Abductive Reasoning Ontology

FLOW_ALGEBRA AbductiveReasoningOntology v1.0
TARGET_URL := "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/logical-reasoning/abductive-reasoning-ontology.html"
LANGUAGE := "en-GB"
DOMAIN := MathematicalOntologies > MathematicalLogicOntologies > LogicalReasoning > AbductiveReasoningOntology

BEGIN_FLOW

ENTITY AbductiveReasoning {
 TYPE := ExplanatoryInferenceProcess
 DEFINITION := "Reasoning that generates and evaluates plausible hypotheses capable of explaining observations under background knowledge and explicit explanatory constraints."
}
ENTITY Observation { TYPE := EvidenceOrPhenomenon }
ENTITY BackgroundKnowledge { TYPE := KnowledgeBase }
ENTITY Hypothesis { TYPE := CandidateExplanation }

RELATIONSHIP AbductiveReasoning --takes_input--> Observation
RELATIONSHIP AbductiveReasoning --uses--> BackgroundKnowledge
RELATIONSHIP AbductiveReasoning --generates--> Hypothesis
RELATIONSHIP Hypothesis --explains--> Observation
RELATIONSHIP AbductiveReasoning --compares--> AlternativeHypothesis

CORE_PATTERN {
 OBSERVE O
 IDENTIFY background B
 GENERATE H1,...,Hn
 FOR_EACH Hi:
  CHECK B∧Hi accounts_for O
  CHECK consistency
  CHECK constraints
  CHECK alternatives
 RETURN admissible_candidates
}

LOGICAL_ABDUCTION {
 GIVEN B,O
 FIND H SUCH_THAT:
  B∧H ⊨ O
  AND B∧H is consistent
 REQUIRE admissible_hypothesis_language
}

NON_ENTAILMENT {
 B∧H⊨O
 DOES_NOT imply B∧O⊨H
}

AFFIRMING_CONSEQUENT_DISTINCTION {
 H->O
 O
 THEREFORE H
 AS_DEDUCTION := invalid
 AS_ABDUCTION := H may_be_candidate_explanation
}

EXPLANATORY_ADEQUACY {
 H SHOULD account_for relevant_observations
}
CONSISTENCY {
 B∧H SHOULD be consistent
 UNLESS alternative_semantics_declared
}
MINIMALITY {
 H MAY be preferred if unnecessary assumptions absent
 REQUIRE declared_minimality_criterion
}
SET_INCLUSION_MINIMALITY {
 H minimal IFF no proper admissible subset also explains O
}
COST_BASED_ABDUCTION {
 cost(H):=SUM costs_of_assumptions
 SEEK explanatory H with minimal cost
 REQUIRE explicit_cost_model
}
PARSIMONY {
 simpler_explanation MAY be preferred
 WARNING := simplicity_is_not_proof
}
EXPLANATORY_SCOPE {
 broader_scope := explains_more_relevant_observations
}
COHERENCE {
 H SHOULD fit background_knowledge
 unless evidence motivates revision
}
NOVEL_PREDICTION {
 H -> derive P not used to construct H
 TEST P for independent_support
}
TESTABILITY {
 H SHOULD permit discriminating observations where applicable
}

ALTERNATIVE_HYPOTHESES {
 H_set := {H1,...,Hn}
 REQUIRE comparative_reasoning_when_selection_depends_on_explanatory_quality
}
UNDERDETERMINATION {
 same observations MAY support multiple incompatible explanations
}
ABDUCTIVE_AMBIGUITY {
 IF multiple admissible hypotheses remain
 THEN return candidate_set
}

DIAGNOSTIC_ABDUCTION {
 observations -> possible_causes_or_faults
}
MODEL_BASED_DIAGNOSIS {
 SystemModel + ObservedBehaviour
  -> candidate_assumptions_or_faults
  -> explanation_of_discrepancy
}
MULTIPLE_FAULT_ABDUCTION {
 H := set_of_faults
 MAY prefer subset_minimal_fault_sets
}
SCIENTIFIC_ABDUCTION {
 Phenomena
  -> explanatory_theories
  -> testable_predictions
  -> empirical_comparison
}
INFERENCE_TO_BEST_EXPLANATION {
 ABBREVIATION := IBE
 PROCESS := generate_alternatives + compare_declared_explanatory_criteria
 WARNING := comparison_criteria_must_be_explicit
}
IBE_CRITERIA := {
 ExplanatoryScope,
 Simplicity,
 Coherence,
 PredictiveAccuracy,
 MechanisticAdequacy,
 IndependentEvidence
}

BAYESIAN_RELATIONSHIP {
 P(H|O) ∝ P(O|H)P(H)
 REQUIRE prior_and_likelihood_model
}
MAP {
 H_MAP := argmax_H P(H|O)
 NOTE := probabilistic_criterion_not_universal_definition_of_abduction
}
MAXIMUM_LIKELIHOOD {
 H_ML := argmax_H P(O|H)
 WARNING := does_not_include_prior
}

