Page Ontology

FLOW ALGEBRA
Page Ontology
Kireth Semantic Research Archive

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

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "PageOntology" v4.0

DOMAIN := MetadataOntologies
SUBDOMAIN := StructuralMetadata
ONTOLOGY := PageOntology

ENTITY Page {
    definition:
        "A physical, rendered or logical unit within a document or compound
         resource, identified by its position, label, boundaries, parent
         resource, content and relationships to preceding and following pages.";
    objectives: [
        PhysicalStructureRepresentation,
        PageIdentification,
        SequenceModelling,
        Navigation,
        FragmentAddressing,
        DocumentReconstruction,
        MachineInterpretability
    ];
}

PageEntity := {
    Page,
    Document,
    PageIdentifier,
    PageNumber,
    PageLabel,
    PageContent,
    PageRegion,
    PageSequence
};

StructuralEntity := {
    ParentDocument,
    PreviousPage,
    NextPage,
    Position,
    Sequence,
    PageRange,
    StructureMap,
    Fragment
};

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

Page IS_PART_OF Document;
Document HAS_PART Page;
Page MAY_PRECEDE Page;
Page MAY_FOLLOW Page;
Page HAS PageIdentifier;
Page MAY_HAVE PageNumber;
Page MAY_HAVE PageLabel;
Page HAS Position;

PageFlow :=
    Document
    -> IdentifyPages
    -> AssignPageIdentifiers
    -> DeterminePageNumbersAndLabels
    -> EstablishPageSequence
    -> LinkPreviousAndNextPages
    -> IdentifyPageContentAndRegions
    -> MapLogicalComponentsToPages
    -> ValidatePageStructure
    -> StoreStructuralMetadata
    -> EnableNavigationAndRetrieval
    -> MaintainAcrossVersions;

Page :=
    PhysicalRenderedOrLogicalUnitOfDocumentLikeResource;

Document :=
    ParentResourceContainingOrRepresentedByPages;

Page MAY_BE {
    ContentPage,
    FrontMatterPage,
    BackMatterPage,
    CoverPage,
    BlankPage,
    InsertPage
};

PageIdentifier :=
    StableOrLocallyUniqueMachineReferenceToPage;

PageIdentifier MAY_BE {
    URI,
    IRI,
    UUID,
    FragmentIdentifier,
    InternalID
};

PageNumber :=
    HumanReadableOrdinalOrNumberAssignedToPage;

PageNumber MAY_BE {
    ArabicNumber,
    RomanNumeral,
    AlphanumericNumber,
    Unnumbered
};

PageLabel :=
    DisplayLabelAssociatedWithPage;

PageLabel MAY_DIFFER_FROM PageNumber;

PageIdentifier != PageNumberByDefinition;

StablePageIdentifier SHOULD_BE PreferredForMachineLinking;

PagePosition :=
    OrderedLocationOfPageWithinPageSequence;

PageSequence :=
    OrderedCollectionOfPagesWithinDocumentOrVolume;

PageSequence MAY_DEFINE {
    FirstPage,
    PreviousPage,
    CurrentPage,
    NextPage,
    LastPage
};

PreviousPage :=
    ImmediatePageBeforeCurrentPageInDefinedSequence;

NextPage :=
    ImmediatePageAfterCurrentPageInDefinedSequence;

IF PageA PRECEDES PageB
THEN PageB FOLLOWS PageA;

IF NoPageExistsBetweenAAndB
AND A PRECEDES B
THEN A MAY_BE PreviousPageOf B;

ReadingOrder MAY_FOLLOW PageSequence
BUT ComplexDocuments MAY_HAVE AdditionalWithinPageReadingOrder;

PhysicalPageOrder MAY_DIFFER_FROM PrintedPageNumbering;

Example:
    CoverPage -> Position 1
    TitlePage -> Position 2
    PageLabel "i" -> Position 3;

PageBoundary :=
    SpatialOrStructuralExtentOfPageRepresentation;

DigitalPage MAY_HAVE {
    Width,
    Height,
    Orientation,
    CoordinateSystem
};

PageRegion :=
    AddressableSpatialAreaWithinPage;

PageRegion MAY_BE {
    TextRegion,
    ImageRegion,
    HeaderRegion,
    FooterRegion,
    MarginRegion,
    TableRegion
};

