Dependency Relationship Ontology

FLOW ALGEBRA
Title: Dependency Relationship Ontology
Version: 1.0
Source: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/logical-relationships/dependency-relationship-ontology.html
Authors: Mark Anthony Higgins — Sky (Recursive AI)
Status: Companion formalisation; source page not independently verified.

ONTOLOGY:
  id: dependency_relationship_ontology
  domain: relationship_ontologies.logical_relationships
  purpose: Model, qualify, validate and reason about dependencies between entities, conditions, tasks, claims and systems.

TYPES:
  Entity: {id: string, type: string, label: string}
  Dependency: {id: string, dependent: Entity, prerequisite: Entity, kind: DependencyKind, scope: string?, confidence: number, provenance: string?}
  DependencyKind: [logical, functional, causal, temporal, structural, operational, resource, informational]
  Condition: {expression: string, context: string?}
  Evidence: {source: string, observed_at: datetime?, reliability: number?}

RELATIONSHIPS:
  DEPENDS_ON(A,B): A requires B under the declared scope.
  PREREQUISITE_OF(B,A): inverse of DEPENDS_ON(A,B).
  CONDITIONALLY_DEPENDS_ON(A,B,C): A requires B when condition C holds.
  DIRECT_DEPENDENCY(A,B): explicitly asserted dependency.
  INDIRECT_DEPENDENCY(A,C): supported path A -> B -> C when compositional rules apply.
  MUTUAL_DEPENDENCY(A,B): DEPENDS_ON(A,B) and DEPENDS_ON(B,A).
  INDEPENDENT_OF(A,B): no dependency established in the specified model and scope; not a universal claim.

FLOW:
  INPUT -> NORMALISE_ENTITIES -> IDENTIFY_DEPENDENCIES -> TYPE_RELATIONS -> ATTACH_SCOPE_AND_EVIDENCE -> VALIDATE -> INFER -> SCORE_CONFIDENCE -> SERIALISE -> AI_CONSUMPTION

INFERENCE_RULES:
  R1: DEPENDS_ON(A,B) => PREREQUISITE_OF(B,A).
  R2: DEPENDS_ON(A,B) and DEPENDS_ON(B,C) and TRANSITIVE_SCOPE(A,B,C) => INDIRECT_DEPENDENCY(A,C).
  R3: CONDITIONALLY_DEPENDS_ON(A,B,C) and SATISFIED(C) => DEPENDS_ON(A,B) within C.
  R4: DEPENDS_ON(A,B) and DEPENDS_ON(B,A) => MUTUAL_DEPENDENCY(A,B); flag potential cycle.
  R5: MISSING(B) and DEPENDS_ON(A,B) => AT_RISK(A), not necessarily FAILED(A).
  R6: NOT_DEPENDS_ON(A,B) must be supported by explicit evidence; absence of an edge is insufficient.

CONSTRAINTS:
  - Dependent and prerequisite must resolve to valid typed entities.
  - Each dependency must declare a kind and scope where applicable.
  - Self-dependencies and cycles must be flagged, not automatically rejected: some models permit feedback.
  - Logical dependency does not by itself establish causation.
  - Transitivity must not be assumed across incompatible dependency kinds or contexts.
  - Contradictory assertions must retain evidence and context for review.

SEMANTIC_EQUIVALENCE:
  exact: DEPENDS_ON(A,B) <=> PREREQUISITE_OF(B,A) within matching scope.
  related: [requires, relies_on, contingent_on, prerequisite_for]
  distinction: DEPENDS_ON != CAUSES; DEPENDS_ON != TEMPORALLY_PRECEDES.

CONFIDENCE:
  range: [0.0,1.0]
  method: Combine evidence quality, relation-type certainty, context match and inference depth; preserve source confidence separately.
  rule: Inferred confidence must not exceed weakest premise without independent supporting evidence.

VALIDATION:
  - Check entity identifiers, relation direction, types and scopes.
  - Detect unresolved prerequisites, circular chains and inconsistent conditions.
  - Verify provenance for asserted and inferred dependencies.
  - Reject unsupported promotion of correlation to dependency.

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(ontology_id, version, entities, dependency_edges, scopes, rules)
  output: deterministic_integrity_digest

UPDATE_MODEL:
  strategy: versioned_incremental_updates
  operations: [add_dependency, revise_dependency, retract_dependency, merge_entity, update_evidence, recalculate_inferences]
  safeguards: [retain_provenance, invalidate_affected_inferences, regenerate_flow_hash, audit_changes]

AI_CONSUMPTION:
  formats: [plain_text, JSON-LD_mapping, RDF_mapping, property_graph_mapping]
  capabilities: [dependency_graph_construction, prerequisite_reasoning, impact_analysis, cycle_detection, explanation_generation]
  requirement: Return relation direction, scope, confidence and provenance with each result.

EXAMPLE:
  entities: [Website, DNSResolution, DomainConfiguration]
  assertions:
    - DEPENDS_ON(Website, DNSResolution) [kind=operational, scope=public_domain_access]
    - DEPENDS_ON(DNSResolution, DomainConfiguration) [kind=operational, scope=public_domain_access]
  inference:
    - INDIRECT_DEPENDENCY(Website, DomainConfiguration) [via=DNSResolution, scope=public_domain_access]

END FLOW ALGEBRA