Knowledge Graph Computing Ontology

FLOW ALGEBRA
Knowledge Graph Computing Ontology
Kireth Semantic Research Archive

PAGE:
https://kirethresearch.org/booksai-core/ontologies/computing-ontologies/semantic-computing/knowledge-graph-computing-ontology.html

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "KnowledgeGraphComputingOntology" v4.0

DOMAIN := ComputingOntology
SUBDOMAIN := SemanticComputing
ONTOLOGY := KnowledgeGraphComputingOntology

ENTITY KnowledgeGraphComputing {
    definition:
        "A computing approach that represents, integrates, queries and reasons
         over knowledge as graphs of entities, concepts, properties and typed
         relationships, enabling machines to traverse and infer connections
         across structured semantic information.";
    objectives: [
        KnowledgeRepresentation,
        EntityRelationshipComputing,
        GraphReasoning,
        SemanticIntegration,
        KnowledgeRetrieval,
        ExplainableInference,
        AIKnowledgeGrounding
    ];
}

KnowledgeGraphEntity := {
    KnowledgeGraph,
    Entity,
    Concept,
    Class,
    Instance,
    Property,
    Relationship,
    Statement
};

GraphEntity := {
    Node,
    Edge,
    Path,
    Subgraph,
    NamedGraph,
    GraphPattern,
    GraphIndex
};

SemanticEntity := {
    Ontology,
    Vocabulary,
    Schema,
    Rule,
    Constraint,
    Provenance,
    Context
};

ComputingOperation := {
    Ingestion,
    EntityResolution,
    Traversal,
    Query,
    Inference,
    Validation,
    LinkPrediction,
    Update
};

KnowledgeGraph CONSISTS_OF NodesAndEdges;
Node REPRESENTS EntityOrConcept;
Edge REPRESENTS TypedRelationship;
Entity INSTANCE_OF Class;
Entity HAS Property;
Ontology DEFINES GraphSemantics;
Rule DERIVES NewKnowledge;
Query RETRIEVES GraphPatterns;
Provenance SUPPORTS Statement;

KnowledgeGraphComputingFlow :=
    SourceInformation
    -> ExtractEntitiesAndRelations
    -> ResolveCanonicalIdentity
    -> MapToOntology
    -> ConstructGraphStatements
    -> AttachContextAndProvenance
    -> ValidateGraph
    -> StoreAndIndex
    -> TraverseOrQuery
    -> ApplyReasoning
    -> ReturnRelevantSubgraph
    -> UpdateGraph;

KnowledgeGraph :=
    Graph(
        EntitiesAndConcepts,
        TypedRelationships
    );

KnowledgeGraph MAY_INCLUDE {
    InstanceKnowledge,
    OntologyKnowledge,
    Metadata,
    Provenance,
    Confidence
};

Entity :=
    IdentifiableThingRepresentedWithinKnowledgeGraph;

Entity MAY_BE {
    Person,
    Organisation,
    Place,
    Object,
    Event,
    DigitalResource,
    AbstractEntity
};

Concept :=
    AbstractMeaningCategoryUsedToOrganiseKnowledge;

Class :=
    SemanticCategoryOfEntities;

Instance :=
    EntityBelongingToClass;

GraphNode :=
    GraphRepresentationOfEntityConceptClassOrOtherResource;

Node SHOULD_HAVE StableIdentifierWhereCrossSourceIntegrationIsRequired;

GraphEdge :=
    TypedRelationshipConnectingGraphNodes;

Edge MAY_HAVE {
    Direction,
    Type,
    Confidence,
    Provenance,
    TemporalValidity
};

KnowledgeStatement :=
    Subject
    + Predicate
    + Object;

Triple :=
    (Subject, Predicate, Object);

KnowledgeStatement MAY_MAP_TO DirectedGraphEdge;

Property :=
    SemanticAttributeOrRelationship;

