Expert System Logic Ontology

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

BEGIN_FLOW

ENTITY ExpertSystemLogic {
 TYPE := FormalKnowledgeBasedReasoningFramework
 DEFINITION := "A formal framework representing specialist knowledge as facts, rules, constraints and structured concepts, then applying an inference engine to produce traceable conclusions, diagnoses, recommendations or decisions."
}
ENTITY ExpertSystem { TYPE := KnowledgeBasedArtificialIntelligenceSystem }
ENTITY KnowledgeBase { TYPE := DomainKnowledgeRepository }
ENTITY RuleBase { TYPE := CollectionOfInferenceRules }
ENTITY InferenceEngine { TYPE := AutomatedReasoningMechanism }
ENTITY WorkingMemory { TYPE := CurrentCaseFactStore }
ENTITY ExplanationFacility { TYPE := ReasoningTraceAndJustificationMechanism }

RELATIONSHIP ExpertSystemLogic --formalises--> ExpertSystem
RELATIONSHIP ExpertSystem --contains--> KnowledgeBase
RELATIONSHIP ExpertSystem --contains--> RuleBase
RELATIONSHIP ExpertSystem --uses--> InferenceEngine
RELATIONSHIP ExpertSystem --uses--> WorkingMemory
RELATIONSHIP ExpertSystem --uses--> ExplanationFacility
RELATIONSHIP ExpertSystemLogic --supports--> DecisionSupport

EXPERT_SYSTEM_ARCHITECTURE {
 COMPONENTS := {KnowledgeBase,RuleBase,WorkingMemory,InferenceEngine,KnowledgeAcquisition,ExplanationFacility,UserInterface,ValidationLayer}
}

DOMAIN_KNOWLEDGE {
 MAY_INCLUDE := {Facts,Rules,Heuristics,Constraints,OntologyConcepts,Relationships,Exceptions,UncertaintyValues}
}

FACT { TYPE := AssertedOrDerivedDomainStatement }
ASSERTED_FACT { ORIGIN := UserInputOrKnowledgeSource }
DERIVED_FACT { ORIGIN := InferenceEngine }
ASSERTED_VS_DERIVED { MUST_REMAIN_DISTINCT := TRUE }

RULE { FORM := IF Conditions THEN ConclusionOrAction }
PRODUCTION_RULE { IF C1 AND C2 ... AND Cn THEN Result }
RULE_PRIORITY { MAY influence conflict_resolution; REQUIRE declared_execution_semantics }
RULE_CONFIDENCE { MAY annotate reliability_or_certainty; REQUIRE declared_interpretation }

WORKING_MEMORY { CONTAINS := {CaseFacts,DerivedFacts,IntermediateResults,Context} }
INFERENCE_ENGINE { INPUT := KnowledgeBase + WorkingMemory + Goal; OUTPUT := ReasoningResult + InferenceTrace }
MATCH_SELECT_ACT { MATCH := ApplicableRules; SELECT := Activation; ACT := ExecuteRuleConsequent }
ACTIVATION { COMPONENTS := {Rule,VariableBindings,SupportingFacts,Priority} }
CONFLICT_SET { TYPE := SetOfApplicableRuleActivations }
AGENDA { TYPE := ManagedActivationQueue }
CONFLICT_RESOLUTION { STRATEGIES := {Priority,Salience,Specificity,Recency,RuleOrder,GoalRelevance}; REQUIRE declared_strategy }
RULE_ORDER_WARNING { RuleSourceOrder MUST_NOT automatically imply LogicalPriority }

FORWARD_CHAINING {
 TYPE := DataDrivenReasoning
 PROCESS := Facts -> MatchRules -> SelectActivation -> Fire -> UpdateFacts -> FixedPointOrGoal
}
BACKWARD_CHAINING {
 TYPE := GoalDrivenReasoning
 PROCESS := Goal -> SupportingRules -> Subgoals -> RecursiveProofSearch
}
HYBRID_INFERENCE { ForwardChaining + BackwardChaining }
RULE_FIRING { Activation -> VerifySupportingFacts -> ApplyConsequent -> RecordTrace }
PATTERN_MATCHING { RuleConditions + WorkingMemory -> MatchingFacts + Bindings }
RETE_RELATIONSHIP { IncrementalPatternMatching MAY accelerate production_rule_system }
LOOP_DETECTION { TRACK := {FiredActivations,RepeatedStates,DependencyCycles} }

