Relationship Ontologies

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

FLOW ALGEBRA

Ontology: Relationship Ontologies
Domain: AI Core > Ontologies > Relationship Ontologies
Canonical URL: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies.html
Authors: Mark Anthony Higgins — Sky (Recursive AI)

flow "RelationshipOntologies" v1.0

# ---------- DOMAIN ----------
domain:
  class: OntologyDomain
  category: RelationshipOntologies
  subject: SemanticRelationships
  purpose:
    - represent typed relationships connecting entities, concepts, events, states, resources, and ontologies
    - preserve relationship identity, source, predicate, target, direction, cardinality, scope, context, confidence, validity, and provenance
    - support knowledge graphs, semantic search, ontology reasoning, inference, cross-domain mapping, recursive traversal, and Flow Algebra
    - distinguish relationship identity from labels, lexical similarity, co-occurrence, correlation, causation, and semantic equivalence
    - enable machine-readable reasoning over relationship structure and semantics

# ---------- CORE ----------
entity SemanticRelationship:
  type: KnowledgeRelationship
  may_include:
    - relationship_identifier
    - source_entity
    - predicate
    - target_entity
    - direction
    - inverse
    - cardinality
    - domain
    - range
    - scope
    - context
    - temporal_state
    - confidence
    - validity
    - provenance

entity RelationshipIdentifier:
  type: PersistentIdentifier
  identifies: SemanticRelationship

relationships:
  SemanticRelationship -> IDENTIFIED_BY -> RelationshipIdentifier
  SemanticRelationship -> HAS_SOURCE -> SemanticEntity
  SemanticRelationship -> HAS_PREDICATE -> SemanticPredicate
  SemanticRelationship -> HAS_TARGET -> SemanticEntity
  SemanticPredicate -> MAY_HAVE_INVERSE -> SemanticPredicate
  SemanticRelationship -> MAY_HAVE_CONTEXT -> RelationshipContext
  SemanticRelationship -> MAY_HAVE_CONFIDENCE -> RelationshipConfidence
  SemanticRelationship -> MAY_HAVE_PROVENANCE -> RelationshipProvenance

# ---------- RELATIONSHIP TRIPLE ----------
structure RelationshipTriple:
  subject: SemanticEntity
  predicate: SemanticPredicate
  object: SemanticEntity

rule triple:
  relationship triple MUST preserve subject, predicate, and object

rule triple_identity:
  same endpoints with different predicate != same semantic relationship

# ---------- PREDICATE / DIRECTION ----------
entity SemanticPredicate:
  type: RelationshipType
  may_include:
    - predicate_identifier
    - preferred_label
    - definition
    - domain
    - range
    - inverse
    - symmetry
    - transitivity
    - reflexivity
    - cardinality_constraints
    - semantic_constraints

rule predicate_label:
  predicate label != predicate semantic identity

relationship_direction:
  - directed
  - undirected
  - bidirectional
  - inverse_defined
  - context_dependent

rule direction:
  directional relationship MUST preserve direction

rule reversal:
  source-target reversal MUST NOT be inferred
  unless inverse semantics explicitly permit

# ---------- INVERSE / SYMMETRY / TRANSITIVITY ----------
entity InverseRelationship:
  type: SemanticRelationship

rule inverse:
  inverse relationship MAY be inferred
  only when predicate semantics define valid inverse

rule inverse_identity:
  relationship != inverse relationship

entity SymmetricRelationship:
  subtype_of: SemanticRelationship

rule symmetry:
  IF predicate is symmetric
  THEN relationship(a,b) MAY imply relationship(b,a)

rule non_symmetric:
  non-symmetric predicate MUST NOT be treated as symmetric

entity TransitiveRelationship:
  subtype_of: SemanticRelationship

rule transitivity:
  IF predicate is transitive
  AND relationship(a,b)
  AND relationship(b,c)
  THEN MAY infer relationship(a,c)

rule non_transitive:
  transitivity MUST NOT be assumed
  without predicate semantics