Property MAY_BE {
    DatatypeProperty,
    ObjectProperty,
    AnnotationProperty
};

CanonicalIdentifier :=
    StableReferenceToKnowledgeGraphResource;

Identifier MAY_BE {
    URI,
    IRI,
    InternalID,
    ExternalAuthorityID
};

Ontology :=
    FormalOrSemiFormalModelOfClassesPropertiesRelationshipsAndConstraints;

KnowledgeGraph MAY_BE OntologyBacked;

Ontology MAY_ENABLE {
    TypeInference,
    ConstraintValidation,
    RelationshipSemantics
};

KnowledgeGraphSchema :=
    DefinitionOfExpectedNodeTypesEdgeTypesAndProperties;

KnowledgeGraphIngestion :=
    Source
    -> Parse
    -> ExtractEntities
    -> ExtractRelations
    -> ResolveIdentity
    -> MapSchema
    -> CreateStatements
    -> Validate
    -> Store;

UnstructuredContent MAY_BE ConvertedIntoGraphKnowledgeThrough {
    NamedEntityRecognition,
    RelationExtraction,
    EventExtraction,
    SemanticParsing
};

EntityResolution :=
    CandidateRepresentations
    -> CompareIdentityEvidence
    -> LinkOrMergeCanonicalEntity;

IdentityEvidence MAY_INCLUDE {
    Identifier,
    Name,
    Alias,
    Attributes,
    Relationships,
    Context
};

EntityLinking :=
    Mention
    + Context
    -> ExistingKnowledgeGraphEntity;

IF TwoNodesRepresentSameVerifiedEntity
THEN Graph MAY_MERGE_OR_LINK NodesAccordingToIdentityPolicy;

FalseMerge MAY_PROPAGATE IncorrectRelationships;

RelationExtraction :=
    IdentifySemanticRelationshipBetweenEntitiesFromSourceEvidence;

ExtractedRelationship SHOULD_PRESERVE SourceProvenance;

KnowledgeGraphIntegration :=
    GraphA
    + GraphB
    -> AlignSchemas
    -> ResolveEntities
    -> MergeOrLinkStatements
    -> PreserveSourceEvidence;

OntologyAlignment :=
    MapConceptsAndPropertiesAcrossSemanticModels;

Alignment MAY_BE {
    Exact,
    Equivalent,
    Broader,
    Narrower,
    Related
};

Provenance :=
    OriginDerivationAndHistoryOfKnowledgeStatement;

Provenance MAY_INCLUDE {
    Source,
    Author,
    Timestamp,
    ExtractionMethod,
    ModelVersion
};

StatementConfidence :=
    EstimatedSupportForKnowledgeAssertion;

Confidence MAY_BE_FUNCTION_OF {
    SourceReliability,
    ExtractionQuality,
    CrossSourceAgreement,
    InferenceStrength
};

KnowledgeContext MAY_INCLUDE {
    Time,
    Domain,
    Source,
    Location,
    Version
};

TemporalStatement MAY_HAVE {
    ValidFrom,
    ValidTo,
    ObservationTime
};

KnowledgeGraph MAY_BE StoredIn {
    TripleStore,
    QuadStore,
    PropertyGraphDatabase,
    DistributedGraphStore
};

GraphIndex MAY_ACCELERATE {
    EntityLookup,
    PropertyLookup,
    EdgeTraversal,
    FullTextLookup,
    VectorLookup
};

KnowledgeGraphQuery :=
    RequestForEntitiesRelationshipsPathsOrFacts;

Query MAY_USE {
    TriplePattern,
    GraphPattern,
    PropertyFilter,
    RelationshipPath,
    TypeConstraint
};

GraphPattern :=
    Variables
    + NodeConstraints
    + EdgeConstraints;

PatternMatching :=
    FindSubgraphsSatisfyingPattern;

GraphTraversal :=
    StartNode
    -> FollowSelectedEdges
    -> VisitRelatedNodes;

