Semantic Graph Ontology

FLOW ALGEBRA
Semantic Graph Ontology
Kireth Semantic Research Archive

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

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "SemanticGraphOntology" v4.0

# ---------- DOMAIN ----------
DOMAIN := ComputingOntology
SUBDOMAIN := SemanticComputing
ONTOLOGY := SemanticGraphOntology

# ---------- PRIMARY ENTITY ----------
ENTITY SemanticGraph {
    definition:
        "A graph-based knowledge representation in which nodes and edges carry
         explicit semantic meaning, representing entities, concepts,
         properties and typed relationships that can be queried, integrated
         and reasoned over.";

    objectives: [
        SemanticRepresentation,
        EntityRelationshipModelling,
        KnowledgeIntegration,
        GraphReasoning,
        MeaningAwareTraversal,
        Interoperability,
        ExplainableKnowledge
    ];
}

# ---------- CORE ENTITIES ----------
GraphEntity := {
    SemanticGraph,
    Node,
    Edge,
    Entity,
    Concept,
    Class,
    Instance,
    Property
};

KnowledgeEntity := {
    Ontology,
    KnowledgeGraph,
    Vocabulary,
    Statement,
    Rule,
    Context,
    Provenance
};

GraphStructure := {
    DirectedGraph,
    UndirectedGraph,
    LabelledGraph,
    MultiGraph,
    NamedGraph,
    Subgraph
};

OperationEntity := {
    Traversal,
    PatternMatch,
    Query,
    Inference,
    Mapping,
    Validation,
    Update
};

# ---------- FUNDAMENTAL RELATIONSHIPS ----------
SemanticGraph CONSISTS_OF NodesAndEdges;
Node REPRESENTS EntityOrConcept;
Edge REPRESENTS TypedRelationship;
Entity INSTANCE_OF Class;
Entity HAS Property;
Ontology DEFINES GraphSemantics;
Statement MAY_BE RepresentedBy EdgeOrTriple;
Provenance QUALIFIES Statement;
Rule MAY_DERIVE NewEdgeOrType;

# ---------- SEMANTIC GRAPH FLOW ----------
SourceKnowledge
    -> IdentifyEntitiesAndConcepts
    -> ResolveCanonicalIdentifiers
    -> IdentifyTypedRelationships
    -> MapToOntology
    -> ConstructNodesAndEdges
    -> AttachPropertiesContextAndProvenance
    -> ValidateGraph
    -> ApplyInference
    -> TraverseOrQueryGraph
    -> ReturnRelatedKnowledge
    -> UpdateSemanticGraph;

# ---------- NODE ----------
Node :=
    GraphElementRepresentingSemanticResource;

Node MAY_REPRESENT {
    Entity,
    Concept,
    Class,
    LiteralContainer,
    Event
};

Node SHOULD_HAVE StableIdentityWhereEntityResolutionIsRequired;

# ---------- EDGE ----------
Edge :=
    GraphElementRepresentingRelationshipBetweenNodes;

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

# ---------- DIRECTED EDGE ----------
DirectedEdge :=
    SourceNode
    -> RelationshipType
    -> TargetNode;

Direction SHOULD_BE PreservedWhenRelationshipIsAsymmetric;

# ---------- UNDIRECTED EDGE ----------
UndirectedEdge :=
    SymmetricAssociationBetweenNodes;

UndirectedRepresentation SHOULD_ONLY_BE_USED_WHEN DirectionIsNotSemanticallyRequired;

# ---------- LABEL ----------
NodeLabel MAY_DESCRIBE EntityTypeOrDisplayName;

EdgeLabel MAY_IDENTIFY PredicateOrRelationshipType;

Label != CanonicalIdentity;

# ---------- ENTITY ----------
Entity :=
    DistinctThingRepresentedByGraphNode;

Entity MAY_HAVE MultipleLabelsOrAliases;

# ---------- CONCEPT ----------
Concept :=
    AbstractMeaningCategoryRepresentedWithinGraph;

Concept MAY_HAVE {
    BroaderConcept,
    NarrowerConcept,
    RelatedConcept
};

# ---------- CLASS ----------
Class :=
    SemanticCategoryOfEntities;

Instance :=
    EntityBelongingToClass;

