Knowledge Representation Ontology

FLOW_ALGEBRA KnowledgeRepresentationOntology v1.0
TARGET_URL := "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/knowledge-representation-logic/knowledge-representation-ontology.html"
LANGUAGE := "en-GB"
DOMAIN := MathematicalOntologies > MathematicalLogicOntologies > KnowledgeRepresentationLogic > KnowledgeRepresentationOntology

BEGIN_FLOW

ENTITY KnowledgeRepresentation {
 TYPE := FormalInformationModel
 DEFINITION := "A structured representation of entities, concepts, properties, relations, events, rules, constraints and assertions designed to preserve meaning and support machine interpretation and reasoning."
}
ENTITY Concept { TYPE := ClassOrCategory }
ENTITY Individual { TYPE := InstanceOrEntity }
ENTITY Property { TYPE := AttributeOrRelation }
ENTITY Assertion { TYPE := KnowledgeStatement }
ENTITY Rule { TYPE := InferenceStructure }

RELATIONSHIP KnowledgeRepresentation --contains--> Concept
RELATIONSHIP KnowledgeRepresentation --contains--> Individual
RELATIONSHIP KnowledgeRepresentation --contains--> Property
RELATIONSHIP KnowledgeRepresentation --contains--> Assertion
RELATIONSHIP KnowledgeRepresentation --supports--> AutomatedReasoning

COMPONENTS := {
 Vocabulary,Entities,Concepts,Relations,Assertions,
 Rules,Constraints,Context,Provenance
}

SYNTAX {
 PURPOSE := define_valid_representation_structures
}
SEMANTICS {
 PURPOSE := assign_meaning_to_structures
}
INTERPRETATION {
 symbols_and_expressions -> semantic_objects
}
MODEL {
 TYPE := SemanticStructure
 SATISFIES := representation_axioms
}
WELL_FORMEDNESS {
 expression MUST satisfy representation_grammar
}

CLASS_MEMBERSHIP { FORM := a:C }
BINARY_RELATION { FORM := R(a,b) }
N_ARY_RELATION { FORM := R(a1,...,an) }
EQUALITY { FORM := a=b }
INEQUALITY { FORM := a!=b }
SUBCLASS { FORM := C subclass_of D }
PROPERTY_HIERARCHY { FORM := R subproperty_of S }
EQUIVALENT_CONCEPTS { FORM := C equivalent_to D }
DISJOINT_CONCEPTS { FORM := Disjoint(C,D) }
DOMAIN { FORM := Domain(R)=C }
RANGE { FORM := Range(R)=D }

ONTOLOGY_REPRESENTATION {
 COMPONENTS := {Classes,Individuals,Properties,Axioms}
}
TAXONOMY {
 TYPE := HierarchicalClassification
}
SEMANTIC_NETWORK {
 NODES := ConceptsOrEntities
 EDGES := SemanticRelations
}
FRAME {
 COMPONENTS := {Slots,Values,Defaults,Constraints}
}
PRODUCTION_RULE {
 FORM := IF Condition THEN ConsequenceOrAction
}
FORWARD_RULE_REASONING {
 Facts -> ApplicableRules -> DerivedFacts
}
BACKWARD_RULE_REASONING {
 Goal -> RulesConcludingGoal -> Subgoals
}

LOGIC_BASED_REPRESENTATION {
 USES := {PropositionalLogic,PredicateLogic,DescriptionLogic,RuleLogic}
}
PREDICATE_REPRESENTATION {
 Predicates + Terms + Variables + Quantifiers -> FirstOrderFormulae
}
DESCRIPTION_LOGIC_REPRESENTATION {
 Concepts + Roles + Individuals + Constructors -> OntologicalAxioms
}

KNOWLEDGE_GRAPH {
 TYPE := GraphStructuredKnowledgeRepresentation
 NODES := Entities
 EDGES := TypedRelations
}
TRIPLE {
 FORM := (Subject,Predicate,Object)
}
RDF_RELATIONSHIP {
 TripleRepresentation --relates_to--> RDFGraphModel
}
RDFS_RELATIONSHIP {
 supports := {ClassHierarchy,PropertyHierarchy,Domain,Range}
}
OWL_RELATIONSHIP {
 OntologyRepresentation --may_use--> OWLStyleAxioms
}