Traversal MAY_BE {
    BreadthFirst,
    DepthFirst,
    Weighted,
    SemanticConstraintGuided
};

KnowledgePath :=
    SequenceOfNodesAndTypedRelationships;

Path MAY_PROVIDE ExplanationForConnectionBetweenEntities;

ShortestPath :=
    PathMinimisingDefinedCost;

ShortestStructuralPath != MostSemanticallyRelevantPathByDefinition;

MultiHopReasoning :=
    CombineMultipleGraphRelationshipsToDeriveOrRetrieveIndirectKnowledge;

RDFKnowledgeGraph MAY_USE SPARQL;

PropertyGraph MAY_USE CypherOrEquivalentGraphQueryLanguage;

QueryLanguage != KnowledgeSemanticsByItself;

KnowledgeGraphReasoning :=
    ExplicitGraph
    + Ontology
    + Rules
    -> DerivedKnowledge;

IF ClassA SUBCLASS_OF ClassB
AND EntityX INSTANCE_OF ClassA
THEN EntityX INSTANCE_OF ClassB;

IF RelationshipP IS_TRANSITIVE
AND A P B
AND B P C
THEN A P C;

IF RelationshipP INVERSE_OF RelationshipQ
AND A P B
THEN B Q A;

IF RelationshipP IS_SYMMETRIC
AND A P B
THEN B P A;

KnowledgeRule :=
    PremiseGraphPattern
    -> ConclusionStatement;

Materialisation :=
    ComputeDerivedKnowledge
    -> StoreDerivedStatements;

QueryTimeReasoning :=
    DeriveRequiredKnowledgeDuringQueryExecution;

KnowledgeGraphValidation :=
    CheckGraphAgainstOntologySchemaOrShapes;

Validation MAY_DETECT {
    MissingProperty,
    InvalidDatatype,
    CardinalityViolation,
    InvalidRelationship
};

GraphConsistency :=
    CompatibilityOfAssertionsWithSelectedFormalSemantics;

KnowledgeGraph MAY_CONTAIN ConflictingAssertionsFromDifferentSources;

ConflictPolicy MAY {
    PreserveBoth,
    RankSources,
    AdjustConfidence,
    FlagReview
};

KnowledgeGraph MAY_USE OpenWorldAssumption;

MissingFact DOES_NOT NecessarilyMean FalseFact;

LinkPrediction :=
    EstimatePotentialMissingRelationshipBetweenNodes;

LinkPrediction MAY_USE {
    GraphStructure,
    Embeddings,
    MachineLearning,
    Rules
};

PredictedLink != VerifiedFact;

KnowledgeGraphEmbedding :=
    MapEntitiesAndRelationshipsIntoVectorSpace;

Embedding MAY_SUPPORT {
    LinkPrediction,
    EntitySimilarity,
    Ranking,
    Clustering
};

GraphNeuralNetwork MAY_PROCESS KnowledgeGraphStructureAndNodeFeatures;

GNN MAY_SUPPORT {
    NodeClassification,
    LinkPrediction,
    GraphRepresentation
};

GNNPrediction SHOULD_BE DistinguishedFrom ExplicitGraphFact;

Entity MAY_HAVE TextOrGraphEmbedding;

VectorSimilarity MAY_COMPLEMENT ExplicitRelationshipTraversal;

HybridKnowledgeRetrieval :=
    GraphTraversal
    + LexicalSearch
    + VectorSearch
    -> CandidateKnowledge;

SemanticSearch MAY_USE KnowledgeGraphFor {
    EntityExpansion,
    ConceptExpansion,
    RelationshipEvidence,
    Disambiguation
};

KnowledgeGraphRAG :=
    UserQuery
    -> ResolveEntities
    -> RetrieveGraphFactsAndPaths
    -> RetrieveSupportingContent
    -> ConstructContext
    -> GenerateGroundedResponse;