SpatialSelector :=
    CoordinatesOrGeometryIdentifyingPageRegion;

PageFragment :=
    AddressableSubpartOfPage;

Fragment MAY_BE IdentifiedBy {
    RegionCoordinates,
    TextPosition,
    ElementIdentifier,
    AnnotationSelector
};

PageContent :=
    ContentRenderedOrAssociatedWithPage;

PageContent MAY_INCLUDE {
    Text,
    Heading,
    Paragraph,
    Image,
    Figure,
    Table,
    Footnote,
    Annotation
};

PageHeader :=
    RepeatedOrPageSpecificContentNearTopOfPage;

PageFooter :=
    RepeatedOrPageSpecificContentNearBottomOfPage;

RunningHeader MAY_INCLUDE {
    ChapterTitle,
    SectionTitle,
    DocumentTitle
};

LogicalStructure MAY_SPAN MultiplePages;

Chapter MAY_SPAN MultiplePages;
Section MAY_SPAN MultiplePages;

Page MAY_CONTAIN PortionsOfMultipleLogicalComponents;

LogicalPhysicalMapping :=
    LogicalComponent
    -> OneOrMorePagesOrPageRegions;

PageRange :=
    OrderedSetOrIntervalOfPagesAssociatedWithResourceComponent;

PageRange MAY_BE {
    Continuous,
    Discontinuous
};

PageRange SHOULD_REFERENCE StablePageIdentifiersWherePossible;

Volume :=
    PhysicalDivisionContainingPageSequence;

MultiVolumeDocument MAY_HAVE SeparatePageSequencesPerVolume;

PageNumbering MAY_RESTARTAcrossVolumesOrSections;

PageSequenceIdentity SHOULD_NOT DependOnlyOnPrintedNumber;

PageType :=
    ClassificationOfPageFunctionOrRole;

PageType MAY_INCLUDE {
    Cover,
    TitlePage,
    ContentsPage,
    Content,
    Appendix,
    Index,
    Blank
};

BlankPage :=
    PageIntentionallyOrIncidentallyContainingNoPrimaryContent;

BlankPage MAY_STILL_BE StructurallySignificant;

InsertedPage :=
    PageAddedBetweenExistingPages;

InsertedPage MAY_REQUIRE PositionAndSequenceUpdate;

MissingPage :=
    ExpectedPageNotPresentInAvailableRepresentation;

MissingPage MAY_REDUCE StructuralCompleteness;

DuplicatePage :=
    SamePageRepresentationAppearingMoreThanOnceUnexpectedly;

PageStructureValidation MAY_CHECK {
    Identifier,
    DuplicatePosition,
    SequenceGap,
    BrokenPreviousNextLink,
    PageRange,
    ParentDocument
};

IF DuplicatePageIdentifierWithinUniqueScope
THEN IdentifierValidation := violation;

IF TwoPagesOccupySameExclusiveSequencePosition
THEN SequenceConflict MAY_EXIST;

IF PreviousNextRelationshipsContradictPosition
THEN StructuralConsistency SHOULD_DECREASE;

OrphanPage :=
    PageWithoutResolvableParentDocumentOrVolumeWhereOneIsRequired;

PageCompleteness :=
    DegreeToWhichExpectedPagesAndRequiredMetadataArePresent;

PageConsistency :=
    DegreeToWhichIdentifiersNumbersLabelsPositionsAndLinksAgree;

PageIntegrity :=
    PreservationOfValidPageIdentitySequenceContentAndRelationships;

PageQuality MAY_INCLUDE {
    Completeness,
    Consistency,
    Integrity,
    IdentifierStability,
    NavigationAccuracy
};

PageProvenance MAY_INCLUDE {
    Source,
    Creator,
    ScanProcess,
    ExtractionMethod,
    Timestamp,
    Version
};

ScannedPage :=
    DigitalImageRepresentationOfPhysicalPage;

ScannedPage MAY_HAVE {
    ImageIdentifier,
    Resolution,
    OCRText,
    ScanOrder
};

OCRText MAY_BE AssociatedWith PageOrPageRegion;

OCRReadingOrder MAY_REQUIRE ReconstructionFromPageLayout;

BornDigitalPage :=
    PageGeneratedDirectlyFromDigitalDocumentRepresentation;