INSTANCE_OF :=
    RelationshipBetweenInstanceAndClass;

# ---------- SUBCLASS ----------
SUBCLASS_OF :=
    HierarchicalRelationshipBetweenClasses;

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

# ---------- PROPERTY ----------
Property :=
    SemanticCharacteristicAssociatedWithEntityOrRelationship;

Property MAY_BE {
    LiteralValued,
    EntityValued,
    Contextual
};

# ---------- TRIPLE ----------
SemanticTriple :=
    (Subject, Predicate, Object);

Subject MAY_MAP_TO Node;
Predicate MAY_MAP_TO EdgeType;
Object MAY_MAP_TO NodeOrLiteral;

# ---------- RDF GRAPH ----------
RDFGraph :=
    SET_OF RDFTriples;

RDFGraph IS_A SemanticGraphRepresentation;

# ---------- PROPERTY GRAPH ----------
PropertyGraph :=
    NodesAndEdgesWithAttachedKeyValueProperties;

PropertyGraph MAY_IMPLEMENT SemanticGraph
WHEN LabelsPropertiesAndRelationshipTypesHaveExplicitMeaning;

# ---------- KNOWLEDGE GRAPH ----------
KnowledgeGraph :=
    SemanticGraphContainingDomainKnowledgeAboutEntitiesAndRelationships;

KnowledgeGraph MAY_INCLUDE {
    OntologyTerms,
    InstanceData,
    Provenance,
    Confidence
};

# ---------- ONTOLOGY ----------
Ontology :=
    SemanticSpecificationDefiningGraphClassesPropertiesAndConstraints;

Ontology MAY_DEFINE {
    Domain,
    Range,
    Subclass,
    Equivalence,
    Disjointness,
    PropertyCharacteristics
};

# ---------- VOCABULARY ----------
Vocabulary :=
    ControlledSetOfTermsUsedToLabelOrTypeGraphResources;

SharedVocabulary SUPPORTS SemanticInteroperability;

# ---------- IDENTIFIER ----------
GraphResourceIdentifier :=
    StableReferenceToNodeEdgeOrSemanticTerm;

Identifier MAY_BE {
    URI,
    IRI,
    CanonicalID,
    InternalKey
};

# ---------- ENTITY RESOLUTION ----------
EntityResolution :=
    DetermineWhetherMultipleCandidateNodesRepresentSameEntity;

IF IdentityEvidenceStrong
THEN Nodes MAY_BE MergedOrLinkedAccordingToPolicy;

IncorrectMerge MAY_CREATE FalseRelationshipsAcrossGraph;

# ---------- SAME AS ----------
IdentityRelationship MAY_ASSERT SemanticEquivalenceBetweenResources;

SameAsAssertion SHOULD_REQUIRE StrongEvidenceBecauseItCanPropagateKnowledge;

# ---------- MAPPING ----------
SemanticGraphMapping :=
    SourceGraphTerm
    -> TargetGraphTerm;

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

# ---------- GRAPH INTEGRATION ----------
GraphIntegration :=
    GraphA
    + GraphB
    -> AlignSchemas
    -> ResolveEntities
    -> MergeOrLinkStatements
    -> PreserveProvenance;

# ---------- PROVENANCE ----------
GraphProvenance :=
    OriginAndDerivationMetadataForNodeEdgeOrStatement;

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

# ---------- CONTEXT ----------
GraphContext MAY_INCLUDE {
    Time,
    Source,
    Domain,
    Location,
    Dataset,
    Version
};

Context MAY_CHANGE InterpretationOfRelationship;

# ---------- NAMED GRAPH ----------
NamedGraph :=
    IdentifiedSubgraphOrStatementSet;

NamedGraph MAY_REPRESENT {
    Source,
    Context,
    Tenant,
    Version
};

# ---------- SUBGRAPH ----------
Subgraph :=
    SelectedSubsetOfNodesAndEdgesFromLargerGraph;

Subgraph MAY_BE GeneratedFor {
    Query,
    Analysis,
    Explanation,
    AccessControl
};

