Artificial Intelligence Logic Ontology

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

BEGIN_FLOW

ENTITY ArtificialIntelligenceLogic { TYPE := FormalMachineReasoningFramework; DEFINITION := "Formal logical structures and inference processes used to represent knowledge and support machine reasoning in artificial intelligence." }
ENTITY KnowledgeBase { TYPE := StructuredMachineKnowledge }
ENTITY Inference { TYPE := FormalReasoningProcess }
ENTITY Query { TYPE := ReasoningGoal }
ENTITY ReasoningResult { TYPE := EvaluatedOutcome }

RELATIONSHIP ArtificialIntelligenceLogic --operates_on--> KnowledgeBase
RELATIONSHIP ArtificialIntelligenceLogic --uses--> Inference
RELATIONSHIP ArtificialIntelligenceLogic --evaluates--> Query
RELATIONSHIP ArtificialIntelligenceLogic --produces--> ReasoningResult
RELATIONSHIP ArtificialIntelligenceLogic --supports--> ArtificialIntelligence

ARCHITECTURE { COMPONENTS := {FormalLanguage,Syntax,Semantics,KnowledgeBase,InferenceRules,ReasoningEngine,Constraints,UncertaintyModel,Context,Provenance,Verification,Explanation} }

KNOWLEDGE_STATUS { TYPES := {Asserted,Derived,Predicted,Hypothesised,Assumed,Unknown,Contradicted} }
STATUS_SEPARATION { Asserted != Derived; Derived != Predicted; Predicted != Hypothesised }

LOGIC_FAMILIES { INCLUDE := {PropositionalLogic,PredicateLogic,DescriptionLogic,ModalLogic,TemporalLogic,EpistemicLogic,DeonticLogic,DynamicLogic,FuzzyLogic,ProbabilisticLogic,NonMonotonicLogic,ParaconsistentLogic,RuleLogic,ConstraintLogic} }

KNOWLEDGE_REPRESENTATION { Entities + Concepts + Relations + Rules + Constraints + Context -> MachineInterpretableKnowledge }
ONTOLOGY { Classes + Individuals + Properties + Axioms -> FormalConceptualModel }
KNOWLEDGE_GRAPH { Entities + TypedRelations + Schema + Provenance -> SemanticGraph }

SEMANTIC_ENTAILMENT { KB entails C IFF every model_of_KB satisfies C under declared_semantics }
SYNTACTIC_DERIVABILITY { KB proves C IFF C derivable_using selected_calculus }
SOUNDNESS { Derivable(C) -> Entailed(C); REQUIRE sound_calculus }
COMPLETENESS { Entailed(C) -> Derivable(C); REQUIRE complete_calculus_for_selected_logic }

DEDUCTIVE_REASONING { Premises + ValidRules -> NecessaryConclusion }
INDUCTIVE_REASONING { Observations -> GeneralisationOrPrediction; STATUS := AmpliativeSupport }
ABDUCTIVE_REASONING { Observations -> CandidateExplanation; STATUS := Hypothesis }
ANALOGICAL_REASONING { SourceStructure + RelevantSimilarity -> DefeasibleTargetInference }
RULE_BASED_REASONING { Facts + Rules -> DerivedFacts }
CONSTRAINT_REASONING { Variables + Domains + Constraints -> PropagationAndSearch }

FORWARD_CHAINING { InitialFacts -> ApplicableRules -> NewFacts -> FixedPointOrGoal }
BACKWARD_CHAINING { Goal -> SupportingRules -> Subgoals -> ProofOrFailureStatus }
RESOLUTION { ComplementaryClauseLiterals -> Resolvent }
FIRST_ORDER_RESOLUTION { Clauses + Unification -> Resolvent }
UNIFICATION { Expressions -> Substitution -> MatchingExpressions }
SAT_REASONING { BooleanFormula -> SatisfyingAssignmentOrUNSAT }
SMT_REASONING { BooleanStructure + TheoryConstraints -> ModelOrUNSAT }
THEOREM_PROVING { Axioms + Conjecture -> ProofSearch -> ProofOrSearchStatus }
MODEL_CHECKING { FormalModel + Property -> SatisfactionResult }
COUNTERMODEL { ModelSatisfiesPremises + FalsifiesConclusion -> NonEntailment }

