Foundations of Biological Entities

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

FLOW ALGEBRA
TITLE: Foundations of Biological Entities
VERSION: 1.0
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/biological-entities/foundations-of-biological-entities.html
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
DOMAIN: Biological Entity Graph / Foundations
STATUS: Formal ontology specification; implementation-dependent execution

1. PURPOSE
Represent biological entities and their identities, structures, organisation, components, properties, states, processes, functions, interactions, environments and boundaries in a typed, provenance-aware knowledge graph. Distinguish observations from hypotheses and inferences.

2. TYPE SYSTEM
TYPE Entity = {id: URI, label: String, kind: EntityKind, context: ContextRef, provenance: ProvenanceRef}
ENUM EntityKind = BiologicalEntity | LivingEntity | BiologicalObject | BiologicalSystem | BiologicalStructure | BiologicalOrganisation | BiologicalComponent | BiologicalProperty | BiologicalState | BiologicalProcess | BiologicalFunction | BiologicalInteraction | BiologicalEnvironment | BiologicalBoundary | BiologicalIdentity
TYPE ContextRef = {taxon?: URI, scale?: String, time?: Interval, environment?: URI, model?: URI}
TYPE ProvenanceRef = {source: URI, method?: String, timestamp?: DateTime, version?: String}
TYPE Assertion = {subject: URI, predicate: Relation, object: URI | Literal, evidence: Evidence[], confidence?: Confidence, status: Status}
TYPE Evidence = {source: URI, kind: observed | experimental | curated | inferred, method?: String}
TYPE Confidence = {score: Real[0,1], basis: String, calibration?: URI}
ENUM Status = asserted | inferred | disputed | superseded | rejected

3. CORE RELATIONSHIPS
REL is_a(Entity, Entity) : taxonomic classification
REL part_of(BiologicalComponent | BiologicalStructure, BiologicalObject | BiologicalSystem | BiologicalStructure)
REL has_component(BiologicalSystem | BiologicalObject | BiologicalStructure, BiologicalComponent)
REL organised_as(BiologicalEntity, BiologicalOrganisation)
REL has_property(BiologicalEntity, BiologicalProperty)
REL has_state(BiologicalEntity, BiologicalState)
REL participates_in(BiologicalEntity, BiologicalProcess)
REL performs_function(BiologicalEntity, BiologicalFunction)
REL interacts_with(BiologicalEntity, BiologicalEntity)
REL located_in(BiologicalEntity, BiologicalEnvironment)
REL bounded_by(BiologicalEntity, BiologicalBoundary)
REL has_identity(BiologicalEntity, BiologicalIdentity)
REL changes_state(BiologicalProcess, BiologicalState, BiologicalState)
REL supported_by(Assertion, Evidence)
REL derived_from(Assertion, Assertion)

4. ONTOLOGY MODULES
MODULE BiologicalEntity: general typed biological referents
MODULE LivingEntity: organisms and living systems; life status is time/context-dependent
MODULE BiologicalObject: materially instantiated biological objects
MODULE BiologicalSystem: interacting components and processes
MODULE BiologicalStructure: spatially organised biological material
MODULE BiologicalOrganisation: levels and patterns of organisation
MODULE BiologicalComponent: parts within biological wholes
MODULE BiologicalProperty: attributes, traits and measurable characteristics
MODULE BiologicalState: temporally indexed conditions
MODULE BiologicalProcess: temporally extended biological changes
MODULE BiologicalFunction: context- and theory-dependent functional roles
MODULE BiologicalInteraction: relations among biological participants
MODULE BiologicalEnvironment: external and internal contexts
MODULE BiologicalBoundary: membranes, interfaces and other demarcations
MODULE BiologicalIdentity: persistent identifiers and identity criteria

5. VALIDATION RULES
RULE V1: Every entity has a globally distinguishable identifier, type and provenance reference.
RULE V2: Every relation must satisfy its declared domain and range or be flagged for review.
RULE V3: part_of must not be treated as is_a; composition is not classification.
RULE V4: A state assertion must carry a time or explicitly state that time is unknown.
RULE V5: A biological function claim must retain its functional interpretation and supporting evidence.
RULE V6: An inferred claim must preserve the inference rule and source assertions.
RULE V7: Conflicting observations may coexist with provenance and context; do not silently overwrite.
RULE V8: Similar names alone do not establish biological identity or equivalence.
RULE V9: Absence of evidence must not be promoted to evidence of absence without a justified detection model.
RULE V10: Recursive traversals must track visited nodes and apply depth/resource bounds.

