Multi-Hop Relationship Ontology

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

flow "MultiHopRelationshipOntology" v1.0 {
  ontology:
    id: "multi-hop-relationship-ontology"
    parent: "ai-reasoning-relationships"
    purpose: "Represent evidence-backed reasoning paths across multiple typed relations without treating mere connectivity as entailment."

  types:
    Entity: {id: string, type: string, label: string?}
    Proposition: {id: string, subject: string, predicate: string, object: string, context: string?, provenance: string[]}
    Hop: {id: string, from: string, to: string, relation: string, premise_ids: string[], rule_id: string?, confidence: number}
    ReasoningPath: {id: string, start: string, end: string, hops: Hop[], context: string?, status: enum[candidate, validated, rejected]}
    Evidence: {id: string, source: string, timestamp: datetime?, reliability: number?, supports: string[]}
    Inference: {id: string, conclusion: Proposition, premises: string[], rule_id: string, path_id: string, confidence: number}

  predicates:
    connects(hop: Hop, source: Entity, target: Entity)
    follows(next: Hop, previous: Hop)
    supports(evidence: Evidence, proposition: Proposition)
    entails(path: ReasoningPath, conclusion: Proposition)
    conflicts_with(a: Proposition, b: Proposition)
    derived_from(inference: Inference, path: ReasoningPath)

  constraints:
    - "Every hop must have resolvable, typed endpoints and a defined relation."
    - "Adjacent hops must connect: previous.to == next.from."
    - "Every derived conclusion must cite an applicable, sound inference rule and premises."
    - "A connected graph path alone does not establish logical entailment or causation."
    - "Relation composition is permitted only when a declared rule licenses it."
    - "Do not assume symmetry or transitivity of arbitrary predicates."
    - "Cycles and repeated nodes must be detected; bound traversal depth and cost."
    - "Conflicting contexts, times or entity identities must not be silently merged."
    - "Confidence and evidence reliability values, when supplied, must be within [0,1]."

  inference:
    rule path_continuity:
      if connects(h1,a,b) and connects(h2,b,c)
      then candidate_path(a,[h1,h2],c)
      confidence: "candidate only; not an inferred a-to-c semantic relation"
    rule licensed_composition:
      if relation(h1,a,p,b) and relation(h2,b,q,c) and composition_rule(p,q,r,context)
      then infer_relation(a,r,c)
      confidence: "calibrate using premises, rule validity and dependence"
    rule evidence_trace:
      if entails(path,conclusion) and all_hops_supported(path)
      then derived_from(conclusion,path)
      confidence: "retain complete proof and evidence trace"

  SEMANTIC_EQUIVALENCE:
    - "Normalise aliases using versioned mappings without collapsing related but distinct entities."
    - "Separate same-entity identity from similar concepts and equivalent predicates."
    - "Require contextual compatibility before substituting equivalent entities or relations."

  CONFIDENCE:
    range: [0,1]
    factors: [premise_quality, evidence_independence, rule_soundness, context_match, hop_count, source_reliability]
    policy: "Do not multiply scores blindly or increase confidence merely by chaining hops; account for shared evidence and uncertainty."

  VALIDATION:
    - "Validate endpoint typing, hop continuity, provenance and applicable inference rules."
    - "Reject unsupported shortcuts, context mismatches and circular self-support."
    - "Record competing paths and contradictions rather than hiding them."
    - "Distinguish a graph-reachability result from a logically justified conclusion."

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

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental update"
    steps: [ingest, normalise, validate, update_graph, recheck_paths, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed evidence-backed multi-hop reasoning graph"
    outputs: [reasoning_paths, relation_triples, proof_traces, confidence_annotations, contradictions, provenance_records]
    safeguards: [no_unlicensed_relation_composition, no_unsupported_causal_claims, no_false_identity_merges, preserve_context_and_evidence]
}

END FLOW ALGEBRA