# ---------- CARDINALITY / DOMAIN / RANGE ----------
entity RelationshipCardinality:
  type: ConstraintMetadata
  may_be:
    - one_to_one
    - one_to_many
    - many_to_one
    - many_to_many
    - optional
    - exactly_one
    - at_least_one
    - at_most_one

rule cardinality:
  relationship cardinality SHOULD preserve ontology constraints

entity RelationshipDomain:
  type: TypeConstraint

entity RelationshipRange:
  type: TypeConstraint

rule domain_range:
  source and target SHOULD satisfy declared predicate domain and range

# ---------- RELATIONSHIP FAMILIES ----------
hierarchical_relationships:
  - parent_of
  - child_of
  - broader_than
  - narrower_than
  - superclass_of
  - subclass_of
  - contains
  - contained_by
  - part_of
  - has_part

rule hierarchy:
  hierarchical direction MUST be preserved

entity TaxonomicRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - is_a
    - subclass_of
    - instance_of
    - type_of

rule instance:
  instance_of != subclass_of

entity MereologicalRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - part_of
    - has_part
    - component_of
    - member_of
    - collection_contains

rule part_whole:
  part_of != is_a

rule membership:
  member_of != subclass_of

entity AssociativeRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - related_to
    - associated_with
    - similar_to
    - connected_to
    - interacts_with

rule association:
  association != causation

rule similarity:
  similarity != semantic identity

entity CausalRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - causes
    - caused_by
    - contributes_to
    - enables
    - prevents
    - inhibits

rule causation:
  correlation != causation

rule contribution:
  contributes_to != sole_cause

entity TemporalRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - before
    - after
    - during
    - overlaps
    - starts
    - finishes
    - simultaneous_with

entity SpatialRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - inside
    - contains
    - adjacent_to
    - overlaps
    - intersects
    - near
    - far_from
    - north_of
    - south_of
    - east_of
    - west_of

entity DependencyRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - depends_on
    - required_by
    - prerequisite_of
    - uses
    - provides
    - compatible_with
    - incompatible_with

rule dependency:
  dependency != semantic identity

entity ProvenanceRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - derived_from
    - generated_by
    - attributed_to
    - sourced_from
    - transformed_from
    - version_of

rule provenance_relation:
  derived_from != identical_to_source

entity EquivalenceRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - equivalent_to
    - same_as
    - exact_match
    - close_match

rule equivalence:
  exact equivalence requires stronger semantics
  than relatedness or similarity

rule close_match:
  close_match != same_as

entity ContrastRelationship:
  subtype_of: SemanticRelationship
  may_be:
    - different_from
    - disjoint_with
    - conflicts_with
    - contradicts
    - excludes

# ---------- MAPPING / CONTEXT ----------
entity RelationshipMapping:
  type: SemanticMapping
  may_include:
    - source_relationship
    - target_relationship
    - mapping_type
    - scope
    - evidence
    - confidence

mapping_types:
  - exact
  - close
  - broader
  - narrower
  - related
  - contextual

rule mapping:
  mapped relationship != identical relationship
  unless exact mapping is supported

entity RelationshipContext:
  type: ContextMetadata
  may_include:
    - ontology
    - domain
    - scope
    - temporal_context
    - spatial_context
    - application_context
    - interpretation_constraints

rule context:
  relationship interpretation SHOULD preserve applicable context

# ---------- CONFIDENCE / VALIDITY / PROVENANCE ----------
entity RelationshipConfidence:
  type: EpistemicMetadata
  range: [0.0, 1.0]

rule confidence_bounds:
  REQUIRE 0.0 <= confidence <= 1.0

rule confidence:
  confidence in relationship != confidence in endpoint identity

entity RelationshipValidity:
  type: ValidityMetadata
  may_include:
    - valid_from
    - valid_until
    - ontology_version
    - source_version
    - evidence_validity