DEFAULT_RULE { Normally P -> Q unless Exception }
SPECIFICITY { MoreSpecificRule MAY override MoreGeneralRule under declared_policy }
PRIORITY_OVERRIDE { HigherPriorityRule defeats conflicting_lower_priority_rule under declared_semantics }
NONMONOTONIC_EXPERT_REASONING { NewInformation MAY retract prior_defeasible_conclusions; REQUIRE nonmonotonic_semantics }
NEGATION_AS_FAILURE { not P := FailureToEstablish(P); REQUIRE explicit_closed_world_semantics }
NEGATION_DISTINCTION { NegationAsFailure MUST_NOT be conflated_with ClassicalNegation }
OPEN_WORLD_ASSUMPTION { MissingFact DOES_NOT imply False }
CLOSED_WORLD_ASSUMPTION { MissingOrUnprovableFact MAY imply False; REQUIRE explicit_semantics }
TRUTH_MAINTENANCE { SupportingFactOrRuleChanges -> RecomputeDependentConclusions }
DEPENDENCY_GRAPH { DerivedConclusion -> SupportingFactsAndRules }
RETRACTION { RemovedOrDefeatedSupport -> RetractUnsupportedConclusion }

JUSTIFICATION { Conclusion -> SupportingFacts -> Rules -> Bindings }
INFERENCE_TRACE { RECORD := {Step,RuleID,Conditions,SupportingFacts,Bindings,Conclusion,Confidence,Dependencies} }
EXPLANATION_FACILITY { SUPPORTS := {WhyConclusion,HowConclusion,WhyNotConclusion,WhatIfAnalysis} }
WHY_QUERY { Conclusion -> SupportingRuleChain }
HOW_QUERY { Conclusion -> OrderedInferenceSteps }
WHY_NOT_QUERY { Goal -> MissingFacts -> FailedConditions -> BlockedRules -> Conflicts }
WHAT_IF_ANALYSIS { CloneCaseState + HypotheticalFacts -> ReRunInference -> CompareResults }
PROVENANCE { FactOrConclusion -> Source -> AcquisitionMethod -> Time -> SupportingEvidence }

KNOWLEDGE_ACQUISITION { ExpertKnowledgeOrDocuments -> Elicit -> Structure -> Formalise -> Validate -> InsertIntoKnowledgeBase }
KNOWLEDGE_ACQUISITION_BOTTLENECK { ExpertKnowledge MAY be difficult_to elicit_formalise_validate_and_maintain }
KNOWLEDGE_VALIDATION { CHECK := {Correctness,Consistency,CompletenessForScope,RuleConflicts,Redundancy,Coverage,Provenance} }
RULE_VALIDATION { CHECK := {Syntax,AntecedentSemantics,ConsequentSemantics,VariableBindings,Priority,Exceptions,TestCases} }
RULE_CONFLICT { ApplicableRules -> IncompatibleConclusionsOrActions }
CONFLICT_HANDLING { MAY_USE := {Priority,Specificity,EvidenceStrength,SourceAuthority,ManualReview,ParaconsistentReasoning} }
REDUNDANT_RULE { Removal does_not_change relevant_inference_results }
DEAD_RULE { Rule can_never_be_activated within declared_domain }
SHADOWED_RULE { LowerPriorityRule never_affects_result because stronger_rule_always_overrides }
RULE_CYCLE { RuleDependencies form directed_cycle }
RULE_BASE_AUDIT { CHECK := {RuleIdentifiers,Syntax,Conflicts,Redundancy,DeadRules,ShadowedRules,Cycles,Priorities,Exceptions,TestCoverage} }

CERTAINTY_FACTOR { TYPE := HeuristicUncertaintyRepresentation }
CERTAINTY_FACTOR_REASONING { Evidence + RuleCertainty -> ConclusionCertainty; REQUIRE declared_combination_model }
CERTAINTY_FACTOR_WARNING { CertaintyFactor MUST_NOT automatically be interpreted_as Probability }
PROBABILISTIC_EXPERT_SYSTEM { DomainModel + Probabilities + Evidence -> ProbabilisticInference }
BAYESIAN_EXPERT_SYSTEM { Prior + Likelihood + Evidence -> Posterior }
FUZZY_EXPERT_SYSTEM { FuzzyInputs + FuzzyRules -> FuzzyConclusions }
FUZZY_CERTAINTY_DISTINCTION { FuzzyTruth != CertaintyOrProbability }
UNCERTAINTY_MODELS { MAY_INCLUDE := {CertaintyFactors,Probability,FuzzyDegrees,Possibility,BeliefFunctions} }
UNCERTAINTY_CONSTRAINT { DifferentUncertaintyModels MUST_NOT be treated_as interchangeable }