ABDUCTIVE_LOGIC_PROGRAM {
 COMPONENTS := {BackgroundTheory,Abducibles,IntegrityConstraints}
}
ABDUCIBLE {
 TYPE := HypothesisAtomAllowedForAssumption
}
ABDUCTIVE_SOLUTION {
 H subset_of Abducibles
 REQUIRE:
  BackgroundTheory∪H entails Observation
  AND satisfies IntegrityConstraints
  AND satisfies selected_consistency_semantics
}
NONMONOTONICITY {
 NewEvidence MAY invalidate previous_explanation
}
EXPLANATION_REVISION {
 RECEIVE new evidence E
 RECHECK current hypotheses
 REVISE candidate_set
}

CAUSAL_ABDUCTION {
 Observation -> candidate_causal_antecedents
 REQUIRE causal_model_or_assumptions
}
CAUSAL_WARNING {
 correlation_alone DOES_NOT establish causal_explanation
}
TEMPORAL_ABDUCTION {
 observed_events -> candidate_prior_events_or_states
 REQUIRE temporal_model
}
PLAN_RECOGNITION {
 observed_actions -> candidate_goals_or_plans
}
KNOWLEDGE_GRAPH_ABDUCTION {
 observed_relations + graph_rules
  -> candidate_missing_entities_or_relations
 REQUIRE graph_semantics
}

HYPOTHESIS_GENERATION {
 METHODS := {
  RuleInversion,
  Search,
  ModelBasedGeneration,
  PatternMatching,
  CausalBacktracking,
  LearnedProposalModel
 }
}
SEARCH_SPACE {
 HYPOTHESIS_LANGUAGE := allowed_explanatory_assumptions
}
PRUNING {
 REMOVE H IF:
  inconsistent
  OR violates_constraints
  OR fails_to_explain_observation
}
COUNTEREVIDENCE {
 evidence incompatible_with_or_unlikely_under H
 -> weaken_or_reject according_to framework
}
INDEPENDENT_SUPPORT {
 evidence supporting H independently_of_generation_observation
 -> strengthens evaluation
}
OVERFITTED_EXPLANATION {
 H fits original observations
 BUT lacks predictive/generalising_success
}
AD_HOC_HYPOTHESIS {
 extra assumption added solely to protect H
 MAY reduce parsimony/testability unless independently motivated
}

VERIFY_EXPLANATION(B,O,H) {
 CHECK H admissible
 CHECK B∧H consistent
 CHECK B∧H accounts_for O
 CHECK integrity_constraints
 RETURN candidate_status
}

EXPLANATION_TRACE {
 RECORD := {
  Observation,
  BackgroundKnowledge,
  CandidateHypothesis,
  ExplanationLink,
  ConsistencyCheck,
  Constraints,
  Alternatives,
  SupportingEvidence,
  Counterevidence,
  SelectionCriterion
 }
}

ABDUCTION_VS_DEDUCTION {
 Deduction := B,H -> necessary consequence O
 Abduction := B,O -> candidate H
 reverse_direction_is_not_deduction
}
ABDUCTION_VS_INDUCTION {
 Abduction := explanation_generation
 Induction := pattern_or_generalisation_from_cases
}
ABDUCTION_VS_PROBABILITY {
 Abduction := explanatory_inference
 Probability := quantitative_uncertainty_framework
 MAY_COMBINE := TRUE
 MUST_NOT_CONFLATE := TRUE
}

APPLICATION_RELATIONSHIPS {
 AbductiveReasoning --supports--> Diagnosis
 AbductiveReasoning --supports--> ScientificReasoning
 AbductiveReasoning --supports--> ArtificialIntelligence
 AbductiveReasoning --supports--> FaultDetection
 AbductiveReasoning --supports--> PlanRecognition
 AbductiveReasoning --supports--> KnowledgeRepresentation
 AbductiveReasoning --supports--> CausalReasoning
 AbductiveReasoning --supports--> HypothesisGeneration
}

ONTOLOGY_LINKS {
 PARENT := LogicalReasoningOntology
 RELATED := {
  DeductiveReasoningOntology,
  InductiveReasoningOntology,
  AnalogicalReasoningOntology,
  HypothesisOntology,
  ExplanationOntology,
  CausalInferenceOntology,
  BayesianInferenceOntology,
  LogicProgrammingOntology,
  NonmonotonicLogicOntology,
  BeliefRevisionOntology
 }
}

SEMANTIC_EQUIVALENCE {
 AbductiveReasoning ≈ Abduction
 AbductiveHypothesis ≈ CandidateExplanation
 InferenceToBestExplanation ≈ IBE WHEN explanatory_comparison_context
}