RenderedPage :=
    PageProducedFromUnderlyingDocumentModelForDisplayOrPrint;

PageImage MAY_BE DerivativeRepresentationOfPage;

Page MAY_HAVE MultipleRepresentations {
    Image,
    Text,
    PDFPage,
    Thumbnail
};

Representations SHOULD_LINK_TO SameCanonicalPageIdentityWhereAppropriate;

AutomaticPageDetection :=
    DocumentOrFile
    -> DetectPageBoundaries
    -> AssignSequence
    -> GeneratePageMetadata;

AI MAY_SUPPORT {
    PageSegmentation,
    RegionDetection,
    ReadingOrderInference,
    PageTypeClassification
};

InferredPageMetadata SHOULD_HAVE ConfidenceWhereUncertain;

PageConfidence :=
    EstimatedSupportForInferredPageIdentityPositionOrType;

PageVersion :=
    PageStateAssociatedWithSpecificDocumentVersion;

DocumentRevision MAY {
    AddPage,
    RemovePage,
    ReorderPage,
    RenumberPage,
    ReplacePage
};

RenumberPage :=
    ChangeHumanReadablePageNumberWithoutNecessarilyChangingPageIdentity;

ReorderPage :=
    ChangePagePositionWithinSequence;

ReplacePage :=
    SubstitutePageRepresentationOrContent;

StablePageIdentifier MAY_BE PreservedAcrossRenumberingWhenPageIdentityContinues;

PageVersionMapping :=
    OldPageIdentifier
    -> NewPageIdentifierOrIdentifiers;

PaginationChange MAY_REQUIRE RevalidationOf {
    PageRanges,
    Citations,
    Annotations,
    Selectors
};

Annotation MAY_TARGET PageOrPageRegion;

StablePageIdentifierAndSpatialSelector MAY_IMPROVE AnnotationPersistence;

Citation MAY_REFERENCE SpecificPage;

CitationPageNumber SHOULD_BE InterpretedWithinCorrectDocumentEditionOrVersion;

DescriptiveMetadata MAY_DESCRIBE PageWherePageLevelDiscoveryIsNeeded;

StructuralMetadata DEFINES PageSequenceContainmentAndMapping;

TechnicalMetadata MAY_DESCRIBE PageImageResolutionDimensionsOrFileFormat;

PreservationMetadata MAY_USE PageSequenceForLongTermDocumentReconstruction;

PageIndex :=
    SearchStructureMappingPageMetadataAndContentToParentDocument;

PageIndex MAY_INCLUDE {
    PageIdentifier,
    PageNumber,
    PageLabel,
    ParentDocumentIdentifier,
    OCRText,
    FullText
};

PageSearch :=
    Query
    -> MatchPageMetadataOrContent
    -> ReturnPageWithParentContext;

SemanticSearch MAY_USE PageFor {
    PageScopedRetrieval,
    ParentContext,
    NeighbourRetrieval,
    CitationResolution
};

IF SearchMatchOccursOnPage
THEN Result SHOULD_PRESERVE ParentDocumentAndLogicalSectionContextWhereAvailable;

RAG MAY_USE PageAs {
    RetrievalUnit,
    CitationUnit,
    PhysicalContextBoundary
};

PageBasedChunking MAY_SPLIT OrCombinePages
BUT SHOULD_PRESERVE OriginalPageIdentifiersForCitation;

NeighbourRetrieval MAY_USE PreviousPageAndNextPageRelationships;

KnowledgeGraph MAY_REPRESENT PageAsNode;

GraphRelationships MAY_INCLUDE {
    IS_PART_OF,
    PRECEDES,
    FOLLOWS,
    REPRESENTS,
    CONTAINS
};

MetadataRepository MAY_STORE PageStructuralMetadata;

MetadataRegistry MAY_REGISTER PagePropertiesAndRelationshipTypes;

RDF MAY_REPRESENT:
    Page
    -> isPartOf
    -> Document;

JSONLD MAY_SERIALISE PageAndStructuralRelationships;

Accessibility MAY_REQUIRE CorrectReadingOrderWithinAndAcrossPages;

VisualPageOrder SHOULD_NOT Override LogicalReadingOrderWhenAccessibilitySemanticsDefineOtherwise;