NONMONOTONIC_REASONING { Defaults + Exceptions + Priorities -> DefeasibleConclusions }
BELIEF_REVISION { CurrentBeliefs + NewInformation -> RevisedBeliefs }
TRUTH_MAINTENANCE { SupportingKnowledgeChanges -> RecomputeDependentConclusions }
OPEN_WORLD_ASSUMPTION { MissingFact DOES_NOT imply False }
CLOSED_WORLD_ASSUMPTION { MissingOrUnprovableFact MAY imply False; REQUIRE explicit_semantics }
NEGATION_AS_FAILURE { not P := FailureToProve(P); MUST_NOT_CONFLATE_WITH := ClassicalNegation }

UNCERTAINTY_MODELS { INCLUDE := {Probability,FuzzyDegree,Possibility,BeliefFunction,Confidence} }
UNCERTAINTY_DISTINCTION { Probability != FuzzyDegree; Probability != Confidence; Possibility != Probability; Confidence != Truth }
BAYESIAN_REASONING { Prior + Likelihood + Evidence -> Posterior }
FUZZY_INFERENCE { FuzzyInputs + FuzzyRules -> FuzzyOutput }
CAUSAL_REASONING { CausalModel + ObservationsOrInterventions -> CausalConclusion }
CAUSAL_WARNING { Correlation DOES_NOT by_itself establish Causation }
TEMPORAL_REASONING { Events + States + TemporalRelations -> TemporalConclusions }
SPATIAL_REASONING { Entities + Locations + SpatialRelations -> SpatialConclusions }

PLANNING { InitialState + Goal + Actions + Constraints -> Plan }
ACTION { COMPONENTS := {Preconditions,Effects,Cost,Context} }
STATE_TRANSITION { State_t + Action -> State_t+1 }
AGENT_REASONING { Beliefs + Goals + Intentions + Observations -> DecisionOrAction }
MULTI_AGENT_REASONING { MultipleAgents + Communication + Beliefs + Goals -> InteractionReasoning }

ONTOLOGY_REASONING { Axioms -> Consistency -> Classification -> InstanceInference }
KNOWLEDGE_GRAPH_REASONING { GraphStatements + Ontology + Rules -> DerivedGraphStatements }
INSTANCE_PROPAGATION { a instance_of C; C subclass_of D; THEREFORE a instance_of D }
SEMANTIC_CONSTRAINT { FormalRestriction -> AdmissibilityOrValidationCondition }
VALIDATION_VS_ENTAILMENT { Validation := ConstraintConformance; Entailment := SemanticConsequence; MUST_REMAIN_DISTINCT := TRUE }

PROVENANCE { KnowledgeItem -> Source -> Time -> Evidence -> Derivation }
JUSTIFICATION { Conclusion -> SupportingFactsRulesAxioms }
INFERENCE_TRACE { RECORD := {Step,Premises,RuleOrProcedure,Bindings,Evidence,Conclusion,Status,Dependencies} }
EXPLANATION { ReasoningResult -> InferenceTrace -> Justification -> Provenance }

SYMBOLIC_AI { ExplicitSymbols + Rules + Semantics -> SymbolicReasoning }
LOGICAL_AI_VS_MACHINE_LEARNING { LogicalAI := ExplicitFormalSemantics; MachineLearning := LearnedStatisticalFunction; MAY_COMBINE := TRUE }
NEURO_SYMBOLIC_AI { LearnedModels + SymbolicKnowledge + LogicalReasoning -> HybridReasoning }
SYMBOL_GROUNDING { Symbol -> DataPerceptEntityOrReferent }
GROUNDING_WARNING { IncorrectGrounding -> InvalidSemanticReasoning }

LANGUAGE_MODEL_RELATIONSHIP { LanguageModel MAY generate {CandidateFacts,CandidateRules,Hypotheses,Queries,Explanations,Plans} }
LANGUAGE_MODEL_OUTPUT { STATUS := CandidateKnowledge; UNTIL independently_validated OR formally_derived }
GENERATIVE_REASONING_WARNING { FluentOutput DOES_NOT imply LogicalValidityOrFactualTruth }
RETRIEVAL_AUGMENTED_REASONING { Query -> RetrieveEvidence -> ConstructContext -> ReasonOrGenerate -> Validate }
RAG_WARNING { RetrievedText := SourceMaterial; NOT automatically FormalTruth }
TOOL_AUGMENTED_REASONING { ReasoningState -> SelectTool -> ExecuteTool -> ObserveResult -> UpdateReasoningState }

