Explainable AI Logic Ontology

FLOW_ALGEBRA ExplainableAILogicOntology v1.0
TARGET_URL := "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/ai-logic/explainable-ai-logic-ontology.html"
LANGUAGE := "en-GB"
DOMAIN := MathematicalOntologies > MathematicalLogicOntologies > AILogic > ExplainableAILogicOntology

BEGIN_FLOW

ENTITY ExplainableAILogic {
 TYPE := FormalExplanationAndReasoningFramework
 DEFINITION := "A formal framework for representing, tracing, validating and communicating the reasons, evidence, dependencies and model factors associated with an AI result while distinguishing explanation, proof, evidence, prediction and causal attribution."
}
ENTITY AIResult { TYPE := MachineProducedOutcome }
ENTITY Explanation { TYPE := StructuredAccountOfResultBasis }
ENTITY Evidence { TYPE := SupportingInformation }
ENTITY ReasoningTrace { TYPE := StructuredDerivationRecord }
ENTITY Provenance { TYPE := OriginAndTransformationRecord }

RELATIONSHIP ExplainableAILogic --explains--> AIResult
RELATIONSHIP Explanation --uses--> Evidence
RELATIONSHIP Explanation --may_use--> ReasoningTrace
RELATIONSHIP Explanation --requires--> Provenance
RELATIONSHIP ExplainableAILogic --supports--> HumanInterpretation
RELATIONSHIP ExplainableAILogic --supports--> AIValidation

XAI_ARCHITECTURE {
 COMPONENTS := {AIResult,ExplanationTarget,Evidence,ReasoningTrace,Provenance,ExplanationMethod,Validation,Audience,Context,Uncertainty}
}

EXPLANATION_TARGET {
 MAY_BE := {Prediction,Classification,Recommendation,Decision,LogicalConclusion,GeneratedStatement,Plan,Action}
}
EXPLANANDUM { TYPE := ThingToBeExplained }
EXPLANANS { TYPE := InformationOfferedAsExplanation }
EXPLANATION_RELATION { Explanans -> explains -> Explanandum }

EXPLANATION_GOAL {
 MAY_INCLUDE := {Why,WhyNot,How,WhatIf,Contrastive,Counterfactual,Causal,Evidential,Procedural,Debugging}
}
WHY_EXPLANATION { Result -> SupportingFactorsOrReasoning }
WHY_NOT_EXPLANATION { AlternativeResult -> MissingOrBlockingConditions }
HOW_EXPLANATION { Result -> ProcessOrDerivationSteps }
WHAT_IF_EXPLANATION { ModifiedInputOrAssumption -> RecomputeOrEstimateResult -> Compare }
CONTRASTIVE_EXPLANATION { Why ResultA rather_than ResultB }
COUNTERFACTUAL_EXPLANATION { RelevantChange -> DifferentOutcome }
COUNTERFACTUAL_WARNING { validity depends_on model_and_feasibility_assumptions }
CAUSAL_EXPLANATION { CausalModel + InterventionSemantics -> CausalAccount }
CAUSAL_WARNING { FeatureImportanceOrAssociation MUST_NOT automatically be described_as CausalEffect }
EVIDENTIAL_EXPLANATION { Result -> SupportingEvidence -> SourceProvenance }
LOGICAL_EXPLANATION { Conclusion -> Premises -> RulesOrAxioms -> Derivation }

PROOF { TYPE := FormallyValidDerivation }
EXPLANATION_VS_PROOF {
 Explanation := AccountSelectedForUnderstanding
 Proof := FormallyValidDerivation
 MUST_REMAIN_DISTINCT := TRUE
}
EVIDENCE_VS_PROOF {
 Evidence := InformationSupportingClaim
 Proof := FormalDerivation
 MUST_REMAIN_DISTINCT := TRUE
}
PREDICTION_VS_EXPLANATION {
 Prediction := ModelOutput
 Explanation := AccountOfOutputBasis
 MUST_REMAIN_DISTINCT := TRUE
}

JUSTIFICATION { Result -> SupportingFactsRulesAxiomsOrEvidence }
MINIMAL_JUSTIFICATION { subset_minimal_support under declared_definition }

REASONING_TRACE {
 MAY_BE := {Sequence,Tree,DAG,RuleChain,SolverTrace,ToolTrace}
}
TRACE_STEP {
 COMPONENTS := {StepID,Inputs,RuleOrOperation,Parameters,Output,Dependencies,Source}
}
TRACE_DEPENDENCY { StepB depends_on StepA }
TRACE_VALIDATION { VerifyInputs -> VerifyOperation -> VerifyOutput -> VerifyDependencies }
TRACE_COMPLETENESS { SHOULD include material_steps needed_for_claimed_explanation }
TRACE_FIDELITY { explanation MUST correspond_to actual_process when claimed_as faithful }