CONSTRAINTS {
 C1 := hypotheses MUST be presented as candidate explanations, not deductively established conclusions
 C2 := background knowledge and observation MUST remain distinct
 C3 := explanatory adequacy MUST be checked
 C4 := consistency or declared alternative semantics MUST be checked
 C5 := alternatives MUST be considered when comparative explanation matters
 C6 := parsimony MUST NOT be treated as proof
 C7 := Bayesian comparison MUST identify priors and likelihoods when material
 C8 := causal explanations MUST NOT be inferred from correlation alone
 C9 := logic-programming solutions MUST satisfy integrity constraints
 C10 := new evidence MAY require explanation revision
 C11 := failure to generate alternatives MUST NOT prove uniqueness
 C12 := selection MUST remain scoped to evidence, criteria and hypothesis space
}

REASONING_CHAIN Query Q {
 IDENTIFY observation O
 IDENTIFY background B
 IDENTIFY hypothesis_space
 IDENTIFY integrity_constraints
 IDENTIFY explanatory_criteria
 GENERATE candidates

 FOR_EACH H {
  VERIFY admissibility
  VERIFY consistency
  VERIFY explanation_link
  CHECK constraints
  SEARCH counterevidence
  DERIVE novel_predictions_if_possible
 }

 REMOVE invalid_candidates

 IF multiple_candidates {
  COMPARE scope
  COMPARE simplicity
  COMPARE coherence
  COMPARE predictive_support
  COMPARE independent_evidence
 }

 IF probabilistic_framework {
  IDENTIFY priors
  IDENTIFY likelihoods
  COMPUTE posterior_or_relative_evidence
 }

 IF causal_context
  THEN validate_causal_model_and_alternatives

 IF new_evidence
  THEN revise_candidate_set

 BUILD explanation_trace
 VALIDATE constraints
 RETURN candidate_explanations WITH structured_support
}

CONFIDENCE {
 CORE_ABDUCTIVE_DEFINITION := 1.00
 DEDUCTION_DISTINCTION := 1.00
 EXPLANATION_CONSISTENCY_PATTERN := 1.00
 MINIMALITY_CONCEPT := 1.00
 LOGIC_PROGRAMMING_ABDUCTION := 0.99
 BAYESIAN_RELATIONSHIP := 0.99
 CAUSAL_WARNING := 1.00
 SPECIFIC_EXPLANATION :=
  IF observation_background_and_hypothesis_space_complete
  THEN framework_specific_support
  ELSE REQUIRE missing_information
}

UPDATE_MODEL {
 IMMUTABLE_CORE := {
  ObservationExplanationDistinction,
  CandidateHypothesisStatus,
  ExplanatoryAdequacy,
  AlternativeExplanationAwareness,
  RevisionUnderNewEvidence
 }
 EXTENSIBLE := {
  HypothesisGenerationMethods,
  ExplanatoryCriteria,
  ProbabilisticAbduction,
  CausalAbduction,
  DiagnosticModels,
  LogicProgrammingAbduction,
  PlanRecognition,
  ApplicationDomains,
  RelatedOntologies
 }
 ON_NEW_KNOWLEDGE {
  IDENTIFY new_observation
  UPDATE background_knowledge
  RECHECK existing_hypotheses
  GENERATE new_candidates_if_required
  CHECK alternatives
  CHECK counterevidence
  UPDATE explanatory_support
  UPDATE confidence
 }
}

AI_CONSUMPTION {
 MACHINE_READABLE := TRUE
 HUMAN_INTERPRETABLE := TRUE
 RECURSIVE_REASONING := TRUE
 ENTITY_RESOLUTION := TRUE
 OBSERVATION_RESOLUTION := TRUE
 HYPOTHESIS_GENERATION := TRUE
 EXPLANATION_VALIDATION := TRUE
 ALTERNATIVE_HYPOTHESIS_REASONING := TRUE
 MINIMALITY_REASONING := TRUE
 CAUSAL_ABDUCTION_REASONING := TRUE
 PROBABILISTIC_ABDUCTION_REASONING := TRUE
 LOGIC_PROGRAMMING_ABDUCTION := TRUE
 COUNTEREVIDENCE_REASONING := TRUE
 EXPLANATION_TRACE_GENERATION := TRUE
 VALIDATION_REQUIRED := TRUE
}

FLOW_HASH {
 TARGET := TARGET_URL
 SUBJECT := "Abductive Reasoning Ontology"
 VERSION := "1.0"
 CANONICAL_SIGNATURE := HASH(TARGET + SUBJECT + DOMAIN + VERSION)
}

OUTPUT {
 PRIMARY_ENTITY := AbductiveReasoning
 INTERPRETATION := "Abductive reasoning generates plausible hypotheses that could explain observations under background knowledge. Candidate explanations are checked for consistency, explanatory adequacy, alternatives, counterevidence, testability and declared comparison criteria, while remaining distinct from deductive proof."
}

END_FLOW