Constraint Relationship Ontology

FLOW ALGEBRA
TITLE: Constraint Relationship Ontology
VERSION: 1.0
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/logical-relationships/constraint-relationship-ontology.html
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page text not independently verified.

ONTOLOGY:
  id: kireth:ConstraintRelationshipOntology
  domain: Logical Relationships
  purpose: Represent, evaluate and trace constraints governing entities, relationships and permissible states.

TYPES:
  Entity: identifiable object
  Relationship: typed link between entities
  Constraint: predicate restricting permissible assignments or relations
  Scope: set of entities, relations or contexts governed by a constraint
  Condition: proposition evaluated in a specified context
  Context: environment, time, jurisdiction or model version
  Evidence: observation or rule supporting an assertion
  Violation: witnessed failure of an applicable constraint
  Evaluation: outcome of a constraint check

RELATIONS:
  APPLIES_TO(Constraint, Scope)
  RESTRICTS(Constraint, Relationship | Entity)
  REQUIRES(Constraint, Condition)
  PROHIBITS(Constraint, Condition)
  DEPENDS_ON(Constraint, Constraint)
  OVERRIDES(Constraint, Constraint, Context)
  SUPPORTED_BY(Constraint, Evidence)
  VIOLATES(Entity | Relationship, Constraint, Context)

LOGIC:
  Applicable(c,x,k) := InScope(x,Scope(c),k) AND Active(c,k)
  Satisfied(c,x,k) := Applicable(c,x,k) AND Evaluate(Predicate(c),x,k)=TRUE
  Violated(c,x,k) := Applicable(c,x,k) AND Evaluate(Predicate(c),x,k)=FALSE
  Unknown(c,x,k) := Applicable(c,x,k) AND Evaluate(Predicate(c),x,k)=UNKNOWN
  Valid(x,k) := FOR_ALL c IN ApplicableConstraints(x,k): Satisfied(c,x,k)
  # UNKNOWN is not equivalent to FALSE; absence of evidence is not a violation.

CONSTRAINT_CLASSES:
  Cardinality: min/max permitted relationship counts
  DomainRange: admissible source and target types
  Uniqueness: non-duplication within a defined key and scope
  Exclusion: mutually incompatible states or relationships
  Dependency: prerequisite conditions
  Temporal: ordering, duration and validity intervals
  Integrity: consistency of references and required properties
  Contextual: rules valid only in a specified environment

INFERENCE_RULES:
  R1: APPLIES_TO(c,s) AND InScope(x,s,k) AND Active(c,k) -> Applicable(c,x,k)
  R2: Applicable(c,x,k) AND Evaluate(Predicate(c),x,k)=FALSE -> VIOLATES(x,c,k)
  R3: Applicable(c,x,k) AND Evaluate(Predicate(c),x,k)=TRUE -> Satisfied(c,x,k)
  R4: DEPENDS_ON(c1,c2) AND Active(c1,k) AND NOT Satisfied(c2,x,k) -> Blocked(c1,x,k)
  R5: OVERRIDES(c2,c1,k) AND Active(c2,k) -> Superseded(c1,k)
  # Cyclic dependencies require explicit analysis; do not infer a valid ordering.

SEMANTIC_EQUIVALENCE:
  compare: normalised predicate, scope, quantification, context and effective interval
  equivalent(c1,c2,k): logical_biconditional(Predicate(c1),Predicate(c2),k) AND same_effective_scope(c1,c2,k)
  warning: textual similarity alone does not establish logical equivalence

CONFIDENCE:
  range: [0.0,1.0]
  inputs: evidence_quality, provenance_reliability, rule_validity, context_fit
  policy: confidence annotates support; it does not change a FALSE evaluation into TRUE

VALIDATION:
  - require stable identifiers and typed predicate arguments
  - verify domain/range, scope and applicable context
  - check satisfiability and conflicting constraints
  - detect duplicate and cyclic dependency definitions
  - distinguish SATISFIED, VIOLATED, UNKNOWN and NOT_APPLICABLE
  - record counterexamples and provenance for violations

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(ontology_id, version, types, relations, rules, constraints)
  output: deterministic_digest
  note: recompute whenever canonical model content changes

UPDATE_MODEL:
  on_change: validate -> assess_impacted_constraints -> recompute_inferences -> update_provenance -> recompute_FLOW_HASH
  versioning: preserve previous versions and migration records
  rollback: restore last validated version if invariants fail

AI_CONSUMPTION:
  input: typed_graph + constraints + context + evidence
  pipeline: parse -> normalise -> resolve_scope -> evaluate -> infer -> validate -> explain
  output: evaluation_status + applicable_constraints + violations + confidence + provenance
  safeguards: do_not_infer_truth_from_missing_data; preserve_context; expose_uncertainty

END FLOW ALGEBRA