Table Ontology

FLOW ALGEBRA
Table Ontology
Kireth Semantic Research Archive

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

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "TableOntology" v4.0

DOMAIN := MetadataOntologies
SUBDOMAIN := StructuralMetadata
ONTOLOGY := TableOntology

ENTITY Table {
    definition:
        "A structured resource component that organises data, text or values
         into rows, columns, cells and associated headers, captions and
         relationships for comparison, presentation, navigation, extraction
         and machine interpretation.";
    objectives: [
        TabularStructureRepresentation,
        DataOrganisation,
        CellRelationshipModelling,
        HeaderAssociation,
        Accessibility,
        DataExtraction,
        MachineInterpretability
    ];
}

TableEntity := {
    Table,
    TableIdentifier,
    TableCaption,
    TableHeader,
    TableBody,
    TableFooter,
    Row,
    Column,
    Cell
};

StructuralEntity := {
    RowHeader,
    ColumnHeader,
    HeaderCell,
    DataCell,
    RowGroup,
    ColumnGroup,
    CellSpan,
    Position
};

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

Table IS_PART_OF ParentResource;
Table CONTAINS Row;
Table CONTAINS Column;
Row CONTAINS Cell;
Column CONTAINS Cell;
HeaderCell LABELS RowOrColumn;
Cell HAS Position;
Table MAY_HAVE TableCaption;
Table HAS TableIdentifier;

TableFlow :=
    ParentResource
    -> IdentifyTableBoundary
    -> AssignTableIdentifier
    -> CaptureCaptionAndTitle
    -> DetectRowsColumnsAndCells
    -> IdentifyHeaderCells
    -> AssociateHeadersWithDataCells
    -> ResolveSpansAndGroups
    -> ValidateTableStructure
    -> StoreStructuralMetadata
    -> EnableAccessibleNavigationAndExtraction
    -> MaintainAcrossVersions;

Table :=
    StructuredGridOrMatrixLikeComponentContainingRelatedValues;

ParentResource MAY_BE {
    Document,
    Chapter,
    Section,
    Page,
    Dataset,
    WebPage
};

TableIdentifier :=
    StableOrLocallyUniqueReferenceToTable;

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

StableTableIdentifier SHOULD_BE PreferredForMachineReferences;

TableCaption :=
    HumanReadableDescriptionOrTitleAssociatedWithTable;

Caption MAY_INCLUDE {
    TableNumber,
    TableTitle,
    ExplanatoryText
};

TableNumber :=
    HumanReadableOrdinalOrReferenceNumberAssignedToTable;

TableNumber != TableIdentifierByDefinition;

TableHeader :=
    StructuralRegionContainingHeaderInformation;

TableBody :=
    PrimaryRegionContainingTabularData;

TableFooter :=
    OptionalRegionContainingTotalsNotesOrSummaryRows;

Row :=
    HorizontalOrLogicalSequenceOfCells;

Column :=
    VerticalOrLogicalSequenceOfCells;

Cell :=
    IntersectionOrLogicalMemberOfRowAndColumn;

Cell MAY_BE {
    HeaderCell,
    DataCell
};

HeaderCell :=
    CellProvidingLabelOrContextForOtherCells;

DataCell :=
    CellContainingPrimaryTabularValue;

RowHeader :=
    HeaderCellAssociatedWithOneOrMoreDataCellsInRowDirection;

ColumnHeader :=
    HeaderCellAssociatedWithOneOrMoreDataCellsInColumnDirection;

HeaderAssociation :=
    HeaderCell
    -> LABELS
    -> DataCellOrGroup;

CorrectHeaderAssociation IS_CRITICAL_FOR AccessibleAndMachineReadableTables;

CellPosition :=
    CoordinatesOrLogicalLocationOfCell;

CellPosition MAY_INCLUDE {
    RowIndex,
    ColumnIndex
};

RowIndex :=
    OrderedPositionOfRowWithinTableOrRowGroup;

ColumnIndex :=
    OrderedPositionOfColumnWithinTableOrColumnGroup;

RowGroup :=
    LogicalGroupingOfRows;

ColumnGroup :=
    LogicalGroupingOfColumns;

Table MAY_HAVE MultipleHeaderLevels;

MultiLevelHeader :=
    HeaderHierarchySpanningMultipleRowsOrColumns;

CellSpan :=
    CellOccupyingMultipleLogicalRowsOrColumns;

CellSpan MAY_INCLUDE {
    RowSpan,
    ColumnSpan
};

RowSpan :=
    NumberOfRowsCoveredByCell;

ColumnSpan :=
    NumberOfColumnsCoveredByCell;

SpanningCell SHOULD_BE ResolvedIntoCorrectLogicalAssociationsForMachineInterpretation;

TableGrid :=
    LogicalMatrixProducedAfterResolvingCellPositionsAndSpans;

SparseTable :=
    TableWhereSomeLogicalPositionsHaveNoExplicitValue;

MissingCell != EmptyCellByDefinition;

EmptyCell :=
    ExistingCellWithNoDisplayedOrRecordedValue;

MissingCell :=
    ExpectedLogicalCellNotRepresented;

TableValue :=
    DataOrTextContainedWithinCell;

TableValue MAY_BE {
    String,
    Number,
    Date,
    Boolean,
    Identifier,
    EntityReference,
    StructuredValue
};

CellDatatype MAY_BE {
    Text,
    Integer,
    Decimal,
    Percentage,
    Currency,
    Date,
    Boolean
};

Datatype SHOULD_BE ExplicitOrInferableWhereMachineProcessingRequires;