# ---------- PATH ----------
GraphPath :=
    ordered_sequence(
        Node,
        Edge,
        Node,
        ...
    );

Path MAY_REPRESENT SemanticConnectionBetweenEntities;

# ---------- PATH LENGTH ----------
PathLength :=
    NumberOfEdgesInPath;

ShorterPath DOES_NOT_ALWAYS_MEAN StrongerSemanticRelationship;

# ---------- TRAVERSAL ----------
SemanticTraversal :=
    StartNode
    -> FollowSelectedRelationshipTypes
    -> ReachRelatedNodes;

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

# ---------- PATTERN MATCHING ----------
GraphPattern :=
    NodesVariablesAndRelationshipConstraints;

PatternMatching :=
    GraphPattern
    -> FindMatchingSubgraphs;

# ---------- QUERY ----------
SemanticGraphQuery :=
    RequestForNodesEdgesPathsOrPatternsBasedOnSemanticConstraints;

Query MAY_INCLUDE {
    TypeConstraint,
    PropertyConstraint,
    RelationshipConstraint,
    PathConstraint
};

# ---------- SPARQL RELATIONSHIP ----------
SPARQL MAY_QUERY RDFSemanticGraphsUsingTripleAndGraphPatterns;

# ---------- CYPHER RELATIONSHIP ----------
PropertyGraphSystems MAY_USE GraphQueryLanguagesSuchAsCypherOrEquivalent;

QueryLanguage != SemanticModelByItself;

# ---------- GRAPH REASONING ----------
GraphReasoning :=
    ExplicitGraph
    + OntologyOrRules
    -> DerivedGraphKnowledge;

# ---------- RULE ----------
GraphRule :=
    PatternPremises
    -> DerivedNodeTypeOrRelationship;

# ---------- TRANSITIVE RELATION ----------
IF RelationshipP IS_TRANSITIVE
AND A P B
AND B P C
THEN A P C;

# ---------- SYMMETRIC RELATION ----------
IF RelationshipP IS_SYMMETRIC
AND A P B
THEN B P A;

# ---------- INVERSE RELATION ----------
IF RelationshipP INVERSE_OF RelationshipQ
AND A P B
THEN B Q A;

# ---------- DOMAIN / RANGE ----------
IF PropertyP DOMAIN ClassA
AND X P Y
THEN X MAY_BE_INFERRED_AS INSTANCE_OF ClassA;

IF PropertyP RANGE ClassB
AND X P Y
THEN Y MAY_BE_INFERRED_AS INSTANCE_OF ClassB;

# ---------- EQUIVALENCE ----------
EquivalentClass(A,B) MAY_PROPAGATE TypeMembershipAcrossAAndB;

EquivalentProperty(P,Q) MAY_PROPAGATE RelationshipAssertionsAccordingToFormalSemantics;

# ---------- DISJOINTNESS ----------
IF ClassA DISJOINT_WITH ClassB
AND EntityX INSTANCE_OF Both
THEN GraphKnowledge MAY_BE Inconsistent;

# ---------- VALIDATION ----------
GraphValidation :=
    CheckGraphAgainstSemanticConstraints;

Validation MAY_CHECK {
    RequiredProperty,
    Datatype,
    Cardinality,
    AllowedClass,
    RelationshipShape
};

# ---------- SHAPE ----------
GraphShape :=
    StructuralConstraintOnNodeOrRelationshipPattern;

Shape MAY_BE UsedForDataQualityValidation;

# ---------- CONSISTENCY ----------
SemanticGraphConsistency :=
    CompatibilityOfAssertionsWithSelectedOntologyAndLogic;

# ---------- OPEN WORLD ----------
SemanticGraph MAY_USE OpenWorldAssumption;

MissingEdge DOES_NOT NecessarilyMean RelationshipIsFalse;

# ---------- CONFIDENCE ----------
NodeOrEdge MAY_HAVE ConfidenceScore;

Confidence MAY_REFLECT {
    SourceReliability,
    ExtractionStrength,
    Agreement,
    InferenceStrength
};

# ---------- WEIGHT ----------
GraphEdgeWeight MAY_REPRESENT {
    Cost,
    Strength,
    Probability,
    Similarity
};

