Heading Ontology

FLOW ALGEBRA
Heading Ontology
Kireth Semantic Research Archive

PAGE:
https://kirethresearch.org/booksai-core/ontologies/metadata-ontologies/structural-metadata/heading-ontology.html

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "HeadingOntology" v4.0

DOMAIN := MetadataOntologies
SUBDOMAIN := StructuralMetadata
ONTOLOGY := HeadingOntology

ENTITY Heading {
    definition:
        "A structural label or title associated with a document division,
         identifying the beginning, subject or role of a chapter, section,
         subsection or other logical component and supporting hierarchy,
         navigation, accessibility and machine interpretation.";
    objectives: [
        StructuralLabelling,
        HierarchyRepresentation,
        Navigation,
        ContentSegmentation,
        Accessibility,
        RetrievalContext,
        MachineInterpretability
    ];
}

HeadingEntity := {
    Heading,
    HeadingText,
    HeadingIdentifier,
    HeadingLevel,
    HeadingType,
    ParentHeading,
    ChildHeading,
    HeadingSequence
};

StructuralEntity := {
    Document,
    Chapter,
    Section,
    Subsection,
    ParentComponent,
    PreviousHeading,
    NextHeading,
    Position
};

MetadataEntity := {
    MetadataRecord,
    Language,
    Provenance,
    Version,
    Confidence,
    ResourceIdentifier
};

Heading LABELS StructuralComponent;
StructuralComponent MAY_HAVE Heading;
Heading HAS HeadingText;
Heading HAS HeadingLevel;
Heading MAY_HAVE ParentHeading;
ParentHeading MAY_HAVE ChildHeading;
Heading MAY_PRECEDE Heading;
Heading HAS Position;

HeadingFlow :=
    StructuredResource
    -> IdentifyHeading
    -> CaptureHeadingText
    -> AssignHeadingIdentifier
    -> DetermineHeadingLevel
    -> LinkToStructuralComponent
    -> InferParentChildHierarchy
    -> DetermineHeadingSequence
    -> ValidateHierarchy
    -> StoreStructuralMetadata
    -> EnableNavigationAndAccessibility
    -> MaintainAcrossVersions;

Heading :=
    StructuralTextOrLabelIdentifyingLogicalResourceDivision;

Heading MAY_LABEL {
    Document,
    Chapter,
    Section,
    Subsection,
    Appendix,
    OtherLogicalComponent
};

HeadingText :=
    HumanReadableTextDisplayedOrAssociatedWithHeading;

HeadingIdentifier :=
    StableOrLocallyUniqueReferenceToHeading;

HeadingIdentifier MAY_BE {
    URI,
    IRI,
    UUID,
    ElementID,
    FragmentIdentifier,
    InternalID
};

HeadingLevel :=
    HierarchicalRankOfHeadingWithinDocumentStructure;

HeadingLevel MAY_BE {
    Level1,
    Level2,
    Level3,
    Level4,
    Level5,
    Level6,
    CustomLevel
};

NumericHeadingLevel MAY_BE RepresentedAs Integer;

LowerNumericValue MAY_REPRESENT HigherStructuralRankAccordingToCommonHTMLConvention;

HeadingType :=
    SemanticOrStructuralRoleOfHeading;

HeadingType MAY_INCLUDE {
    DocumentTitleHeading,
    ChapterHeading,
    SectionHeading,
    SubsectionHeading,
    AppendixHeading
};

HeadingPosition :=
    OrderedLocationOfHeadingWithinParentResourceOrReadingOrder;

HeadingSequence :=
    OrderedCollectionOfHeadings;

PreviousHeading :=
    ImmediateHeadingBeforeCurrentHeadingInDefinedSequence;

NextHeading :=
    ImmediateHeadingAfterCurrentHeadingInDefinedSequence;

IF HeadingA PRECEDES HeadingB
THEN HeadingB FOLLOWS HeadingA;

HeadingHierarchy :=
    ParentChildStructureDerivedFromHeadingLevelsAndDocumentSemantics;

ParentHeading :=
    HeadingRepresentingImmediateBroaderStructuralContext;

ChildHeading :=
    HeadingRepresentingImmediateNestedStructuralContext;

IF HeadingB IS_CHILD_OF HeadingA
THEN HeadingA IS_PARENT_OF HeadingB;

HeadingPath :=
    RootHeading
    -> IntermediateHeadings
    -> TargetHeading;

RootHeading :=
    HighestRelevantHeadingWithinDefinedResourceStructure;