POST_HOC_EXPLANATION { generated_after_prediction without necessarily being internal_process }
INTRINSIC_EXPLANATION { derived_directly_from interpretable_model_or_symbolic_structure }
POST_HOC_VS_INTRINSIC { MUST_REMAIN_DISTINCT := TRUE }
LOCAL_EXPLANATION { explains specific_instance_or_result }
GLOBAL_EXPLANATION { describes general_model_or_system_behaviour }
LOCAL_GLOBAL_DISTINCTION { instance_specific_evidence MUST_NOT automatically generalise_to whole_model }
MODEL_SPECIFIC_EXPLANATION { requires access_to particular_model_structure }
MODEL_AGNOSTIC_EXPLANATION { treats model_as queryable_input_output_function }

FEATURE_ATTRIBUTION { Prediction -> FeatureContributionScores }
ATTRIBUTION_SCORE { Feature -> NumericContributionOrImportance under declared_method }
ATTRIBUTION_WARNING { score is method_and_baseline_dependent and MUST_NOT automatically mean causation }
BASELINE { reference_input_or_expected_value used_by attribution_method }
BASELINE_SENSITIVITY { changing baseline MAY change attribution }
SHAP_RELATIONSHIP { ShapleyValueBasedExplanation -> FeatureAttribution }
SHAP_WARNING { values explain model_output_relative_to reference and do_not_by_themselves establish causality }
LIME_RELATIONSHIP { LocalSurrogateModel -> ApproximateLocalExplanation }
LIME_WARNING { surrogate_fidelity is local_and_approximate }
SALIENCY_RELATIONSHIP { GradientOrActivationSignal -> InputRelevanceVisualisation }
SALIENCY_WARNING { visual_prominence MUST_NOT automatically mean causal_importance }
ATTENTION_EXPLANATION_RELATIONSHIP { attention_weights MAY provide model_internal_signal }
ATTENTION_WARNING { attention_weights MUST_NOT automatically be treated_as complete_explanation }

RULE_BASED_EXPLANATION { FiredRules + SupportingFacts -> Conclusion }
EXPERT_SYSTEM_EXPLANATION { Conclusion -> RuleChain -> WorkingMemoryFacts -> Provenance }
PROLOG_EXPLANATION { QueryAnswer -> SLDResolutionSteps -> Clauses -> Unifiers }
CLP_EXPLANATION { SolutionOrFailure -> Constraints -> PropagationSteps -> SearchDecisions }
SAT_EXPLANATION { SATResult -> AssignmentOrCertificate }
UNSAT_EXPLANATION { UNSATResult -> ProofOrUnsatCore where available }
UNSAT_CORE { subset_of_constraints jointly_unsatisfiable }
ONTOLOGY_EXPLANATION { Entailment -> SupportingAxioms -> ReasonerDerivationOrJustification }
KNOWLEDGE_GRAPH_EXPLANATION { DerivedRelation -> GraphPathRulesEvidence }
RAG_EXPLANATION { GeneratedAnswer -> RetrievedSources -> UsedEvidence -> GenerationOrReasoningSteps }
RAG_WARNING { retrieval_provenance DOES_NOT guarantee generated_claim_is_supported }
LLM_EXPLANATION_WARNING { generated_rationale MUST_NOT automatically be treated_as faithful_record_of_internal_computation }
VERIFIABLE_REASON_SUMMARY { Result -> KeyPremises -> KeyOperations -> Evidence -> Conclusion }

PROVENANCE {
 COMPONENTS := {Source,AuthorOrSystem,Timestamp,Version,Transformation,Derivation}
}
SOURCE_PROVENANCE { Evidence -> Origin }
MODEL_PROVENANCE { Result -> ModelID -> ModelVersion }
DATA_PROVENANCE { Result -> DatasetOrInputVersion }
TOOL_PROVENANCE { ToolResult -> Tool -> Parameters -> Time -> Status }
DERIVATION_PROVENANCE { DerivedResult -> SupportingResultsAndOperations }
PROVENANCE_INTEGRITY { links MUST correspond_to actual_source_and_processing_history }