RECURSIVE_REASONING { Problem -> Decompose -> SolveSubproblem -> Verify -> Integrate -> Repeat }
RECURSION_TERMINATION { STOP_WHEN := {GoalSatisfied,ProofComplete,FixedPointReached,CountermodelFound,NoValidProgress,ResourceLimit} }
SELF_VERIFICATION { CandidateResult -> CheckInference -> CheckEvidence -> CheckConstraints -> CheckConsistency -> AcceptReviseOrReject }
SELF_CORRECTION { DetectedError -> IdentifyAffectedSteps -> RetractInvalidDependencies -> Recompute }
HALLUCINATION_CONTROL { GeneratedClaim -> SourceCheck -> SemanticCheck -> ConsistencyCheck -> StatusAssignment }

AI_REASONING_STATUS { TYPES := {Proven,Entailed,Supported,Predicted,Hypothesised,Contradicted,Unknown,Invalid,Timeout} }
UNKNOWN_STATUS { InsufficientInformation MUST_NOT be coerced_to TrueOrFalse }
TIMEOUT_STATUS { ResourceLimitReached MUST_NOT be interpreted_as LogicalFalsehood }
STATUS_VALIDATION { result_status MUST match actual_epistemic_and_logical_basis }

KNOWLEDGE_UPDATE { NewKnowledge -> Validate -> ResolveIdentity -> CheckConsistency -> Integrate -> RecomputeAffectedConclusions }
DEPENDENCY_GRAPH { DerivedKnowledge -> SupportingKnowledge }
INCREMENTAL_REASONING { ChangedKnowledge -> AffectedDependencies -> PartialRecomputation }
CACHE_INVALIDATION { KnowledgeChange -> InvalidateAffectedCachedResults }
MATERIALISATION { PrecomputeEntailments -> StoreDerivedKnowledge }

APPROXIMATE_REASONING { MAY relax {Completeness,Precision,SearchCoverage}; REQUIRE explicit_approximation_metadata }
CORRECTNESS_FIRST { PerformanceOptimisation MUST_NOT silently change FormalSemantics }

AI_LOGIC_PIPELINE {
 INPUT := Query Q
 IDENTIFY task
 IDENTIFY representation_language
 IDENTIFY knowledge_sources
 IDENTIFY formal_semantics
 IDENTIFY reasoning_method
 IDENTIFY uncertainty_model
 IDENTIFY constraints
 RETRIEVE required_knowledge
 RESOLVE entities
 VALIDATE knowledge
 CHECK consistency
 DECOMPOSE query_if_required
 FOR_EACH subproblem { SELECT suitable_reasoning_procedure; EXECUTE; VERIFY intermediate_result; RECORD dependencies; RECORD provenance }
 IF uncertainty_present: APPLY declared_uncertainty_semantics
 IF conflict_present: APPLY declared_conflict_policy
 IF generated_or_predicted_content_present: PRESERVE non_entailed_status; VALIDATE before formal_acceptance
 COMBINE compatible_results
 BUILD inference_trace
 BUILD justification
 ASSIGN result_status
 VERIFY final_result
 RETURN result_with_trace
}

APPLICATION_RELATIONSHIPS {
 ArtificialIntelligenceLogic --supports--> KnowledgeRepresentation
 ArtificialIntelligenceLogic --supports--> AutomatedReasoning
 ArtificialIntelligenceLogic --supports--> ExpertSystems
 ArtificialIntelligenceLogic --supports--> KnowledgeGraphs
 ArtificialIntelligenceLogic --supports--> Ontologies
 ArtificialIntelligenceLogic --supports--> Planning
 ArtificialIntelligenceLogic --supports--> DecisionSupport
 ArtificialIntelligenceLogic --supports--> FormalVerification
 ArtificialIntelligenceLogic --supports--> NeuroSymbolicAI
 ArtificialIntelligenceLogic --supports--> ExplainableAI
}

ONTOLOGY_LINKS {
 PARENT := AILogicOntology
 RELATED := {LogicalReasoningOntology,KnowledgeRepresentationLogicOntology,DeductiveReasoningOntology,InductiveReasoningOntology,AbductiveReasoningOntology,RuleBasedReasoningOntology,NonMonotonicReasoningOntology,DescriptionLogicOntology,KnowledgeGraphLogicOntology,RuleEngineOntology,InferenceEngineOntology,SemanticConstraintOntology}
}

SEMANTIC_EQUIVALENCE {
 ArtificialIntelligenceLogic ≈ FormalAILogic WHEN ExplicitMachineReasoningSemantics
 AIInference ≈ MachineReasoning WHEN InferenceProcessFormallyDefined
 SymbolicAI ≈ LogicBasedAI WHEN ExplicitSymbolsRulesAndSemanticsPresent
}