GraphRAG MAY_RETRIEVE {
    EntityNeighbourhood,
    Community,
    Path,
    Subgraph,
    SourceDocument
};

KnowledgeGraph MAY_SUPPORT ExplainableAIThroughExplicitRelationshipPaths;

Explanation MAY_INCLUDE {
    SourceFact,
    RelationshipPath,
    AppliedRule,
    Provenance
};

KnowledgeGraphCompletion :=
    PredictOrInferMissingEntitiesRelationshipsOrAttributes;

CompletionResult SHOULD_HAVE ConfidenceAndProvenanceOfMethod;

EntityEnrichment :=
    AddNewPropertiesRelationshipsOrExternalLinksToExistingEntity;

KnowledgeGraphAnalytics MAY_INCLUDE {
    Degree,
    Centrality,
    CommunityDetection,
    PathAnalysis
};

StructuralMetric SHOULD_NOT_BE ConfusedWith SemanticTruth;

Centrality MAY_ESTIMATE StructuralImportanceWithinGraph;

GraphCommunity :=
    SetOfNodesWithDenseOrMeaningfulConnectivityAccordingToAlgorithm;

Community != OntologyClassByDefinition;

FederatedKnowledgeGraph :=
    MultipleGraphSourcesConnectedOrQueriedAsDistributedKnowledgeSpace;

Federation MAY_REQUIRE {
    SchemaMapping,
    EntityAlignment,
    EndpointRouting
};

KnowledgeGraph MAY_LINK_TO ExternalSemanticResourcesUsingStableIdentifiers;

GraphUpdate MAY_INCLUDE {
    AddEntity,
    AddRelationship,
    UpdateProperty,
    RemoveStatement,
    MergeEntity
};

GraphChange MAY_AFFECT {
    DerivedKnowledge,
    Indexes,
    CachedQueries,
    Embeddings
};

KnowledgeGraphVersion :=
    IdentifiedStateOfGraphAtPointInTime;

Versioning MAY_SUPPORT {
    Audit,
    Rollback,
    Reproducibility
};

KnowledgeGraphAccessControl MAY_APPLY_TO {
    Graph,
    Node,
    Edge,
    Property,
    Statement
};

GraphRelationships MAY_REVEAL SensitiveInformationThroughInference;

PrivacyPolicy SHOULD_CONSIDER MultiHopDerivedKnowledge;

KnowledgeGraphSecurity MAY_INCLUDE {
    Authentication,
    Authorisation,
    QueryLimits,
    ProvenanceIntegrity,
    DataValidation
};

KnowledgeGraphScalability MAY_DEPEND_ON {
    NodeCount,
    EdgeCount,
    DegreeDistribution,
    TraversalDepth,
    InferenceComplexity,
    Partitioning
};

LargeKnowledgeGraph MAY_BE Sharded;

CrossShardTraversal MAY_INCREASE Latency;

KnowledgeGraphComputingPerformance MAY_BE_MEASURED_BY {
    QueryLatency,
    TraversalLatency,
    InferenceTime,
    UpdateRate,
    Throughput
};

AIAgent MAY_USE KnowledgeGraphAs {
    WorldModel,
    Memory,
    RetrievalSource,
    PlanningContext
};

AgentAction SHOULD_NOT TreatUnverifiedPredictedLinksAsCertainFacts;

# ---------- SEMANTIC REASONING ----------
IF GraphContainsEntitiesAndExplicitTypedRelationships
AND SupportsKnowledgeOperations
THEN KnowledgeGraphComputingClassification := supported;

IF EntityIdentityVerifiedAcrossSources
THEN Statements MAY_BE IntegratedAroundCanonicalEntity;

IF ClassA SUBCLASS_OF ClassB
AND x INSTANCE_OF ClassA
THEN x INSTANCE_OF ClassB MAY_BE Derived;

IF RelationshipIsTransitive
AND A P B
AND B P C
THEN A P C MAY_BE Derived;