WeightSemantics MUST_BE Explicit;

# ---------- TEMPORAL GRAPH ----------
TemporalSemanticGraph :=
    GraphWhoseNodesOrEdgesHaveTemporalValidity;

TemporalEdge MAY_HAVE {
    ValidFrom,
    ValidTo,
    ObservationTime
};

# ---------- DYNAMIC GRAPH ----------
DynamicSemanticGraph :=
    GraphWhoseStructureOrPropertiesChangeOverTime;

# ---------- GRAPH UPDATE ----------
GraphUpdate MAY_INCLUDE {
    AddNode,
    AddEdge,
    RemoveNode,
    RemoveEdge,
    UpdateProperty
};

# ---------- CASCADE ----------
RemovingNode MAY_AFFECT ConnectedEdges;

DeletionPolicy SHOULD_DEFINE WhetherEdgesAreRemovedArchivedOrPreservedAsHistoricalKnowledge;

# ---------- VERSIONING ----------
SemanticGraphVersion :=
    IdentifiedGraphStateAtPointInTime;

Versioning SUPPORTS {
    Reproducibility,
    Audit,
    Rollback
};

# ---------- GRAPH INDEX ----------
GraphIndex MAY_ACCELERATE {
    NodeLookup,
    PropertyLookup,
    RelationshipTraversal,
    FullTextSearch
};

# ---------- VECTOR RELATIONSHIP ----------
NodeOrDocument MAY_HAVE Embedding;

Embedding MAY_SUPPORT SemanticSimilaritySearchAcrossGraphResources;

VectorSimilarity != TypedGraphRelationship;

# ---------- GRAPH EMBEDDING ----------
GraphEmbedding :=
    NumericRepresentationDerivedFromGraphStructureOrSemantics;

GraphEmbedding MAY_SUPPORT {
    NodeSimilarity,
    LinkPrediction,
    Classification
};

# ---------- LINK PREDICTION ----------
LinkPrediction :=
    EstimateLikelihoodOfMissingOrFutureRelationship;

PredictedLink SHOULD_BE DistinguishedFrom AssertedOrVerifiedLink;

# ---------- COMMUNITY ----------
GraphCommunity :=
    GroupOfNodesWithRelativelyDenseInternalRelationshipsAccordingToDefinedMethod;

Community MAY_SUPPORT Exploration
BUT DoesNotAutomaticallyRepresentOntologyClass;

# ---------- CENTRALITY ----------
CentralityMetric MAY_ESTIMATE StructuralImportanceOfNode;

StructuralImportance != SemanticAuthorityByDefinition;

# ---------- SEMANTIC SEARCH ----------
SemanticSearch MAY_USE GraphToExpandQueryAcrossEntitiesConceptsAndRelationships;

GraphEvidence MAY_CONTRIBUTE_TO Ranking;

# ---------- RAG ----------
GraphRAG :=
    Query
    -> ResolveEntities
    -> TraverseSemanticGraph
    -> RetrieveRelevantSubgraphOrEvidence
    -> ConstructContext
    -> GenerateResponse;

# ---------- EXPLANATION ----------
GraphExplanation :=
    RelevantNodes
    + RelationshipPath
    + Provenance
    -> HumanOrMachineReadableReasoningEvidence;

# ---------- INTEROPERABILITY ----------
SemanticGraphInteroperability MAY_REQUIRE {
    SharedIdentifiers,
    SharedOntology,
    Mapping,
    LinkedData
};

# ---------- FEDERATION ----------
FederatedSemanticGraph :=
    MultipleGraphSourcesQueriedOrLinkedAsDistributedKnowledgeSpace;

# ---------- ACCESS CONTROL ----------
GraphAccessControl MAY_APPLY_TO {
    Node,
    Edge,
    Property,
    NamedGraph,
    Subgraph
};

# ---------- PRIVACY ----------
GraphStructure MAY_REVEAL SensitiveRelationshipsThroughTraversalOrInference;

PrivacyControl SHOULD_CONSIDER DerivedRelationships;

# ---------- SECURITY ----------
SemanticGraphSecurity MAY_INCLUDE {
    Authentication,
    Authorisation,
    QueryLimits,
    ProvenanceIntegrity,
    GraphValidation
};

