Conditional Relationship Ontology

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

ONTOLOGY:
  ConditionalRelationship := (antecedent: Proposition, consequent: Proposition, context: Context, modality: Modality, evidence: EvidenceSet)
  Proposition := expression with truth evaluation under an interpretation
  Context := assumptions, temporal scope, jurisdiction/domain, and evaluation environment
  Modality := material | strict | defeasible | probabilistic | operational
  EvidenceSet := zero or more provenance-linked observations or justifications

TYPED_ENTITIES:
  Condition: Proposition
  Consequence: Proposition
  Rule: ConditionalRelationship
  Evaluation: (rule_id, context_id, antecedent_truth, consequent_truth, status)
  Exception: (rule_id, exception_condition, priority)
  Provenance: (source_id, method, timestamp, version)

RELATIONSHIPS:
  HAS_ANTECEDENT(rule, proposition)
  HAS_CONSEQUENT(rule, proposition)
  EVALUATED_IN(rule, context)
  QUALIFIED_BY(rule, exception)
  SUPPORTED_BY(rule, evidence)
  OVERRIDES(exception_or_rule, rule)

FLOW_RULES:
  MATERIAL_IMPLICATION: A -> B := NOT(A) OR B.
  MODUS_PONENS: (A -> B) AND A entails B, for classical material implication in the same context.
  MODUS_TOLLENS: (A -> B) AND NOT(B) entails NOT(A), under classical logic.
  CHAINING: (A -> B) AND (B -> C) entails (A -> C), where contexts and modalities are compatible.
  CONTRAPOSITION: (A -> B) entails (NOT B -> NOT A) only in logics supporting contraposition.
  DEFEASIBLE: A normally implies B unless a higher-priority applicable exception defeats the rule.
  PROBABILISTIC: P(B | A, context) is a conditional probability, not a logical entailment.
  OPERATIONAL: IF condition THEN action specifies a workflow trigger, not necessarily a truth-functional implication.

VALIDATION:
  - Antecedent and consequent must be well-typed propositions.
  - Record logic and modality explicitly before applying inference rules.
  - Evaluate both propositions under a consistent context and temporal scope.
  - Do not infer causation from material implication or conditional probability alone.
  - Detect conflicting consequents and resolve only with documented precedence or report unresolved conflict.
  - Preserve source evidence and exceptions; distinguish unknown from false.

SEMANTIC_EQUIVALENCE:
  - Treat two rules as equivalent only if they preserve meaning under the specified logic, context and modality.
  - Normalise syntactic variants without collapsing strict, defeasible and probabilistic conditionals.
  - Preserve antecedent/consequent direction.

CONFIDENCE:
  representation: calibrated value in [0,1] with method and evidence provenance
  policy: confidence in evidence or rule reliability is distinct from proposition truth.
  propagation: use a declared inference-specific aggregation method; do not assume independence.

FLOW_HASH:
  canonicalise: ontology version, rule identifiers, typed propositions, modality, context, exceptions, and provenance references
  algorithm: SHA-256 of UTF-8 canonical serialisation
  purpose: integrity and change detection; not proof of logical validity

UPDATE_MODEL:
  - Ingest changed rules and evidence with version and timestamp.
  - Revalidate typing, conflicts, scope and exception precedence.
  - Recompute affected inference dependencies and FLOW_HASH.
  - Retain audit history and invalidate stale derived conclusions.

AI_CONSUMPTION:
  format: typed rule graph with machine-readable context and provenance
  operations: retrieve, match, evaluate, infer, explain, audit
  guardrails: report uncertainty; respect modality; avoid unjustified causal claims
  output: conclusions with applicable rules, assumptions, exceptions, and confidence basis

END FLOW ALGEBRA