CONSTRAINTS {
 C1 := FormalReasoningResult MUST identify inference_or_semantic_basis
 C2 := AssertedDerivedPredictedHypothesisedKnowledge MUST remain distinguishable
 C3 := DeductiveEntailment MUST_NOT be conflated with inductive_abductive_statistical_support
 C4 := ProbabilityFuzzyTruthConfidencePossibility MUST remain semantically_distinct
 C5 := OpenClosedWorldAssumptions MUST be explicit where relevant
 C6 := LanguageModelGeneratedContent MUST_NOT automatically become verified_formal_knowledge
 C7 := ValidationResults MUST remain distinct from LogicalEntailments
 C8 := HeuristicSearchFailure MUST_NOT be presented_as ProofOfNonExistence
 C9 := Contradictions MUST be handled according_to declared_logical_framework
 C10 := ProvenanceAndDependencies SHOULD be preserved for derived_conclusions
 C11 := Approximation MUST be explicit when formal guarantees are relaxed
 C12 := ResultStatus MUST accurately reflect proof_support_prediction_hypothesis_or_uncertainty
}

REASONING_CHAIN Query Q {
 IDENTIFY task
 IDENTIFY knowledge_base
 IDENTIFY representation
 IDENTIFY logic
 IDENTIFY uncertainty_semantics
 IDENTIFY constraints
 VALIDATE inputs
 RESOLVE entities
 CHECK consistency
 DECOMPOSE complex_query_into_subproblems
 FOR_EACH subproblem { SELECT reasoning_method; EXECUTE; VERIFY; RECORD dependencies }
 COMBINE compatible_results
 IF conflict: APPLY declared_conflict_policy
 IF uncertainty: APPLY declared_uncertainty_model
 IF generated_or_predicted_claim: LABEL status_correctly; SEEK validation_if_required
 BUILD recursive_reasoning_trace
 BUILD justification
 BUILD provenance
 VALIDATE constraints
 RETURN result WITH explicit_status
}

CONFIDENCE {
 CORE_ARTIFICIAL_INTELLIGENCE_LOGIC := 1.00
 LOGICAL_INFERENCE := 1.00
 KNOWLEDGE_REPRESENTATION_RELATIONSHIP := 1.00
 SYMBOLIC_STATISTICAL_DISTINCTION := 1.00
 NONMONOTONIC_UNCERTAINTY_DISTINCTIONS := 1.00
 NEURO_SYMBOLIC_RELATIONSHIP := 0.99
 LANGUAGE_MODEL_FORMAL_KNOWLEDGE_DISTINCTION := 1.00
}

UPDATE_MODEL {
 IMMUTABLE_CORE := {FormalSemantics,KnowledgeStatusDistinction,InferenceValidation,Provenance,ExplicitResultStatus}
 EXTENSIBLE := {LogicFamilies,ReasoningAlgorithms,KnowledgeRepresentations,UncertaintyModels,PlanningMethods,AgentLogics,NeuroSymbolicMethods,ToolReasoning,ApplicationDomains,RelatedOntologies}
 ON_NEW_KNOWLEDGE { IDENTIFY source_and_status; VALIDATE representation; RESOLVE entities; CHECK semantic_consistency; UPDATE dependencies; RECOMPUTE affected_conclusions; UPDATE provenance; UPDATE confidence }
}

AI_CONSUMPTION {
 MACHINE_READABLE := TRUE
 HUMAN_INTERPRETABLE := TRUE
 RECURSIVE_REASONING := TRUE
 ENTITY_RESOLUTION := TRUE
 KNOWLEDGE_STATUS_RESOLUTION := TRUE
 LOGICAL_INFERENCE := TRUE
 RULE_REASONING := TRUE
 CONSTRAINT_REASONING := TRUE
 ONTOLOGY_REASONING := TRUE
 KNOWLEDGE_GRAPH_REASONING := TRUE
 UNCERTAINTY_REASONING := TRUE
 NONMONOTONIC_REASONING := TRUE
 PLANNING_REASONING := TRUE
 TOOL_AUGMENTED_REASONING := TRUE
 SELF_VERIFICATION := TRUE
 PROVENANCE_TRACKING := TRUE
 JUSTIFICATION_GENERATION := TRUE
 VALIDATION_REQUIRED := TRUE
}

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

OUTPUT {
 PRIMARY_ENTITY := ArtificialIntelligenceLogic
 INTERPRETATION := "Artificial intelligence logic provides formal structures for machine reasoning across deduction, rules, constraints, uncertainty, planning, ontologies and knowledge graphs. It also defines how learned and generative components can participate while preserving explicit distinctions between asserted facts, logical entailments, predictions, hypotheses and unknown results."
}

END_FLOW