OPEN_WORLD_ASSUMPTION {
 absence_of_statement DOES_NOT imply false
}
CLOSED_WORLD_ASSUMPTION {
 absence_or_failure_to_prove MAY imply false
 REQUIRE explicit_semantics
}
UNIQUE_NAME_ASSUMPTION {
 distinct_names imply distinct_entities
 NOT universal
}

IDENTITY_RESOLUTION {
 determine whether identifiers_or_mentions refer_to same_entity
}
ENTITY_LINKING {
 Mention -> CandidateEntities -> ResolvedEntity
}
COREFERENCE {
 MultipleMentions -> SameReferent
}
ALIAS {
 alternative_name_or_identifier_for_same_entity
}
ENTITY_MERGE {
 IF identifiers_proven_equivalent
 THEN unify_records_and_preserve_provenance
}
ENTITY_MERGE_WARNING {
 similarity_alone MUST_NOT establish identity
}

SCHEMA {
 TYPE := StructuralKnowledgeModel
}
SCHEMA_LEVEL {
 defines classes_properties_constraints
}
INSTANCE_LEVEL {
 contains concrete_entities_relationships_values
}
META_LEVEL {
 statements_about_schema_assertions_or_provenance
}
SCHEMA_ALIGNMENT {
 SourceSchema + TargetSchema -> CorrespondenceSet
}
ONTOLOGY_ALIGNMENT {
 SourceOntology + TargetOntology -> ConceptAndPropertyMappings
}
EXACT_MATCH {
 REQUIRE semantic_equivalence
}
BROADER_MATCH { A broader_than B }
NARROWER_MATCH { A narrower_than B }
RELATED_MATCH { A semantically_related_to B without_equivalence }

DATA_INTEGRATION {
 Sources -> Normalisation -> EntityResolution -> SchemaMapping -> IntegratedKnowledge
}
KNOWLEDGE_ACQUISITION {
 SOURCES := {HumanExperts,Documents,Databases,Sensors,APIs,MachineLearning,Ontologies}
}
KNOWLEDGE_EXTRACTION {
 Input -> Entities -> Relations -> Events -> Assertions
}
EVENT {
 TYPE := OccurrenceOrProcess
}
TEMPORAL_SCOPE {
 Assertion -> TimeInterval
}
SPATIAL_SCOPE {
 Assertion -> LocationOrRegion
}
CONTEXT {
 TYPE := ScopeOfInterpretation
}

PROVENANCE {
 Statement -> Source -> AcquisitionMethod -> Time -> TransformationHistory
}
DERIVATION_PROVENANCE {
 DerivedStatement -> SupportingStatements -> RulesOrAlgorithms
}
VERSIONING {
 KnowledgeBase_v1 -> ChangeSet -> KnowledgeBase_v2
}
CHANGE_SET {
 COMPONENTS := {Additions,Deletions,Modifications}
}
KNOWLEDGE_UPDATE {
 ExistingKnowledge + ChangeSet -> UpdatedKnowledge
}
CONSISTENCY_CHECK {
 detect incompatible_assertions_or_axioms
}
CONFLICT_RESOLUTION {
 MAY_USE := {SourcePriority,TemporalRecency,EvidenceStrength,DomainAuthority,ManualReview}
 REQUIRE explicit_policy
}
TRUTH_MAINTENANCE_RELATIONSHIP {
 track_dependencies -> retract_unsupported_derived_facts
}
NONMONOTONIC_KNOWLEDGE {
 adding_facts MAY retract_defeasible_conclusions
}

PROBABILISTIC_KNOWLEDGE {
 Statement + Probability
 REQUIRE probabilistic_semantics
}
FUZZY_KNOWLEDGE {
 ConceptMembership + Degree
 REQUIRE fuzzy_semantics
}
CONFIDENCE_ANNOTATION {
 Statement + ConfidenceScore
 WARNING := confidence_not_automatically_probability_or_truth_degree
}

