AI Reasoning Relationships

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

FLOW ALGEBRA
TITLE: AI Reasoning Relationships
DOMAIN: Relationship Ontologies / AI Reasoning Relationships
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/ai-reasoning-relationships.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "AIReasoningRelationships" v1.0 {
  ontology:
    id: "ai-reasoning-relationships"
    parent: "relationship-ontologies"
    purpose: "Represent evidence-backed relationships between premises, rules, conclusions, hypotheses, explanations and decisions in AI reasoning systems."

  types:
    Proposition: {id: string, statement: string, context: string?, truth_status: enum[true, false, unknown, inconsistent], provenance: string[]}
    Premise: {id: string, proposition_id: string, role: enum[asserted, assumed, observed, inferred]}
    ReasoningRule: {id: string, name: string, kind: enum[deductive, inductive, abductive, probabilistic, defeasible], premises: string[], conclusion_pattern: string, version: string}
    Inference: {id: string, rule_id: string, premise_ids: string[], conclusion_id: string, confidence: number, timestamp: datetime?, evidence: string[]}
    Hypothesis: {id: string, proposition_id: string, competing_hypotheses: string[], status: enum[proposed, supported, rejected, unresolved]}
    Explanation: {id: string, inference_ids: string[], evidence_ids: string[], limitations: string[]}
    Decision: {id: string, alternatives: string[], selected: string?, rationale: string[], context: string}
    Relationship: {id: string, subject: string, predicate: string, object: string, context: string?, confidence: number, provenance: string[]}

  predicates:
    supports(evidence: string, proposition: Proposition)
    contradicts(a: Proposition, b: Proposition)
    entails(premises: Premise[], conclusion: Proposition)
    inferred_by(conclusion: Proposition, rule: ReasoningRule)
    depends_on(inference: Inference, premise: Premise)
    explains(explanation: Explanation, inference: Inference)
    alternative_to(a: Hypothesis, b: Hypothesis)
    informs(decision: Decision, proposition: Proposition)
    revises(new_inference: Inference, old_inference: Inference)

  constraints:
    - "All relationship endpoints must resolve to typed identifiers."
    - "Confidence values must lie within [0,1]."
    - "Each inferred conclusion must reference a rule and its actual premises."
    - "Distinguish deductive entailment from probabilistic, inductive and abductive support."
    - "Do not treat correlation, temporal succession or co-occurrence as causation."
    - "Preserve conflicting evidence rather than silently overwriting it."
    - "Do not treat a generated explanation as independent evidence."
    - "Avoid circular support: an inference must not validate its own premises."
    - "Context, temporal scope and ontology version must be retained where material."

  inference:
    rule modus_ponens:
      if accepted(p) and accepted(implies(p,q)) and same_context(p,q)
      then derive(q)
      confidence: "logical validity is separate from premise reliability"
    rule contradiction_flag:
      if accepted(p) and accepted(not(p)) and same_context(p,not(p))
      then flag_inconsistency(p)
      confidence: "retain both source records pending reconciliation"
    rule traceable_conclusion:
      if valid_rule(r) and verified_premises(r) and applicable_context(r)
      then create_inference_record(r)
      confidence: "calculate under declared uncertainty policy; never manufacture certainty"
    rule revision:
      if new_evidence(e) and affects(e,existing_inference)
      then reevaluate(existing_inference)
      confidence: "retain superseded inference and change provenance"

  SEMANTIC_EQUIVALENCE:
    - "Normalise concepts against versioned ontologies and preserve original terms."
    - "Distinguish equivalence, similarity, implication, contradiction and identity."
    - "Do not merge context-dependent statements without checking scope and qualifiers."

  CONFIDENCE:
    range: [0,1]
    factors: [premise_reliability, evidence_quality, rule_applicability, model_uncertainty, context_match, independent_replication]
    policy: "Separate epistemic confidence from formal validity; no automatic confidence inflation through inference chains."

  VALIDATION:
    - "Check identifier resolution, types, rule arity, premises and conclusions."
    - "Check logical consistency and detect circular inference dependencies."
    - "Check evidence provenance, contextual scope and temporal validity."
    - "Label unsupported or underdetermined conclusions as unresolved."
    - "Record assumptions, exceptions and competing hypotheses."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed assertions, rules, evidence links and provenance"
    note: "Compute at execution; no hash value is claimed here."

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental revision"
    steps: [ingest, normalise, validate, detect_conflicts, revise_beliefs, recompute_inferences, audit, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed reasoning knowledge graph with auditable inference traces"
    outputs: [premise_links, rule_applications, conclusions, confidence_annotations, explanations, provenance_records, conflict_flags]
    safeguards: [no_unsupported_entailment, no_causal_overclaim, preserve_uncertainty, distinguish_assumption_from_fact, human_review_for_high_stakes_decisions]
}

END FLOW ALGEBRA