# ---------- SCALABILITY ----------
SemanticGraphScalability MAY_DEPEND_ON {
    NodeCount,
    EdgeCount,
    DegreeDistribution,
    TraversalDepth,
    Partitioning
};

# ---------- PARTITIONING ----------
LargeGraph MAY_BE PartitionedAcrossShards;

CrossPartitionTraversal MAY_INCREASE LatencyAndNetworkCost;

# ---------- PERFORMANCE ----------
GraphPerformance MAY_BE_MEASURED_BY {
    TraversalLatency,
    PatternMatchLatency,
    QueryThroughput,
    UpdateRate,
    InferenceCost
};

# ---------- SEMANTIC REASONING ----------
IF GraphNodesRepresentEntitiesOrConcepts
AND EdgesRepresentExplicitTypedRelationships
THEN SemanticGraphClassification := supported;

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

IF EdgeTypeIsTransitive
AND A Edge B
AND B Edge C
THEN A Edge C MAY_BE Derived;

IF IdentityResolutionMergesTwoNodes
THEN TheirRelationships MAY_BE CombinedAccordingToPolicy;

IF PredictedLinkHasNoVerifiedEvidence
THEN It SHOULD_REMAIN DistinctFromAssertedFact;

IF ProtectedEdgeIsNotAuthorised
THEN Traversal MUST_NOT ExposeItAccordingToPolicy;

IF GraphPartitioningSeparatesFrequentlyTraversedNodes
THEN QueryCost MAY_INCREASE;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "semantic graph" ~= "meaning-aware graph";
    "knowledge graph" ~= "semantic knowledge graph" WHEN typed_semantics_present;
    "semantic edge" ~= "typed semantic relationship";
    "semantic node" ~= "entity or concept node";
    "graph traversal" ~= "relationship traversal";
    "graph reasoning" ~= "semantic graph inference";
    "graph pattern matching" ~= "semantic graph pattern query";
    "graph integration" ~= "semantic graph integration";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_START_ENTITIES(q) ->
    RESOLVE_IDENTITIES(q) ->
    IDENTIFY_TYPES_AND_CONCEPTS(q) ->
    IDENTIFY_RELATIONSHIP_CONSTRAINTS(q) ->
    TRAVERSE_OR_MATCH_GRAPH(q) ->
    APPLY_ONTOLOGY_AND_RULES(q) ->
    APPLY_ACCESS_CONTROL(q) ->
    ATTACH_CONTEXT_AND_PROVENANCE(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_SUBGRAPH_OR_RESULTS;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        graph_semantic_consistency,
        identity_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: SemanticGraph;
    ontology: SemanticGraphOntology;
    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_node:
        validate_identifier
        -> classify
        -> attach_properties
        -> attach_provenance
        -> integrate;

    new_edge:
        validate_source_target
        -> classify_relationship
        -> attach_context
        -> attach_confidence
        -> attach_provenance
        -> integrate;

    new_ontology_mapping:
        validate
        -> align_classes_and_properties
        -> update_graph_semantics
        -> integrate;

    graph_revision:
        preserve_previous_version
        -> update_nodes_and_edges
        -> recompute_inferences
        -> update_indexes
        -> recompute_confidence
        -> regenerate_flow_hash;

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

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + GraphEntity
    + KnowledgeEntity
    + GraphStructure
    + OperationEntity
    + SemanticTriple
    + GraphIntegration
    + GraphReasoning
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
SemanticGraphOntology
    -> IdentifyEntitiesConceptsAndClasses
    -> ResolveCanonicalNodeIdentity
    -> ConstructTypedNodesAndEdges
    -> AttachPropertiesContextAndProvenance
    -> MapGraphToOntology
    -> ValidateSemanticConstraints
    -> ApplyRulesAndGraphInference
    -> TraverseRelationshipPaths
    -> MatchSemanticGraphPatterns
    -> EnforceGraphAccessPolicies
    -> ReturnRelevantSubgraphsAndKnowledge
    -> PreserveExplainableRelationshipPaths
    -> MaintainMachineInterpretableSemanticGraph;

END FLOW