LeafHeading :=
    HeadingWithoutChildHeadingsWithinCurrentStructure;

HeadingDepth :=
    NumberOfParentHeadingEdgesFromRootHeading;

HeadingLevelAndHierarchy SHOULD_BE SemanticallyConsistent;

SkippedHeadingLevel :=
    TransitionFromHigherLevelToDeeperLevelWithoutExpectedIntermediateLevel;

SkippedHeadingLevel MAY_BE {
    AllowedByProfile,
    Warning,
    StructuralError
};

HeadingLevel SHOULD_NOT BeSelectedOnlyForVisualAppearance;

VisualStyle != StructuralLevelByDefinition;

Heading MAY_HAVE StylingIndependentOfSemanticHierarchy;

HeadingNumber :=
    HumanReadableNumberOrOutlineLabelAssociatedWithHeading;

HeadingNumber MAY_BE {
    Integer,
    DecimalOutline,
    RomanNumeral,
    AlphanumericLabel
};

HeadingNumber != HeadingIdentifierByDefinition;

OutlineNumber :=
    HierarchicalNumberSuchAs {
        "1",
        "1.1",
        "1.1.1"
    };

OutlineNumber MAY_SUPPORT StructuralNavigation
BUT SHOULD_NOT Replace ExplicitHierarchyRelationships;

HeadingLanguage :=
    LanguageOfHeadingText;

Heading MAY_HAVE MultilingualVariants;

TranslatedHeading :=
    HeadingTextInAnotherLanguageReferringToSameStructuralComponent;

AlternativeHeading :=
    AdditionalHeadingLabelForSameComponentAccordingToMetadataModel;

UntitledStructuralComponent MAY_EXISTWithoutHeading;

Heading MAY_EXISTWithoutExplicitVisibleTextInSpecialisedMachineStructures
BUT AccessibilityAndUsabilityImplications SHOULD_BE Considered;

HeadingBoundary :=
    StructuralPointAtWhichAssociatedContentDivisionBegins;

Heading MAY_DEFINE StartOfSection
UNTIL NextHeadingOfSameOrHigherRelevantLevelAccordingToParsingRules;

HeadingScope :=
    ContentStructurallyGovernedByHeading;

HeadingScope MAY_INCLUDE {
    Paragraphs,
    Lists,
    Figures,
    Tables,
    ChildSections
};

HeadingToSectionMapping :=
    Heading
    -> LABELS
    -> Section;

HeadingToChapterMapping :=
    Heading
    -> LABELS
    -> Chapter;

OneStructuralComponent SHOULD_NOT HaveMultiplePrimaryHeadingsUnlessModelAllows;

HeadingExtraction :=
    Resource
    -> DetectCandidateHeading
    -> DetermineLevel
    -> LinkToContentDivision;

HeadingDetection MAY_USE {
    Markup,
    Typography,
    Position,
    Numbering,
    LinguisticFeatures,
    AIInference
};

MarkupBasedHeading :=
    HeadingExplicitlyEncodedInStructuredDocumentMarkup;

VisualHeading :=
    TextVisuallyStyledAsHeadingWithoutExplicitSemanticMarkup;

VisualHeading MAY_REQUIRE StructuralInference;

FalseHeading :=
    VisuallyProminentTextIncorrectlyInterpretedAsStructuralHeading;

AutomaticHeadingDetection SHOULD_DISTINGUISH StructuralHeadingFromDecorativeText;

AI MAY_SUPPORT {
    HeadingDetection,
    LevelInference,
    TitleExtraction,
    HierarchyRepair
};

InferredHeading SHOULD_HAVE ConfidenceWhereUncertain;

HeadingConfidence :=
    EstimatedSupportForHeadingClassificationLevelOrRelationship;

HeadingValidation MAY_CHECK {
    Identifier,
    Text,
    Level,
    ParentRelationship,
    Sequence,
    DuplicateID,
    HierarchicalCycle
};

IF DuplicateHeadingIdentifierWithinUniqueScope
THEN IdentifierValidation := violation;

HierarchicalCycle :=
    HeadingIsItsOwnAncestorThroughParentHeadingPath;

IF HierarchicalCycleDetected
THEN ValidationStatus := violation;

IF HeadingLevelContradictsExplicitParentRelationship
THEN HierarchyConsistency SHOULD_DECREASE;

HeadingCompleteness :=
    DegreeToWhichExpectedStructuralDivisionsHaveAppropriateHeadings;

