Context Relationship Ontology

FLOW ALGEBRA
Context Relationship Ontology
Kireth Semantic Library | Relationship Ontologies > Semantic Relationships
Source: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/semantic-relationships/context-relationship-ontology.html
Authors: Mark Anthony Higgins — Sky (Recursive AI)
Specification: Companion formalisation v1.0 | 2026-10-08

PURPOSE
Represent, qualify and reason over relationships whose interpretation depends on context. Context is an explicit, typed scope rather than an implicit assumption. Rules below define intended operations and constraints; execution requires a conforming interpreter.

TYPES
Entity := {id: URI, type: URI, labels: Set[String]}
Context := {id: URI, domain: URI?, locale: String?, time: Interval?, location: URI?, audience: URI?, purpose: URI?, assumptions: Set[Assertion], version: String}
Predicate := {id: URI, domain: Set[URI], range: Set[URI], inverse: URI?, properties: Set[String]}
Assertion := {subject: Entity, predicate: Predicate, object: Entity|Literal, context: Context, provenance: Evidence, confidence: Real[0,1], status: asserted|inferred|disputed|retracted}
Evidence := {source: URI, method: String, observed_at: DateTime, reliability: Real[0,1]}
ContextMapping := {source_context: URI, target_context: URI, constraints: Set[Condition], transformation: String, evidence: Evidence}

RELATIONSHIPS
IN_CONTEXT(assertion, context) := assertion.context.id = context.id
CONTEXT_OF(context, entity) := entity is explicitly scoped by context
APPLIES_IN(predicate, context) := predicate is valid under context assumptions
CONTEXT_OVERLAP(c1,c2) := compatible shared scope dimensions exist
CONTEXT_CONFLICT(c1,c2) := at least one required scope dimension is incompatible
CONTEXT_REFINES(c_specific,c_general) := every constraint of c_general is satisfied by c_specific
CONTEXT_MAPS_TO(c1,c2,mapping) := mapping explicitly preserves stated interpretation conditions

OPERATORS
SCOPE(a,c) -> a with context c, only if the evidence supports c
REFINE(c, additional_constraints) -> c' with stricter compatible constraints
PROJECT(a,c_target,mapping) -> translated assertion or UNRESOLVED
COMPARE(a,b) -> EQUIVALENT | COMPATIBLE | DIFFERENT | CONFLICT | UNKNOWN
MERGE(c1,c2) -> combined context if constraints are satisfiable; otherwise CONFLICT

INFERENCE RULES
R1: ASSERTED(a) AND VALID_CONTEXT(a.context) => ELIGIBLE_FOR_REASONING(a)
R2: IN_CONTEXT(a,c1) AND CONTEXT_REFINES(c2,c1) AND PRESERVED(a,c2) => CANDIDATE(SCOPE(a,c2))
R3: CONTEXT_MAPS_TO(c1,c2,m) AND SATISFIES(a,m.constraints) AND VALID(m.evidence) => CANDIDATE(PROJECT(a,c2,m))
R4: SAME_SUBJECT_PREDICATE(a,b) AND CONTEXT_OVERLAP(a.context,b.context) AND INCOMPATIBLE_OBJECTS(a,b) => REVIEW_CONFLICT(a,b)
R5: CONTEXT_CONFLICT(a.context,b.context) => DO_NOT_INFER_CONTRADICTION_FROM_OBJECT_DIFFERENCE(a,b)
R6: CONTEXT_REFINES(c2,c1) AND CONTEXT_REFINES(c3,c2) => CONTEXT_REFINES(c3,c1), provided all constraints remain satisfiable
R7: MISSING_REQUIRED_CONTEXT(a) => UNKNOWN, not FALSE
R8: RETRACTED(a) => EXCLUDE_FROM_ACTIVE_INFERENCE(a)

SEMANTIC_EQUIVALENCE
EQUIVALENT(a,b) iff compatible subject and object identity, compatible predicate semantics, and mutually valid contextual mappings preserve truth conditions.
SIMILAR(a,b) does not imply EQUIVALENT(a,b).
Context-specific equivalence must not be promoted to global identity.

CONFIDENCE
confidence(a) in [0,1]. Inferred confidence must not exceed the weakest required premise and mapping confidence without separately justified calibration.
Independent evidence may be aggregated only under an explicit calibrated aggregation model; correlated evidence must not be double-counted.
Low confidence is not a negation. Unverified assertions retain UNKNOWN status when appropriate.

VALIDATION
V1: Entity, predicate and context identifiers must be well-formed and resolvable where possible.
V2: Subject and object satisfy predicate domain and range constraints.
V3: Every assertion carries a context, provenance and bounded confidence.
V4: Time intervals have ordered endpoints; locale and spatial scopes are internally consistent.
V5: Mapping must declare what is preserved, transformed or lost.
V6: Contradiction detection requires overlapping, compatible contexts.
V7: Cyclic context refinement is rejected unless the cycle is equivalence-preserving.
V8: Retractions and superseded assertions remain auditable.

FLOW_HASH
Canonicalise the typed assertion graph, context constraints, mapping versions, rule-set version and provenance references with deterministic ordering and Unicode normalisation. FLOW_HASH := SHA-256(canonical_bytes). Exclude volatile display-only metadata; any semantic change changes the hash.

UPDATE_MODEL
1. Ingest candidate assertion or context update.
2. Validate types, provenance, constraints and temporal scope.
3. Compare against active assertions within overlapping contexts.
4. Resolve duplicates, retain disputes, and record supersession/retraction events.
5. Recompute only affected context projections and derived assertions.
6. Regenerate FLOW_HASH and publish a versioned audit trail.
7. Do not silently overwrite evidence or promote local claims to universal claims.

AI_CONSUMPTION
Input: entity/predicate query, target context, evidence requirements, confidence threshold.
Output: matching assertions, context identifiers, qualified interpretations, inference paths, provenance, confidence, conflicts and UNKNOWN outcomes.
Always disclose context-dependent assumptions. Preserve distinctions between asserted and inferred knowledge. Never infer equivalence, contradiction or universal applicability from similarity alone.

EXAMPLE
Context UK_2026 := {domain: road_transport, locale: en-GB, time: 2026, location: UK}
Context US_2026 := {domain: road_transport, locale: en-US, time: 2026, location: US}
Assertion A: (vehicle, travels_on, left_side) IN_CONTEXT UK_2026
Assertion B: (vehicle, travels_on, right_side) IN_CONTEXT US_2026
COMPARE(A,B) = DIFFERENT_CONTEXTS, not a logical contradiction.

LIMITATIONS
This companion specification is authored from the ontology topic and visible page metadata. The site's embedded downloadable formal specification was not available in the retrieved page text. It is not represented as a verbatim extraction or an independently tested executable implementation.