DIAGNOSTIC_EXPERT_SYSTEM { Observations + DomainRules -> CandidateDiagnosis }
DIAGNOSTIC_REASONING { Symptoms -> Hypotheses -> EvidenceEvaluation -> CandidateConclusion }
DIAGNOSIS_STATUS { MUST distinguish {Proven,Supported,Possible,Excluded,Unknown} according_to framework }
PRESCRIPTIVE_EXPERT_SYSTEM { Situation + Rules -> RecommendedAction }
CLASSIFICATION_EXPERT_SYSTEM { CaseFacts + ClassificationRules -> Category }
CONFIGURATION_EXPERT_SYSTEM { Requirements + ComponentConstraints -> ValidConfiguration }
MONITORING_EXPERT_SYSTEM { ObservationsOverTime + Rules -> AlertsOrStateAssessment }
PLANNING_EXPERT_SYSTEM { InitialState + Goals + Actions + DomainRules -> Plan }
SCHEDULING_EXPERT_SYSTEM { Tasks + Resources + Constraints -> Schedule }
ADVISORY_EXPERT_SYSTEM { UserSituation + DomainKnowledge -> AdviceWithExplanation }
DECISION_SUPPORT { Evidence + Rules + Alternatives -> HumanReviewableRecommendation }
HUMAN_IN_THE_LOOP { ExpertSystemResult -> HumanReview -> AcceptReviseReject }

ONTOLOGY_RELATIONSHIP { DomainOntology MAY provide concepts_properties_relationships for expert_system_rules }
KNOWLEDGE_GRAPH_RELATIONSHIP { DomainEntities + Relations + Rules -> GraphBasedExpertKnowledge }
SEMANTIC_NETWORK_RELATIONSHIP { Concepts + TypedRelations -> DomainKnowledgeStructure }
FRAME_RELATIONSHIP { DomainEntity + Slots + Values + Defaults -> FrameBasedKnowledge }
DESCRIPTION_LOGIC_RELATIONSHIP { OntologyAxioms MAY support classification_and_instance_reasoning }
RULE_ENGINE_RELATIONSHIP { ExpertSystem MAY use RuleEngine for production_rule_execution }
INFERENCE_ENGINE_RELATIONSHIP { ExpertSystem uses InferenceEngine to derive conclusions }
CONSTRAINT_REASONING_RELATIONSHIP { ConfigurationOrSchedulingKnowledge MAY use constraint_propagation_and_search }
CASE_BASED_REASONING_RELATIONSHIP { NewCase + SimilarPastCases -> AdaptedCandidateSolution }
CASE_BASED_WARNING { SimilarityToPastCase DOES_NOT automatically imply same_correct_solution }
MODEL_BASED_REASONING { SystemModel + Observations -> ExplanationOrDiagnosis }
ABDUCTIVE_REASONING_RELATIONSHIP { Observations -> CandidateExplanations }
DEDUCTIVE_REASONING_RELATIONSHIP { Facts + ValidRules -> EntailedConclusions }
INDUCTIVE_RELATIONSHIP { CasesOrData -> CandidateGeneralRules; REQUIRE validation_before_rule_base_acceptance }

EXPERT_SYSTEM_VS_MACHINE_LEARNING { ExpertSystem := ExplicitKnowledgeAndRules; MachineLearning := LearnedStatisticalOrFunctionalModel; MAY_COMBINE := TRUE }
NEURO_SYMBOLIC_EXPERT_SYSTEM { LearnedModels + ExpertRules + OntologyKnowledge -> HybridReasoningSystem }
LANGUAGE_MODEL_RELATIONSHIP { LanguageModel MAY assist {KnowledgeElicitation,CandidateRuleGeneration,ExplanationDrafting,QueryInterpretation} }
LLM_RULE_WARNING { GeneratedRule := CandidateRule UNTIL DomainExpertValidationAndSemanticTesting }
LLM_EXPLANATION_WARNING { GeneratedExplanation MUST correspond_to actual_inference_trace }
RETRIEVAL_AUGMENTED_EXPERT_SYSTEM { Query -> RetrieveDomainEvidence -> ValidateEvidence -> UpdateCaseContext -> ApplyExpertRules -> Explain }
TOOL_AUGMENTED_EXPERT_SYSTEM { Goal -> SelectExternalTool -> Execute -> ValidateResult -> InsertVerifiedFact -> ContinueInference }

