RESOLVE entity identifiers and relevant scale/boundary.
RETRIEVE assertions with provenance and validation status.
EXECUTE only applicable typed rules and bounded graph traversal.
RETURN conclusions with supporting paths, assumptions, uncertainties and source identifiers.
IF evidence insufficient RETURN unknown or unresolved rather than fabricated certainty.
DO NOT interpret this declarative specification as executable software without an implementation.

15. EXAMPLE GRAPH
SYSTEM: cardiovascular_system [scale=Organismal, boundary=declared anatomical/functional scope]
COMPONENT: heart [kind=Organ]
COMPONENT: blood_vessel_network [kind=BiologicalSystem]
PROCESS: blood_circulation [kind=BiologicalProcess]
EDGE: has_component(cardiovascular_system, heart)
EDGE: has_subsystem(cardiovascular_system, blood_vessel_network)
EDGE: has_process(cardiovascular_system, blood_circulation)
ASSERT: each example relation requires source evidence in a production graph.

16. OUTPUT CONTRACT
OUTPUT {graph, validated_assertions, derived_assertions, unresolved_conflicts,
        confidence_records, provenance, flow_hash, version, update_log}

END FLOW ALGEBRA