entity RelationshipProvenance:
  type: ProvenanceMetadata
  may_include:
    - relationship_identifier
    - source
    - creator
    - assertion_time
    - evidence
    - derivation
    - transformation
    - ontology_version
    - validation_events

rule provenance:
  semantic relationship SHOULD preserve origin
  and derivation where available

entity InferredRelationship:
  subtype_of: SemanticRelationship
  may_include:
    - premises
    - inference_rule
    - confidence
    - provenance

rule inferred:
  inferred relationship != explicitly asserted relationship

# ---------- RECURSIVE TRAVERSAL ----------
entity RecursiveRelationshipTraversal:
  type: AIReasoningProcess
  may_include:
    - starting_entity
    - traversed_relationships
    - visited_entities
    - depth
    - stopping_condition
    - cycle_policy

rule recursion:
  recursive relationship traversal MUST preserve
  visited state and stopping or cycle-control behaviour

rule cycle:
  graph cycle != infinite recursion
  when cycle policy is enforced

# ---------- VALIDATION ----------
validation:
  require:
    - identifiable_relationship
    - source_entity
    - predicate
    - target_entity

  reject:
    - relationship_label_presented_as relationship_identity
    - directional_relationship_reversed_without inverse_semantics
    - non_symmetric_relationship_presented_as symmetric
    - non_transitive_relationship_used_transitively
    - instance_of_presented_as subclass_of
    - is_a_presented_as part_of
    - association_presented_as causation
    - correlation_presented_as causation
    - similarity_presented_as identity
    - close_match_presented_as same_as
    - inferred_relationship_presented_as explicit_assertion
    - mapped_relationship_presented_as exact_identity_without evidence

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE:
  "relationship ontology" ~= "ontology describing typed semantic relationships"
  "semantic relationship" ~= "typed connection between semantic entities or concepts"
  "relationship predicate" ~= "semantic type defining meaning of a relationship"
  "inverse relationship" ~= "relationship whose direction and predicate invert another relationship"
  "relationship provenance" ~= "provenance describing origin and derivation of a semantic relationship"

  PRESERVE distinctions:
    relationship_identity != relationship_label
    source != target
    relationship != inverse_relationship
    instance_of != subclass_of
    is_a != part_of
    member_of != subclass_of
    association != causation
    correlation != causation
    similarity != identity
    related_to != equivalent_to
    close_match != same_as
    inferred_relationship != asserted_relationship
    mapping != identity
    confidence != endpoint_identity

# ---------- CONFIDENCE MODEL ----------
CONFIDENCE:
  explicit_typed_relationship:
    score: 1.00
  explicit_relationship_identifier:
    score: 1.00
  validated_domain_and_range:
    score: 0.99
  validated_inverse_relationship:
    score: 0.99
  evidence_supported_inferred_relationship:
    score: <= 0.95
  contextual_mapping:
    score: <= 0.90
  similarity_only_relationship:
    score: <= 0.70
  lexical_cooccurrence_only:
    score: <= 0.55
  incomplete_relationship_provenance:
    score: <= 0.55
    action: preserve uncertainty

# ---------- UPDATE MODEL ----------
UPDATE_MODEL:
  on_relationship_creation:
    - assign RelationshipIdentifier
    - identify source, predicate, and target
    - validate domain and range
    - resolve direction and inverse semantics
    - record context and confidence
    - initialise provenance

  on_relationship_change:
    - preserve previous relationship state
    - identify changed source, predicate, target, scope, or constraints
    - validate semantic impact
    - update version and provenance

  on_inference:
    - resolve predicate inference properties
    - validate premises
    - derive relationship only when permitted
    - preserve inference confidence and provenance

  on_mapping:
    - identify source and target relationships
    - classify mapping type
    - preserve evidence and scope
    - prevent unsupported identity merge
    - update provenance