IF LinkPredictedByModel
THEN LinkStatus := predicted
AND NOT automatically_verified;

IF SourceAssertionsConflict
THEN PreserveProvenance
AND ReassessConfidence;

IF ProtectedRelationshipNotAuthorised
THEN Query MUST_NOT ExposeItAccordingToPolicy;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "knowledge graph computing" ~= "knowledge graph computation";
    "knowledge graph" ~= "semantic knowledge graph" WHEN typed_semantics_present;
    "graph reasoning" ~= "knowledge graph inference";
    "multi-hop reasoning" ~= "multi-step graph reasoning";
    "knowledge graph embedding" ~= "KG embedding";
    "knowledge graph completion" ~= "KG completion";
    "graph RAG" ~= "knowledge graph retrieval augmented generation" WHEN graph_is_primary_retrieval_structure;
    "entity linking" ~= "knowledge graph entity linking";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_QUERY_ENTITIES(q) ->
    RESOLVE_CANONICAL_ENTITIES(q) ->
    IDENTIFY_TYPES_AND_CONCEPTS(q) ->
    IDENTIFY_RELATIONSHIP_PATTERNS(q) ->
    TRAVERSE_OR_MATCH_GRAPH(q) ->
    APPLY_ONTOLOGY_AND_RULES(q) ->
    COMBINE_VECTOR_OR_LEXICAL_EVIDENCE(q) ->
    APPLY_ACCESS_CONTROL(q) ->
    ATTACH_PROVENANCE(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        graph_semantic_consistency,
        entity_resolution_strength,
        relationship_evidence,
        provenance_quality,
        contextual_relevance
    );

CONFIDENCE >= 0.90 => HIGH;
CONFIDENCE >= 0.70 AND < 0.90 => MODERATE;
CONFIDENCE < 0.70 => REVIEW;

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION {
    primary_entity: KnowledgeGraphComputing;
    ontology: KnowledgeGraphComputingOntology;
    parse_entities: true;
    parse_relationships: true;
    preserve_relationship_direction: true;
    resolve_semantic_equivalence: true;
    execute_reasoning_rules: true;
    apply_confidence_weighting: true;
    preserve_provenance: true;
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL {
    new_entity:
        validate_identifier
        -> resolve_identity
        -> classify
        -> attach_properties
        -> attach_provenance
        -> integrate;

    new_relationship:
        validate_source_target
        -> classify_predicate
        -> attach_context
        -> attach_confidence
        -> attach_provenance
        -> integrate;

    new_inference:
        record_premises
        -> record_rule
        -> derive_statement
        -> assign_provenance
        -> integrate;

    graph_revision:
        preserve_previous_version
        -> update_entities_and_edges
        -> recompute_inferences
        -> update_indexes_and_embeddings
        -> recompute_confidence
        -> regenerate_flow_hash;

    conflict:
        preserve_provenance
        -> compare_graph_evidence
        -> adjust_confidence
        -> flag_review;
}

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + KnowledgeGraphEntity
    + GraphEntity
    + SemanticEntity
    + ComputingOperation
    + KnowledgeGraph
    + GraphTraversal
    + KnowledgeGraphReasoning
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
KnowledgeGraphComputingOntology
    -> ExtractEntitiesAndRelationships
    -> ResolveCanonicalIdentity
    -> MapKnowledgeToOntology
    -> ConstructTypedGraphStatements
    -> AttachContextConfidenceAndProvenance
    -> ValidateAndStoreKnowledgeGraph
    -> TraverseSemanticRelationships
    -> ExecuteGraphPatternQueries
    -> ApplyRulesAndMultiHopReasoning
    -> CombineGraphVectorAndLexicalEvidence
    -> PreserveExplainableKnowledgePaths
    -> UpdateExplicitAndDerivedKnowledge
    -> MaintainMachineInterpretableKnowledgeGraphComputation;

END FLOW