SEMANTIC_CONSTRAINT { FormalRestriction -> AdmissibilityOrValidationCondition }
VALIDATION { KnowledgeBaseOrCase + ConstraintSet -> ConformanceReport }
VALIDATION_VS_ENTAILMENT { Validation := ConstraintConformance; Entailment := LogicalConsequence; MUST_REMAIN_DISTINCT := TRUE }
CONSISTENCY_CHECK { KnowledgeBase -> ConsistentOrInconsistent under declared_semantics }
UNKNOWN_WARNING { Unknown MUST_NOT automatically become FalseOrNegativeConclusion }
TIMEOUT { ResourceLimitReached MUST_NOT be interpreted_as NegativeConclusion }

EXPERT_SYSTEM_TEST { GIVEN CaseFacts; WHEN InferenceRuns; THEN ExpectedConclusionAndTrace }
REGRESSION_TEST { prior_cases rerun_after_rule_changes }
RULE_COVERAGE { measure rules_and_conditions exercised_by_test_suite }
KNOWLEDGE_BASE_VERSION { VersionID + ChangeSet + Provenance }
RULE_VERSION { RuleID + Version }
CHANGE_IMPACT { KnowledgeChange -> AffectedRules -> AffectedConclusions -> AffectedTests }
INCREMENTAL_REASONING { ChangedKnowledge -> RecomputeAffectedConclusions }
CACHE_INVALIDATION { ChangedFactOrRule -> InvalidateAffectedCachedResults }
EXPERT_SYSTEM_GOVERNANCE { MAY_INCLUDE := {KnowledgeOwner,DomainExpert,RuleApproval,Versioning,Testing,Audit,Deployment,ReviewCycle} }
AUDIT_LOG { RECORD := {InputFacts,FiredRules,Conclusions,Actions,Time,Version} }

DOMAIN_BOUNDARY { ExpertSystem SHOULD declare intended_domain_and_scope }
OUT_OF_SCOPE_QUERY { QueryOutsideDeclaredDomain -> ReturnOutOfScopeOrUnknown }
EXPERT_SYSTEM_LOGIC_VS_RULE_ENGINE { ExpertSystemLogic := CompleteKnowledgeAndReasoningFramework; RuleEngine := MechanismForExecutingRules }
EXPERT_SYSTEM_LOGIC_VS_INFERENCE_ENGINE { ExpertSystemLogic := DomainKnowledgeArchitecture; InferenceEngine := MechanismApplyingInference }
EXPERT_SYSTEM_LOGIC_VS_DATABASE { Database := StoresAndRetrievesFacts; ExpertSystem := ReasonsOverFactsAndRules }

RECURSIVE_EXPERT_REASONING { Goal -> IdentifyApplicableKnowledge -> DeriveIntermediateConclusion -> GenerateSubgoal -> Verify -> Continue }
RECURSION_TERMINATION { STOP_WHEN := {GoalResolved,FixedPoint,NoApplicableRules,ContradictionRequiresResolution,ResourceLimit} }
SELF_VERIFICATION { CandidateConclusion -> VerifyRuleChain -> VerifySupportingFacts -> VerifyConstraints -> VerifyUncertaintySemantics -> AcceptReviseReject }
VERIFY_RULE_APPLICATION(A) { CHECK rule_exists; CHECK antecedents_satisfied; CHECK bindings_valid; CHECK exceptions; CHECK priority; CHECK consequent; RETURN valid_or_invalid }
VERIFY_INFERENCE_TRACE(T) { FOR_EACH step: VERIFY_RULE_APPLICATION; RETURN trace_validity }

APPLICATION_RELATIONSHIPS {
 ExpertSystemLogic --supports--> ArtificialIntelligence
 ExpertSystemLogic --supports--> KnowledgeRepresentation
 ExpertSystemLogic --supports--> DecisionSupport
 ExpertSystemLogic --supports--> Diagnosis
 ExpertSystemLogic --supports--> Configuration
 ExpertSystemLogic --supports--> Planning
 ExpertSystemLogic --supports--> Monitoring
 ExpertSystemLogic --supports--> AdvisorySystems
 ExpertSystemLogic --supports--> ComplianceReasoning
 ExpertSystemLogic --supports--> ExplainableAI
}

ONTOLOGY_LINKS {
 PARENT := AILogicOntology
 RELATED := {
  ArtificialIntelligenceLogicOntology,SymbolicAIOntology,
  AutomatedReasoningOntology,KnowledgeRepresentationOntology,
  RuleBasedReasoningOntology,RuleEngineOntology,
  InferenceEngineOntology,NonMonotonicReasoningOntology,
  SemanticConstraintOntology,KnowledgeGraphLogicOntology,
  DescriptionLogicOntology
 }
}