KNOWLEDGE_VS_DATA {
 Data := recorded_symbols_or_measurements
 Information := data_interpreted_in_context
 Knowledge := structured_information_with_semantic_relationships
}
KNOWLEDGE_VS_BELIEF {
 Belief := agent_relative_acceptance
 KnowledgeRepresentation := formal_encoding_not_guarantee_of_truth
}

SEMANTIC_FIDELITY {
 transformation SHOULD preserve intended_meaning
}
LOSSLESS_TRANSFORMATION {
 preserves information relevant_to_declared_semantics
}
LOSSY_TRANSFORMATION {
 removes distinctions
 REQUIRE documented_loss
}
NORMALISATION {
 equivalent_forms -> canonical_representation
}
REIFICATION {
 Statement -> StatementEntity -> Metadata
}
N_ARY_RELATION_PATTERN {
 RelationInstance -> ParticipantRoles
}

INTEGRITY_CONSTRAINT {
 restricts admissible_data_or_state
}
VALIDATION {
 Data + ConstraintSet -> ConformsOrViolates
}
VALIDATION_VS_ENTAILMENT {
 Validation := check_constraints
 Entailment := derive_semantic_consequences
 MUST_REMAIN_DISTINCT := TRUE
}
ENTAILMENT {
 KB entails phi
 IFF every model_of_KB satisfies phi
}
QUERY_ANSWERING {
 MAY_USE := {GraphMatching,LogicalEntailment,RuleEvaluation,DatabaseRetrieval}
 REQUIRE query_semantics
}
EXPLANATION {
 Answer -> SupportingKnowledge -> Derivation -> Provenance
}
JUSTIFICATION {
 EntailedStatement -> SupportingAxiomsOrFacts
}

KNOWLEDGE_QUALITY {
 DIMENSIONS := {Accuracy,Completeness,Consistency,Timeliness,Provenance,Relevance,Uniqueness}
}
COMPLETENESS {
 representation contains required_knowledge_for_declared_scope
 WARNING := open_world_absence_does_not_establish_completeness
}

TRADEOFF {
 Expressivity vs ComputationalComplexity vs Decidability vs Interpretability
}
MACHINE_INTERPRETABILITY {
 semantics sufficiently_explicit_for_automated_processing
}
HUMAN_INTERPRETABILITY {
 structure understandable_to_human_reviewers
}

APPLICATION_RELATIONSHIPS {
 KnowledgeRepresentation --supports--> Ontologies
 KnowledgeRepresentation --supports--> KnowledgeGraphs
 KnowledgeRepresentation --supports--> ExpertSystems
 KnowledgeRepresentation --supports--> SemanticWeb
 KnowledgeRepresentation --supports--> ArtificialIntelligence
 KnowledgeRepresentation --supports--> AutomatedReasoning
 KnowledgeRepresentation --supports--> DataIntegration
 KnowledgeRepresentation --supports--> NaturalLanguageUnderstanding
 KnowledgeRepresentation --supports--> DecisionSupport
}

ONTOLOGY_LINKS {
 PARENT := KnowledgeRepresentationLogicOntology
 RELATED := {
  LogicalReasoningOntology,
  PredicateLogicOntology,
  DescriptionLogicOntology,
  RuleBasedReasoningOntology,
  NonMonotonicReasoningOntology,
  OntologyOntology,
  KnowledgeGraphOntology,
  SemanticNetworkOntology,
  FrameOntology,
  LogicProgrammingOntology,
  ProvenanceOntology
 }
}

SEMANTIC_EQUIVALENCE {
 KnowledgeRepresentation ≈ FormalKnowledgeModel WHEN explicit_semantics
 Individual ≈ Instance WHEN class_membership_context
 Assertion ≈ KnowledgeStatement
 Property ≈ Relation WHEN semantic_relation_context
}

CONSTRAINTS {
 C1 := every formal representation MUST identify syntax and semantics
 C2 := schema-level and instance-level knowledge MUST remain distinguishable
 C3 := entity identity MUST NOT be inferred from superficial similarity alone
 C4 := open-world absence MUST NOT automatically be interpreted as false
 C5 := unique-name assumptions MUST be explicit
 C6 := provenance SHOULD be preserved through transformation and integration
 C7 := confidence MUST NOT automatically be interpreted as probability or truth degree
 C8 := validation MUST remain distinct from entailment
 C9 := nonmonotonic probabilistic and fuzzy extensions MUST identify semantics
 C10 := mappings MUST distinguish equivalence from broader/narrower/related relations
 C11 := updates SHOULD preserve dependencies where derived facts may require retraction
 C12 := transformations MUST preserve intended meaning or record semantic loss
}