6. INFERENCE RULES
RULE I1: has_component(A,B) => part_of(B,A), when the relationship is explicitly inverse in the selected model.
RULE I2: part_of(A,B) AND part_of(B,C) => part_of(A,C), only if the selected part_of subtype is transitive and the context is compatible.
RULE I3: is_a(A,B) AND is_a(B,C) => is_a(A,C), when all three denote compatible class-level concepts.
RULE I4: has_state(E,S1,t1) AND has_state(E,S2,t2) does not imply contradiction when t1 != t2.
RULE I5: interacts_with(A,B) does not imply interacts_with(B,A) unless the interaction subtype is symmetric.
RULE I6: derived_from(X,Y) => retain provenance of Y in the derivation trace for X.

7. SEMANTIC_EQUIVALENCE
INPUT: entity_a, entity_b, context
CHECK: identity criteria, entity kinds, taxonomic scope, biological scale, temporal scope, source and evidence
OUTPUT: exact_identity | equivalent_in_context | related | distinct | unresolved
CONSTRAINT: semantic similarity is not proof of equivalence.

8. CONFIDENCE
CONFIDENCE.score in [0,1]
CONFIDENCE.basis must identify evidence quality, methodological assumptions and inference dependencies.
Never assign a numeric score merely because an assertion is syntactically valid.
Propagated confidence requires a documented, calibrated aggregation rule; otherwise return unquantified/unknown.

9. FLOW_HASH
CANONICALISE: normalise identifiers, ordered field names, relation names, ontology version and context; preserve meaningful distinctions.
FLOW_HASH = SHA256(canonical_serialisation(flow_specification))
PURPOSE: reproducible integrity identifier, not scientific proof or a confidence measure.

10. UPDATE_MODEL
ON new evidence:
  preserve prior version and provenance
  validate new assertion and context
  compare against existing claims
  append supported assertion or mark disputed/superseded with rationale
  recompute affected derived assertions
  recalculate FLOW_HASH for changed specification
  emit change log and version identifier

11. RECURSIVE GRAPH FLOW
FLOW BiologicalFoundationsResolve(seed, relation_filter, max_depth):
  REQUIRE seed exists AND max_depth >= 0
  frontier := [(seed, 0)]
  visited := {}
  results := []
  WHILE frontier not empty:
    (node, depth) := pop(frontier)
    IF node in visited: CONTINUE
    add node to visited
    append node with evidence and context to results
    IF depth < max_depth:
      FOR each validated edge satisfying relation_filter from node:
        append (edge.target, depth + 1) to frontier
  RETURN {results, visited_count, unresolved_edges, provenance_trace}

12. AI_CONSUMPTION
READ: typed graph + ontology version + provenance + confidence metadata
REASON: use only permitted relation semantics and validated inference rules
OUTPUT: assertions, evidence links, rule trace, uncertainty, contradictions and graph version
RESTRICTIONS: do not invent missing biological entities, observational evidence or experimental results.

13. CROSS-DOMAIN LINKS
MAP biological structure -> anatomy and morphology
MAP biological process -> physiology and biochemistry
MAP biological identity -> taxonomy and biodiversity informatics
MAP biological interaction -> ecology and systems biology
MAP biological property -> measurement and scientific metadata
MAP biological evidence -> experimental and data provenance ontologies
All mappings require context-specific validation.

14. ACCEPTANCE TESTS
TEST T1: cell part_of tissue, tissue part_of organ; transitive part_of can be inferred only for compatible subrelations.
TEST T2: organism has_state juvenile at t1 and adult at t2; no automatic contradiction.
TEST T3: interaction A -> B; reverse edge is not automatically inferred.
TEST T4: two aliases share a label but distinct identifiers; do not merge without identity evidence.
TEST T5: contradictory measurements with separate provenance remain available for review.
TEST T6: cyclic graph traversal terminates through visited tracking and depth bound.

15. SOURCE STRUCTURE
The source index links fifteen foundational ontology topics: Biological Entity, Living Entity, Biological Object, Biological System, Biological Structure, Biological Organisation, Biological Component, Biological Property, Biological State, Biological Process Entity, Biological Function Entity, Biological Interaction Entity, Biological Environment Entity, Biological Boundary and Biological Identity.

END FLOW ALGEBRA