HeadingConsistency :=
    DegreeToWhichHeadingLevelsHierarchyAndNumberingFollowSharedRules;

HeadingClarity :=
    DegreeToWhichHeadingTextClearlyIdentifiesAssociatedContent;

HeadingQuality MAY_INCLUDE {
    Completeness,
    Consistency,
    Clarity,
    Accessibility,
    IdentifierStability
};

HeadingProvenance MAY_INCLUDE {
    Source,
    Creator,
    ExtractionMethod,
    Timestamp,
    Version
};

HeadingVersion :=
    HeadingStateAssociatedWithSpecificResourceVersion;

ResourceRevision MAY {
    AddHeading,
    RemoveHeading,
    RenameHeading,
    RelevelHeading,
    ReorderHeading,
    ReparentHeading
};

RenameHeading :=
    ChangeHeadingTextWithoutNecessarilyChangingStructuralIdentity;

RelevelHeading :=
    ChangeHeadingLevel;

ReparentHeading :=
    ChangeImmediateParentHeadingOrStructuralParent;

ReorderHeading :=
    ChangeHeadingPositionWithinReadingOrder;

StableHeadingIdentifier MAY_BE PreservedAcrossRenameWhereIdentityContinues;

RelevelOrReparent MAY_REQUIRE RecalculationOfHeadingPathAndChildRelationships;

HeadingVersionMapping :=
    OldHeadingIdentifier
    -> NewHeadingIdentifierOrIdentifiers;

TableOfContents MAY_BE GeneratedFrom HeadingHierarchy;

Outline :=
    OrderedHierarchicalRepresentationOfHeadingsAndAssociatedComponents;

DocumentOutline MAY_SUPPORT {
    Navigation,
    Search,
    Accessibility,
    Summarisation
};

Breadcrumb MAY_BE DerivedFrom HeadingPath;

HeadingIndex :=
    SearchStructureMappingHeadingTextAndIdentifiersToStructuralComponents;

HeadingSearch :=
    Query
    -> MatchHeadingText
    -> ReturnAssociatedComponentWithContext;

SemanticSearch MAY_USE HeadingFor {
    QueryMatching,
    SectionRanking,
    ParentContext,
    ResultExplanation
};

HeadingText MAY_BE HighValueSignalFor SectionSubjectOrIntent;

RAG MAY_USE HeadingFor {
    ChunkLabelling,
    ParentContext,
    HierarchicalRetrieval,
    ContextCompression
};

Chunk SHOULD_RETAIN RelevantHeadingPathWhenDerivedFromSectionContent;

HeadingAwareChunking MAY_IMPROVE ContextPreservation;

KnowledgeGraph MAY_REPRESENT HeadingAsNodeOrPropertyOfStructuralComponent;

GraphRelationships MAY_INCLUDE {
    LABELS,
    IS_PARENT_OF,
    IS_CHILD_OF,
    PRECEDES,
    FOLLOWS
};

MetadataRepository MAY_STORE HeadingStructuralMetadata;

MetadataRegistry MAY_REGISTER HeadingPropertiesLevelsAndRelationshipTypes;

HTML MAY_REPRESENT HeadingsUsing h1Throughh6Elements;

HTMLHeadingRank SHOULD_REFLECT DocumentStructureRatherThanVisualSize;

ARIA MAY_DEFINE HeadingRoleAndLevelForAccessibleInterfaces;

Accessibility MAY_REQUIRE MeaningfulHeadingHierarchy;

ScreenReaders MAY_USE HeadingsFor RapidDocumentNavigation;

EmptyHeading MAY_CREATE AccessibilityAndNavigationProblems;

DuplicateVisibleHeadingText MAY_BE Valid
IF StructuralContextsDiffer;

HeadingIdentifier SHOULD_DISAMBIGUATE MachineReferences;

XML MAY_REPRESENT HeadingOrTitleElementsAccordingToDocumentSchema;

Markdown MAY_REPRESENT HeadingLevelsUsing HeadingSyntax;

PDFTaggedStructure MAY_INCLUDE HeadingElementsWhenProperlyTagged;

DescriptiveMetadata MAY_USE HeadingTextAsEvidenceFor {
    Subject,
    Summary,
    Keywords
};

StructuralMetadata DEFINES HeadingHierarchyAndComponentRelationship;

Annotation MAY_TARGET HeadingOrAssociatedSection;

Citation MAY_REFERENCE HeadingOrSectionWhenStableIdentifiersExist;