REASONING_CHAIN Query Q {
 IDENTIFY representation_language
 IDENTIFY schema
 IDENTIFY entities
 IDENTIFY properties
 IDENTIFY assertions
 IDENTIFY rules
 IDENTIFY constraints
 IDENTIFY context
 IDENTIFY provenance

 VALIDATE syntax
 RESOLVE entity_identity
 NORMALISE representations
 CHECK schema_consistency

 IF integration_requested {
  ALIGN schemas
  MAP concepts_and_properties
  RESOLVE duplicates
  PRESERVE provenance
 }

 IF inference_requested {
  SELECT logical_or_rule_semantics
  DERIVE consequences
  RECORD justifications
 }

 IF validation_requested {
  APPLY integrity_constraints
  KEEP validation_distinct_from_entailment
 }

 IF update_requested {
  APPLY change_set
  CHECK conflicts
  RETRACT dependent_knowledge_if_required
 }

 IF query_requested {
  SELECT query_semantics
  COMPUTE answers
  BUILD explanation
 }

 VALIDATE constraints
 RETURN representation_result WITH semantic_trace
}

CONFIDENCE {
 CORE_KNOWLEDGE_REPRESENTATION := 1.00
 LOGIC_BASED_REPRESENTATION := 1.00
 ONTOLOGY_RELATIONSHIP := 1.00
 KNOWLEDGE_GRAPH_RELATIONSHIP := 1.00
 OPEN_WORLD_DISTINCTION := 1.00
 PROVENANCE_ROLE := 1.00
 VALIDATION_ENTAILMENT_DISTINCTION := 1.00
 SPECIFIC_RESULT :=
  IF language_schema_entities_and_semantics_complete THEN 1.00
  ELSE REQUIRE missing_information
}

UPDATE_MODEL {
 IMMUTABLE_CORE := {
  FormalRepresentation,
  ExplicitSemantics,
  EntityConceptRelationStructure,
  Context,
  Provenance
 }
 EXTENSIBLE := {
  RepresentationLanguages,
  OntologyConstructors,
  KnowledgeGraphModels,
  RuleSystems,
  UncertaintyModels,
  ValidationMethods,
  IntegrationMethods,
  ApplicationDomains,
  RelatedOntologies
 }
 ON_NEW_KNOWLEDGE {
  IDENTIFY new_statement
  RESOLVE entities
  VALIDATE syntax
  CHECK schema_semantics
  CHECK consistency
  UPDATE provenance
  DERIVE new_consequences_if_required
  UPDATE confidence
 }
}

AI_CONSUMPTION {
 MACHINE_READABLE := TRUE
 HUMAN_INTERPRETABLE := TRUE
 RECURSIVE_REASONING := TRUE
 ENTITY_RESOLUTION := TRUE
 CONCEPT_RESOLUTION := TRUE
 RELATION_RESOLUTION := TRUE
 ONTOLOGY_REASONING := TRUE
 KNOWLEDGE_GRAPH_REASONING := TRUE
 SCHEMA_ALIGNMENT := TRUE
 CONTEXT_REASONING := TRUE
 PROVENANCE_TRACKING := TRUE
 CONSISTENCY_REASONING := TRUE
 QUERY_REASONING := TRUE
 JUSTIFICATION_GENERATION := TRUE
 VALIDATION_REQUIRED := TRUE
}

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

OUTPUT {
 PRIMARY_ENTITY := KnowledgeRepresentation
 INTERPRETATION := "Knowledge representation structures entities, concepts, properties, relations, rules, context and provenance in forms whose semantics can be interpreted by humans and machines. Ontologies, logical models, frames, semantic networks and knowledge graphs provide complementary structures for integration, querying and reasoning while explicit assumptions preserve semantic fidelity."
}

END_FLOW