EVIDENCE {
 MAY_BE := {Observation,Document,DatabaseRecord,SensorReading,FormalAxiom,ToolResult,ExperimentalResult}
}
EVIDENCE_RELEVANCE { Evidence -> supports_or_refutes -> Claim }
EVIDENCE_STRENGTH { MAY_DEPEND_ON := {SourceQuality,Directness,Independence,Recency,Method,Consistency} }
SOURCE_CONFLICT { EvidenceA conflicts_with EvidenceB }
CONFLICT_EXPLANATION { identify conflicting_claims_sources_timestamps_assumptions }

UNCERTAINTY {
 MAY_INCLUDE := {Probability,Confidence,FuzzyDegree,Possibility,UnknownStatus}
}
UNCERTAINTY_DISTINCTION {
 Probability != Confidence
 Probability != FuzzyTruth
 Confidence != LogicalTruth
 Unknown != False
}
UNCERTAINTY_EXPLANATION { Result -> UncertaintyMeasure -> Interpretation -> SourceOfUncertainty }
CONFIDENCE_WARNING { confidence_score MUST have declared_semantics }

EXPLANATION_FIDELITY { explanation accurately_reflects target_system_behaviour within declared_scope }
EXPLANATION_ACCURACY { factual_and_logical_claims in explanation are correct }
EXPLANATION_COMPLETENESS { contains sufficient_material_information for declared_goal }
EXPLANATION_RELEVANCE { focuses_on information relevant_to user_question }
EXPLANATION_CONSISTENCY { equivalent_reasoning SHOULD produce compatible_explanations }
EXPLANATION_STABILITY { irrelevant_small_changes SHOULD_NOT cause disproportionate_changes where stability_expected }
EXPLANATION_ROBUSTNESS { remains reliable under permitted_perturbations }
EXPLANATION_SIMPLICITY { minimise unnecessary_complexity while preserving material_truth }
SIMPLICITY_FIDELITY_TRADEOFF { simpler_explanation MAY omit detail; REQUIRE no_material_misrepresentation }

FAITHFULNESS_TEST { CompareExplanationClaims with ActualModelOrReasoningBehaviour }
PERTURBATION_TEST { ModifyRelevantFeature -> ObserveOutputChange -> CompareWithExplanation }
COUNTERFACTUAL_VALIDATION { CandidateCounterfactual -> CheckOutcomeChange -> CheckFeasibility -> CheckConstraintSatisfaction }
RULE_TRACE_TEST { ExplanationRuleChain -> ReplayInference -> ConfirmConclusion }
PROVENANCE_TEST { ExplanationSourceLinks -> VerifyExistenceAndUse }
REGRESSION_TEST { prior_explanations rerun_after_model_or_rule_changes }
EXPLANATION_VERSION { ExplanationID + ModelVersion + DataVersion + MethodVersion }
CHANGE_IMPACT { ModelOrKnowledgeChange -> AffectedResults -> AffectedExplanations -> Revalidation }

SYMBOLIC_XAI { ExplicitRules + Facts + Derivation -> TraceableExplanation }
SUBSYMBOLIC_XAI { LearnedModel + ExplanationMethod -> ApproximateOrModelSpecificExplanation }
NEURO_SYMBOLIC_XAI { LearnedModel + SymbolicKnowledge + FormalReasoning -> HybridExplanation }
CAUSAL_XAI { CausalModel + Intervention -> CausalExplanation }
COUNTERFACTUAL_XAI { Instance + DesiredOutcome + FeasibilityConstraints -> CounterfactualCandidate }
CONTRASTIVE_XAI { ActualOutcome + AlternativeOutcome -> DifferenceExplanation }
EXAMPLE_BASED_EXPLANATION { Result -> SimilarOrInfluentialExamples }
EXAMPLE_WARNING { similarity_or_influence MUST_NOT automatically imply causal_reason }
CONCEPT_BASED_EXPLANATION { ModelBehaviour -> HumanMeaningfulConcepts }

NATURAL_LANGUAGE_EXPLANATION { StructuredExplanation -> HumanReadableNarrative }
NLG_EXPLANATION_CONSTRAINT { generated_narrative MUST preserve structured_explanation_semantics }
HALLUCINATION_CONTROL { ExplanationClaim -> EvidenceCheck -> TraceCheck -> ProvenanceCheck -> StatusAssignment }
UNSUPPORTED_EXPLANATION_CLAIM { claim_without sufficient_evidence_or_trace }
EXPLANATION_STATUS { MAY_INCLUDE := {Verified,Supported,Approximate,Partial,Hypothetical,Unsupported,Unknown} }
STATUS_CONSTRAINT { explanation_status MUST match evidence_and_fidelity_level }