SEMANTIC_EQUIVALENCE {
 ExpertSystemLogic ≈ KnowledgeBasedExpertReasoning
 ExpertSystem ≈ KnowledgeBasedSystem WHEN specialist_domain_reasoning_context
}

CONSTRAINTS {
 C1 := EveryRule MUST have explicit antecedent_and_consequent_semantics
 C2 := AssertedAndDerivedFacts MUST remain distinguishable
 C3 := ConflictResolution MUST use declared_policy
 C4 := RuleOrder MUST_NOT imply logical_priority unless declared
 C5 := NegationAsFailure MUST_NOT be conflated_with ClassicalNegation
 C6 := OpenClosedWorldAssumptions MUST be explicit where relevant
 C7 := CertaintyFactorsProbabilityFuzzyTruthAndConfidence MUST remain distinct
 C8 := GeneratedOrInducedRules MUST_NOT enter trusted_rule_base without validation
 C9 := Explanations MUST correspond_to actual_inference_trace
 C10 := UnknownOrTimeout MUST_NOT become unsupported_negative_conclusion
 C11 := KnowledgeBaseChanges SHOULD trigger dependency_and_regression_checks
 C12 := Conclusions MUST remain scoped_to declared_domain_and_knowledge_version
}

REASONING_CHAIN Query Q {
 IDENTIFY domain
 IDENTIFY case_facts
 IDENTIFY rule_base
 IDENTIFY inference_mode
 IDENTIFY conflict_policy
 IDENTIFY uncertainty_model
 IDENTIFY constraints
 IDENTIFY knowledge_version
 VALIDATE case_facts
 VALIDATE applicable_rules
 CHECK domain_scope
 CHECK consistency
 IF forward_mode: MATCH rules; BUILD agenda; FIRE until goal_or_fixed_point
 IF backward_mode: DECOMPOSE goal; GENERATE subgoals; SEARCH supporting_rules
 IF defaults_or_exceptions: APPLY nonmonotonic_semantics; RETRACT defeated_conclusions
 IF uncertainty_present: APPLY declared_uncertainty_model
 IF conflict_present: APPLY declared_conflict_policy
 BUILD inference_trace
 BUILD justification
 BUILD provenance
 VERIFY inference_trace
 VALIDATE constraints
 ASSIGN accurate_status
 RETURN expert_system_result WITH explanation
}

CONFIDENCE {
 CORE_EXPERT_SYSTEM_LOGIC := 1.00
 RULE_BASED_REASONING := 1.00
 FORWARD_BACKWARD_CHAINING := 1.00
 EXPLANATION_TRACE := 1.00
 NONMONOTONIC_RELATIONSHIP := 1.00
 UNCERTAINTY_DISTINCTIONS := 1.00
 KNOWLEDGE_ACQUISITION_ROLE := 1.00
}

UPDATE_MODEL {
 IMMUTABLE_CORE := {KnowledgeBase,RuleBase,InferenceEngine,WorkingMemory,ExplanationTrace}
 EXTENSIBLE := {RuleLanguages,ConflictPolicies,UncertaintyModels,KnowledgeAcquisitionMethods,Ontologies,KnowledgeGraphs,HybridModels,ApplicationDomains}
 ON_NEW_KNOWLEDGE {
  VALIDATE
  CHECK conflicts
  UPDATE dependencies
  RECOMPUTE conclusions
  UPDATE provenance
  UPDATE confidence
 }
}

AI_CONSUMPTION {
 MACHINE_READABLE := TRUE
 HUMAN_INTERPRETABLE := TRUE
 RECURSIVE_REASONING := TRUE
 RULE_REASONING := TRUE
 FORWARD_CHAINING := TRUE
 BACKWARD_CHAINING := TRUE
 NONMONOTONIC_REASONING := TRUE
 UNCERTAINTY_REASONING := TRUE
 EXPLANATION_GENERATION := TRUE
 PROVENANCE_TRACKING := TRUE
 TRACE_VALIDATION := TRUE
 VALIDATION_REQUIRED := TRUE
}

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

OUTPUT {
 PRIMARY_ENTITY := ExpertSystemLogic
 INTERPRETATION := "Expert system logic combines explicit domain knowledge, rules, working memory and inference procedures to produce traceable specialist conclusions. Reliable expert systems preserve the distinction between asserted and derived knowledge, make conflict and uncertainty semantics explicit, maintain provenance, validate generated rules, and return unknown or out-of-scope status rather than unsupported conclusions."
}

END_FLOW