Association Ontology

FLOW ALGEBRA
Association Ontology — Foundations of Relationships
Version: 1.0
Source: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/foundations-of-relationships/association-ontology.html
Authors: Mark Anthony Higgins — Sky (Recursive AI)

PURPOSE
Formalise associations between entities, concepts, observations and evidence while distinguishing association from identity, causation and entailment.

TYPES
Entity := {id: IRI, label: String, types: Set[IRI]}
Association := {id: IRI, subject: Entity, predicate: IRI, object: Entity, context: Context, evidence: Set[Evidence], confidence: Real[0,1], status: Status}
Context := {domain: String?, temporal_scope: Interval?, spatial_scope: String?, conditions: Set[String]}
Evidence := {source: IRI, method: String, observed_at: DateTime?, reliability: Real[0,1]}
Status := asserted | inferred | disputed | deprecated

RELATIONSHIP OPERATORS
ASSOCIATE(a,p,b,c) -> Association
HAS_ASSOCIATION(a,b) := exists r (r.subject=a and r.object=b and r.status != deprecated)
DIRECTED(r) := ordered(r.subject,r.object)
SYMMETRIC(p) := forall a,b (p(a,b) -> p(b,a)) where declared(p,symmetric)
TRANSITIVE(p) := forall a,b,c ((p(a,b) and p(b,c)) -> p(a,c)) where declared(p,transitive)
INVERSE(p,q) := forall a,b (p(a,b) <-> q(b,a)) where declared(p,inverseOf,q)

CLASSIFICATION
AssociationKind := structural | semantic | statistical | functional | temporal | spatial | social | evidential
CLASSIFY(r,k) requires k in AssociationKind and supporting classification criteria
RELATED_TO(a,b) does not imply SAME_AS(a,b)
CORRELATED_WITH(a,b) does not imply CAUSES(a,b)
ASSOCIATED_WITH(a,b) does not imply ASSOCIATED_WITH(b,a) unless symmetry is explicitly declared

INFERENCE
R1: asserted(r) and valid(r) -> eligible_for_reasoning(r)
R2: declared(p,inverseOf,q) and p(a,b) -> infer q(b,a)
R3: declared(p,subPropertyOf,q) and p(a,b) -> infer q(a,b)
R4: declared(p,transitive) and p(a,b) and p(b,c) -> infer p(a,c)
R5: conflicting_evidence(r) -> mark_disputed(r); never silently discard conflicting sources
R6: absent_evidence(r) -> unknown(r); do not infer false(r)

SEMANTIC_EQUIVALENCE
EQUIVALENT_PREDICATE(p,q) only if domain, range, direction, context and logical meaning align
EQUIVALENT_ENTITY(a,b) requires explicit identity evidence or a justified equivalence mapping
Do not merge entities solely because they share associations.

CONFIDENCE
CONFIDENCE(r) in [0,1]
Evidence confidence must reflect provenance, independence, relevance and uncertainty.
For derived claims, record derivation path and a calibrated confidence estimate.
Do not multiply confidence values as if evidence were independent without justification.

VALIDATION
V1: association id, subject, predicate and object must exist
V2: confidence within [0,1]
V3: domain/range constraints satisfied when declared
V4: temporal claims must be evaluated within their applicable interval
V5: inferred associations must preserve provenance and rule identifiers
V6: cycles are permitted unless the predicate is declared acyclic
V7: distinguish missing evidence from negative evidence

FLOW_HASH
canonical := normalise(association.id, subject.id, predicate, object.id, context, evidence, status)
FLOW_HASH := SHA256(UTF8(canonical))
Canonicalisation must define stable ordering for unordered sets and normalise identifiers and dates.

UPDATE_MODEL
On new evidence: validate -> append provenance -> reassess confidence -> detect conflicts -> update status -> recompute FLOW_HASH -> propagate only justified inferences.
Retain version history and support retraction of conclusions whose premises no longer hold.

AI_CONSUMPTION
input: entity graph + association declarations + evidence + constraints
process: parse -> type-check -> validate -> classify -> infer -> assess confidence -> trace provenance
output: association graph + justified inferences + uncertainty + conflicts + audit trail
policy: no association-to-causation leap; no implicit symmetry or transitivity; no fabricated provenance.

END FLOW ALGEBRA