USER_QUERY { MAY_REQUEST := {Why,WhyNot,How,Evidence,Sources,Confidence,Counterfactual,Alternative} }
EXPLANATION_SELECTION { UserQuery + Audience + Context -> ExplanationType }
PERSONALISED_EXPLANATION { adapt terminology_and_detail to user_context; MUST_NOT alter underlying_facts_or_reasoning }
INTERACTIVE_EXPLANATION { Explanation -> FollowUpQuestion -> RefinedExplanation }
DRILL_DOWN { Summary -> SupportingDetail -> Trace -> Evidence }
ABSTRACTION_LEVEL { MAY_BE := {Summary,Intermediate,Technical,Formal} }

EXPLANATION_GRAPH {
 Nodes := {Results,Claims,Evidence,Rules,ModelFactors,Sources}
 Edges := {Supports,Derives,Contradicts,DependsOn,GeneratedBy,RetrievedFrom}
}
EXPLANATION_GRAPH_QUERY { Result -> TraverseSupportDependencies -> ReturnRelevantSubgraph }
SEMANTIC_EXPLANATION { ExplanationGraph + Ontology -> TypedExplanation }
ONTOLOGY_ALIGNMENT { explanation_terms -> ontology_entities }
ENTITY_RESOLUTION { explanation_mentions -> canonical_entities }
CONTRADICTION_DETECTION { explanation_claims -> detect logical_or_evidential_conflicts }

TEMPORAL_EXPLANATION { Result -> TimeRelevantEvidence -> TemporalDependencies }
TEMPORAL_VALIDITY { explanation valid_for declared_time_or_model_state }
EXPLANATION_EXPIRY { underlying_data_or_model_changes MAY make explanation_stale }

DECISION_EXPLANATION { Decision -> Inputs -> RulesOrModelFactors -> Constraints -> Alternatives }
RECOMMENDATION_EXPLANATION { Recommendation -> ContextFeatures -> Evidence -> ModelOrRuleBasis }
PLAN_EXPLANATION { Plan -> Goals -> Actions -> Preconditions -> Constraints }
ACTION_EXPLANATION { Action -> Trigger -> Policy -> ReasoningResult }
SAFETY_EXPLANATION { ResultOrAction -> ApplicableSafetyConstraints -> Checks -> Outcome }
CONSTRAINT_EXPLANATION { Result -> SatisfiedConstraints -> ViolatedConstraints -> Tradeoffs }
EXPLANATION_OF_FAILURE { Failure -> FailedCondition -> MissingEvidence -> ConstraintViolation -> ResourceLimit }
UNKNOWN_EXPLANATION { UnknownResult -> MissingInformation -> UnresolvedConflict -> UnsupportedInference }
TIMEOUT_EXPLANATION { Timeout -> ResourceLimit -> IncompleteSearchStatus }

EXPLAINABLE_AI_LOGIC_VS_INTERPRETABILITY {
 Explainability := AccountOfWhyOrHowResultOccurs
 Interpretability := DegreeSystemCanBeUnderstood
 RELATED_NOT_IDENTICAL := TRUE
}
EXPLAINABLE_AI_LOGIC_VS_TRANSPARENCY {
 Transparency := VisibilityIntoSystemDataModelProcess
 Explainability := StructuredAccountOfResultBasis
}
EXPLAINABLE_AI_LOGIC_VS_AUDITABILITY {
 Auditability := AbilityToInspectAndVerifyRecords
 Explainability := AccountOfResultBasis
}

RECURSIVE_EXPLANATION {
 Result -> IdentifyExplanationGoal -> GatherEvidence -> BuildDependencyStructure -> ValidateClaims -> IdentifyGaps -> Refine -> ReturnExplanation
}
RECURSION_TERMINATION {
 STOP_WHEN := {ExplanationGoalSatisfied,EvidenceExhausted,RequiredFidelityReached,NoValidProgress,ResourceLimit}
}
SELF_VERIFICATION {
 CandidateExplanation -> VerifyEvidence -> VerifyTrace -> VerifyProvenance -> VerifyStatus -> AcceptReviseReject
}

APPLICATION_RELATIONSHIPS {
 ExplainableAILogic --supports--> ArtificialIntelligence
 ExplainableAILogic --supports--> SymbolicAI
 ExplainableAILogic --supports--> ExpertSystems
 ExplainableAILogic --supports--> AutomatedReasoning
 ExplainableAILogic --supports--> KnowledgeGraphs
 ExplainableAILogic --supports--> DecisionSupport
 ExplainableAILogic --supports--> ModelValidation
 ExplainableAILogic --supports--> HumanOversight
 ExplainableAILogic --supports--> Auditability
}