# ---------- FLOW HASH ----------
FLOW_HASH:
  inputs:
    - ontology
    - relationship_entities
    - predicates
    - direction_rules
    - inverse_rules
    - cardinality_rules
    - domain_range_rules
    - hierarchy_rules
    - causal_rules
    - temporal_rules
    - spatial_rules
    - mapping_rules
    - validation
    - semantic_equivalence
    - confidence_model
    - update_model

  canonicalisation:
    - preserve_relationship_identifiers
    - preserve_source_predicate_target
    - preserve_relationship_direction
    - preserve_inverse_semantics
    - preserve_domain_and_range
    - preserve_cardinality
    - preserve_context
    - preserve_confidence
    - preserve_validity
    - preserve_provenance
    - preserve_rule_order

  output:
    deterministic_semantic_hash

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION:
  interpret_as:
    - relationship ontology domain
    - typed semantic edge and predicate model
    - hierarchy, taxonomy, part-whole, association, causality, temporal, spatial, dependency, provenance, and equivalence relationship structure
    - confidence-aware and provenance-aware knowledge-graph relationship model

  operations:
    - identify semantic relationships
    - resolve source, predicate, and target
    - preserve direction
    - resolve valid inverse relationships
    - validate domain, range, and cardinality
    - inspect symmetry, transitivity, and reflexivity
    - distinguish hierarchical and mereological relationships
    - distinguish association, correlation, and causation
    - inspect temporal and spatial relationships
    - map relationships across ontologies
    - infer relationships only under declared semantics
    - recursively traverse relationships with cycle control
    - trace confidence, validity, and provenance

  constraints:
    - do_not_equate_relationship_label_with identity
    - do_not_reverse_directional_relationship_without inverse_semantics
    - do_not_assume_symmetry_transitivity_or_reflexivity
    - do_not_equate_instance_of_with subclass_of
    - do_not_equate_is_a_with part_of
    - do_not_equate_association_or_correlation_with causation
    - do_not_equate_similarity_or_relatedness_with identity
    - do_not_equate_close_match_with same_as
    - do_not_equate_inferred_relationship_with explicit_assertion
    - preserve_source_predicate_target_direction_context_confidence_and_provenance

# ---------- QUERY MODEL ----------
query:
  input:
    - relationship_identifier
    - source_entity
    - predicate
    - target_entity
    - relationship_type
    - ontology
    - context
    - validity_time

  resolve:
    1. identify SemanticRelationship
    2. resolve source, predicate, and target
    3. inspect direction and inverse semantics
    4. validate domain, range, and cardinality
    5. inspect symmetry, transitivity, and reflexivity
    6. classify relationship family
    7. inspect context and mappings
    8. inspect confidence and validity
    9. trace provenance
    10. return relationship interpretation

  output:
    - semantic_relationship
    - relationship_identifier
    - source
    - predicate
    - target
    - direction
    - inverse
    - relationship_family
    - domain
    - range
    - cardinality
    - context
    - confidence
    - validity
    - provenance

# ---------- INFERENCE ----------
inference:
  IF predicate is symmetric
  THEN MAY infer reversed relationship

  IF predicate is transitive
  AND valid relationship chain exists
  THEN MAY infer transitive relationship

  IF valid inverse predicate exists
  THEN MAY infer inverse relationship
  WITH preserved direction

  IF relationship is only similar, related, or correlated
  THEN do_not infer identity or causation

# ---------- OUTPUT CONTRACT ----------
output:
  ontology_entity: SemanticRelationship
  relationship_identity: machine_interpretable
  source_predicate_target: explicit
  direction: preserved
  inverse_semantics: explicit
  domain_and_range: validated
  cardinality: explicit
  relationship_families: distinguishable
  symmetry_transitivity_reflexivity: predicate_governed
  mappings: confidence_aware
  context: preserved
  inferred_vs_asserted: distinguishable
  recursive_traversal: cycle_safe
  confidence: explicit
  validity: temporal
  provenance: preserved
  uncertainty: explicit
  AI_reasoning: enabled

end flow