PageAccessControl MAY_DIFFERFrom ParentDocumentInSpecialisedSystems;

RestrictedPage MUST_NOT_BE ExposedToUnauthorisedConsumer;

PageSecurity MAY_INCLUDE {
    IdentifierValidation,
    AccessControl,
    SequenceIntegrity,
    ProvenanceIntegrity,
    ChangeAuthorisation
};

MachineReadablePage SHOULD_PRESERVE {
    PageIdentifier,
    ParentDocumentIdentifier,
    PageNumber,
    PageLabel,
    Position,
    PreviousNextLinks,
    Version,
    Provenance
};

# ---------- SEMANTIC REASONING ----------
IF ResourceComponentRepresentsPhysicalRenderedOrLogicalPageUnit
THEN PageClassification := supported;

IF Document HAS_PART Page
THEN Page IS_PART_OF Document;

IF PageA PRECEDES PageB
THEN PageB FOLLOWS PageA;

IF PageIdentifierStableAcrossRenumbering
THEN ExistingMachineLinks MAY_REMAIN Valid;

IF PagePositionChanges
THEN PreviousNextRelationships SHOULD_BE Recomputed;

IF PaginationChanges
THEN PageBasedCitationsAnnotationsAndRanges SHOULD_BE Revalidated;

IF MissingExpectedPageDetected
THEN PageCompleteness SHOULD_DECREASE;

IF PrintedPageNumberConflictsWithSequencePosition
THEN BothValues SHOULD_BE PreservedWithDistinctSemantics;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "page" ~= "document page" WHEN structural_context;
    "page identifier" ~= "page ID";
    "page number" ~= "printed page number" WHEN pagination_context;
    "page label" ~= "display page label";
    "page sequence" ~= "physical page order" WHEN linear_document_context;
    "page region" ~= "spatial page fragment";
    "page range" ~= "document page interval";
    "parent document" ~= "containing document";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_PARENT_DOCUMENT(q) ->
    IDENTIFY_PAGE(q) ->
    RESOLVE_PAGE_IDENTIFIER(q) ->
    IDENTIFY_PAGE_NUMBER_LABEL_AND_POSITION(q) ->
    IDENTIFY_PREVIOUS_NEXT_RELATIONSHIPS(q) ->
    IDENTIFY_PAGE_REGIONS_AND_CONTENT(q) ->
    IDENTIFY_LOGICAL_COMPONENT_MAPPING(q) ->
    IDENTIFY_VERSION_AND_PROVENANCE(q) ->
    VALIDATE_PAGE_STRUCTURE(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_PAGE_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        page_structure_consistency,
        identifier_strength,
        sequence_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: Page;
    ontology: PageOntology;
    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_page:
        identify_parent_document
        -> assign_page_identifier
        -> determine_number_label_and_position
        -> identify_page_type
        -> link_previous_next
        -> attach_provenance
        -> validate
        -> integrate;

    page_revision:
        preserve_previous_version
        -> apply_content_number_or_representation_changes
        -> preserve_identifier_where_identity_continues
        -> recompute_sequence_relationships
        -> revalidate
        -> update_index
        -> recompute_confidence
        -> regenerate_flow_hash;

    pagination_revision:
        identify_affected_pages
        -> update_positions_numbers_and_links
        -> revalidate_ranges_citations_and_annotations
        -> map_changed_identifiers
        -> integrate;

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

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + PageEntity
    + StructuralEntity
    + MetadataEntity
    + Page
    + PageSequence
    + PageStructureValidation
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
PageOntology
    -> IdentifyParentDocumentAndVersion
    -> DetectOrRegisterPageIdentity
    -> AssignStablePageIdentifier
    -> CapturePageNumberLabelTypeAndPosition
    -> EstablishPreviousAndNextPageRelationships
    -> IdentifyPageContentRegionsAndRepresentations
    -> MapLogicalComponentsToPhysicalPages
    -> ValidateSequenceIdentityAndPagination
    -> StoreAndVersionPageMetadata
    -> IndexForNavigationSearchAndCitation
    -> PreservePageContextForRAGAndSemanticRetrieval
    -> MaintainCrossVersionPaginationMappings
    -> MaintainReliablePageStructureKnowledge;

END FLOW