HeadingInteroperability MAY_REQUIRE {
    StableIdentifiers,
    SharedLevelSemantics,
    ParentRelationships,
    VersionInformation
};

AccessControl MAY_RESTRICT StructuralComponentsAndTheirHeadings;

RestrictedHeading MUST_NOT RevealProtectedComponentToUnauthorisedConsumerWherePolicyForbids;

HeadingSecurity MAY_INCLUDE {
    IdentifierValidation,
    OutputEscaping,
    AccessControl,
    ProvenanceIntegrity,
    ChangeAuthorisation
};

MachineReadableHeading SHOULD_PRESERVE {
    HeadingIdentifier,
    HeadingText,
    HeadingLevel,
    ParentHeading,
    AssociatedComponent,
    Position,
    Version,
    Provenance
};

# ---------- SEMANTIC REASONING ----------
IF StructuralLabelIdentifiesLogicalDocumentDivision
THEN HeadingClassification := supported;

IF HeadingB IS_CHILD_OF HeadingA
THEN HeadingA IS_PARENT_OF HeadingB;

IF HeadingA PRECEDES HeadingB
THEN HeadingB FOLLOWS HeadingA;

IF HeadingLevelChanges
THEN HeadingHierarchy SHOULD_BE Revalidated;

IF HeadingIdentifierStableAcrossRename
THEN ExistingLinks MAY_REMAIN Valid;

IF HeadingTextMatchesQuery
THEN AssociatedSection MAY_RECEIVE RetrievalBoostAccordingToSearchPolicy;

IF HeadingHierarchyContainsCycle
THEN ValidationStatus := violation;

IF HeadingIsOnlyVisuallyStyledWithoutSemanticMarkup
THEN StructuralRole MAY_REQUIRE InferenceOrRepair;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "heading" ~= "document heading" WHEN structural_context;
    "heading text" ~= "heading label";
    "heading level" ~= "heading rank";
    "parent heading" ~= "broader structural heading";
    "child heading" ~= "nested heading";
    "heading hierarchy" ~= "document outline hierarchy";
    "heading identifier" ~= "heading ID";
    "heading path" ~= "outline path";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_RESOURCE(q) ->
    IDENTIFY_HEADING(q) ->
    RESOLVE_HEADING_IDENTIFIER(q) ->
    IDENTIFY_HEADING_TEXT_LEVEL_AND_TYPE(q) ->
    IDENTIFY_ASSOCIATED_COMPONENT(q) ->
    IDENTIFY_PARENT_CHILD_RELATIONSHIPS(q) ->
    IDENTIFY_PREVIOUS_NEXT_RELATIONSHIPS(q) ->
    IDENTIFY_VERSION_AND_PROVENANCE(q) ->
    VALIDATE_HEADING_STRUCTURE(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_HEADING_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        heading_structure_consistency,
        identifier_strength,
        hierarchy_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: Heading;
    ontology: HeadingOntology;
    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_heading:
        identify_resource
        -> detect_or_receive_heading
        -> assign_heading_identifier
        -> capture_heading_text
        -> determine_level_and_type
        -> link_structural_component
        -> identify_parent_and_position
        -> attach_provenance
        -> validate
        -> integrate;

    heading_revision:
        preserve_previous_version
        -> apply_text_level_parent_or_position_changes
        -> preserve_identifier_where_identity_continues
        -> recompute_hierarchy_and_sequence
        -> revalidate
        -> update_outline_and_index
        -> recompute_confidence
        -> regenerate_flow_hash;

    resource_revision:
        identify_affected_headings
        -> update_positions_parent_links_and_paths
        -> map_changed_identifiers
        -> validate_structure
        -> integrate;

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

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + HeadingEntity
    + StructuralEntity
    + MetadataEntity
    + Heading
    + HeadingHierarchy
    + HeadingValidation
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
HeadingOntology
    -> IdentifyStructuredResource
    -> DetectHeadingAndAssociatedComponent
    -> AssignStableHeadingIdentifier
    -> CaptureHeadingTextLevelTypeAndPosition
    -> BuildParentChildHeadingHierarchy
    -> EstablishPreviousAndNextRelationships
    -> ValidateLevelsCyclesAndStructuralConsistency
    -> StoreAndVersionHeadingMetadata
    -> GenerateOutlineTableOfContentsAndNavigation
    -> PreserveHeadingContextForSearchAndRAG
    -> SupportAccessibilityAndMachineInterpretation
    -> MaintainCrossVersionHeadingMappings
    -> MaintainReliableHeadingStructureKnowledge;

END FLOW