ONTOLOGY_LINKS {
 PARENT := AILogicOntology
 RELATED := {
  ArtificialIntelligenceLogicOntology,SymbolicAIOntology,
  AutomatedReasoningOntology,ExpertSystemLogicOntology,
  LogicProgrammingOntology,PrologOntology,
  ConstraintLogicProgrammingOntology,LogicalInferenceOntology,
  KnowledgeGraphLogicOntology,SemanticConstraintOntology,
  ProvenanceOntology
 }
}

SEMANTIC_EQUIVALENCE {
 ExplainableAILogic ≈ FormalAIExplanationLogic
 ExplanationTrace ≈ StructuredReasoningTrace WHEN actual_process_correspondence
 Justification ≈ SupportingKnowledgeSet WHEN formal_reasoning_context
}

CONSTRAINTS {
 C1 := Explanation MUST identify target_and_goal
 C2 := ExplanationProofEvidencePredictionAndCausation MUST remain distinguishable
 C3 := FaithfulExplanation MUST correspond_to actual_system_behaviour
 C4 := PostHocExplanation MUST be labelled
 C5 := AttributionScores MUST_NOT automatically mean causation
 C6 := LocalExplanations MUST_NOT automatically generalise_to global_behaviour
 C7 := UncertaintyMeasures MUST retain declared_semantics
 C8 := GeneratedExplanation MUST preserve structured_evidence
 C9 := Provenance MUST correspond_to actual_sources
 C10 := UnknownTimeoutAndPartialStatus MUST_NOT become certainty
 C11 := Counterfactuals MUST satisfy feasibility_constraints
 C12 := ExplanationVersion SHOULD track model_data_method_versions
}

REASONING_CHAIN Query Q {
 IDENTIFY result_to_explain
 IDENTIFY explanation_goal
 IDENTIFY audience_and_context
 IDENTIFY available_evidence
 IDENTIFY provenance
 SELECT explanation_method
 GATHER evidence
 BUILD dependency_structure
 VERIFY trace_if_available
 LABEL posthoc_if_applicable
 VALIDATE counterfactuals_and_causal_claims
 CHECK evidence_and_provenance
 ASSIGN explanation_status
 RETURN explanation WITH verifiable_support
}

CONFIDENCE {
 CORE_XAI_LOGIC := 1.00
 EXPLANATION_PROOF_DISTINCTION := 1.00
 EVIDENCE_PROVENANCE := 1.00
 POSTHOC_INTRINSIC_DISTINCTION := 1.00
 LOCAL_GLOBAL_DISTINCTION := 1.00
 ATTRIBUTION_CAUSALITY_DISTINCTION := 1.00
}

UPDATE_MODEL {
 IMMUTABLE_CORE := {ExplanationTarget,ExplanationGoal,Evidence,Provenance,Fidelity,ExplicitStatus}
 EXTENSIBLE := {ExplanationMethods,AttributionMethods,CounterfactualMethods,CausalMethods,AudienceModels,ExplanationGraphs,ApplicationDomains}
 ON_NEW_KNOWLEDGE {
  INVALIDATE affected_explanations
  REBUILD dependencies
  REVALIDATE evidence_and_trace
  UPDATE provenance
  UPDATE confidence
 }
}

AI_CONSUMPTION {
 MACHINE_READABLE := TRUE
 HUMAN_INTERPRETABLE := TRUE
 RECURSIVE_REASONING := TRUE
 EXPLANATION_GRAPH_REASONING := TRUE
 EVIDENCE_REASONING := TRUE
 PROVENANCE_TRACKING := TRUE
 TRACE_VALIDATION := TRUE
 COUNTERFACTUAL_REASONING := TRUE
 CAUSALITY_GUARD := TRUE
 UNCERTAINTY_REASONING := TRUE
 SELF_VERIFICATION := TRUE
 VALIDATION_REQUIRED := TRUE
}

FLOW_HASH {
 TARGET := TARGET_URL
 SUBJECT := "Explainable AI Logic Ontology"
 VERSION := "1.0"
 CANONICAL_SIGNATURE := HASH(TARGET + SUBJECT + DOMAIN + VERSION)
}

OUTPUT {
 PRIMARY_ENTITY := ExplainableAILogic
 INTERPRETATION := "Explainable AI logic structures explanations around explicit targets, evidence, provenance, reasoning traces, uncertainty and validation. It distinguishes formal proof from explanatory narrative, intrinsic traces from post-hoc approximations, local from global explanations, and attribution from causality while supporting counterfactual, contrastive, symbolic and neuro-symbolic explanation methods."
}

END_FLOW