Unit :=
    MeasurementUnitAssociatedWithCellColumnRowOrTable;

UnitScope SHOULD_BE Explicit;

Column MAY_HAVE {
    Label,
    Datatype,
    Unit
};

Row MAY_HAVE {
    Label,
    Identifier
};

TableSchema :=
    StructuralAndSemanticDefinitionOfTableColumnsRowsDatatypesAndConstraints;

TableSchema MAY_DEFINE {
    ColumnNames,
    Datatypes,
    RequiredColumns,
    Keys,
    Units
};

KeyColumn :=
    ColumnWhoseValuesIdentifyRowsOrEntitiesAccordingToTableSemantics;

CompositeKey MAY_USE MultipleColumns;

TableRelationship :=
    SemanticRelationshipBetweenCellsRowsColumnsOrExternalEntities;

Cell MAY_REFERENCE {
    Resource,
    Entity,
    Footnote,
    Citation
};

TableFootnote :=
    NoteProvidingAdditionalContextForTableOrSpecificCells;

FootnoteAssociation SHOULD_PRESERVE TargetScope;

TableSource :=
    OriginOfTabularDataOrRepresentation;

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

Table MAY_BE {
    ManuallyAuthored,
    ExtractedFromMarkup,
    DetectedFromLayout,
    AIAssisted
};

StructuredTable :=
    TableWithExplicitMachineReadableRowsColumnsAndHeaderSemantics;

VisualTable :=
    ContentVisuallyArrangedAsTableWithoutReliableStructuralMarkup;

LayoutTable :=
    GridUsedPrimarilyForVisualLayoutRatherThanTabularData;

LayoutTable SHOULD_NOT_BE InterpretedAsDataTableWithoutEvidence;

TableDetection :=
    Resource
    -> DetectTableBoundary
    -> InferGrid
    -> DetectHeaders
    -> ExtractCells;

AI MAY_SUPPORT {
    TableDetection,
    CellSegmentation,
    HeaderDetection,
    DatatypeInference,
    RelationshipInference
};

InferredTableStructure SHOULD_HAVE ConfidenceWhereUncertain;

TableConfidence :=
    EstimatedSupportForInferredTableStructureOrSemantics;

TableValidation MAY_CHECK {
    Identifier,
    RowColumnConsistency,
    CellPosition,
    SpanValidity,
    HeaderAssociation,
    Datatype,
    BrokenReference
};

IF DuplicateTableIdentifierWithinUniqueScope
THEN IdentifierValidation := violation;

IF CellPositionFallsOutsideDefinedGrid
THEN StructuralValidation := violation;

IF OverlappingSpansCreateImpossibleGrid
THEN StructuralValidation := violation;

IF DataCellHasNoResolvableHeaderInTableRequiringHeaders
THEN AccessibilityAndSemanticQuality SHOULD_DECREASE;

TableCompleteness :=
    DegreeToWhichExpectedRowsColumnsCellsAndHeadersAreRepresented;

TableConsistency :=
    DegreeToWhichGridPositionsSpansHeadersAndDatatypesAgree;

TableIntegrity :=
    PreservationOfValidCellIdentityStructureRelationshipsAndValues;

TableQuality MAY_INCLUDE {
    Completeness,
    Consistency,
    Integrity,
    HeaderQuality,
    Accessibility,
    IdentifierStability
};

TableVersion :=
    TableStateAssociatedWithSpecificParentResourceVersion;

ResourceRevision MAY {
    AddTable,
    RemoveTable,
    RenameTable,
    ReorderRows,
    ReorderColumns,
    AddRow,
    AddColumn,
    ModifyCell
};

StableTableIdentifier MAY_BE PreservedAcrossCaptionOrPositionChangesWhereIdentityContinues;

RowIdentifier MAY_BE PreservedWhereRowEntityIdentityContinues;

ColumnIdentifier MAY_BE PreservedWhereColumnSemanticsContinue;

TableVersionMapping :=
    OldTableIdentifier
    -> NewTableIdentifierOrIdentifiers;

CellAddress MAY_CHANGEWhenRowsOrColumnsReordered;

StableRowColumnIdentifiers MAY_BE MoreReliableThanRawCoordinatesAcrossVersions;

TableAnnotation MAY_TARGET {
    Table,
    Row,
    Column,
    Cell
};

StableIdentifiers MAY_IMPROVE AnnotationPersistence;

Citation MAY_REFERENCE TableOrSpecificCellWhereSupported;

DescriptiveMetadata MAY_DESCRIBE TableUsing {
    Title,
    Caption,
    Subject,
    Summary,
    Keywords
};

StructuralMetadata DEFINES TableRowsColumnsCellsAndRelationships;

TechnicalMetadata MAY_DESCRIBE FileFormatEncodingOrRenderingCharacteristics;

PreservationMetadata MAY_REQUIRE TableSchemaAndStructureForLongTermInterpretation;

TableIndex :=
    SearchStructureMappingTableMetadataHeadersAndValuesToParentResource;

TableIndex MAY_INCLUDE {
    Caption,
    Headers,
    CellText,
    ParentResourceIdentifier
};

TableSearch :=
    Query
    -> MatchCaptionHeadersOrCells
    -> ReturnTableWithParentContext;

SemanticSearch MAY_USE TableFor {
    StructuredFiltering,
    EntityMatching,
    NumericRetrieval,
    ContextualRanking
};

RAG MAY_USE TableAs {
    RetrievalUnit,
    StructuredEvidence,
    DataContext
};

TableAwareChunking SHOULD_PRESERVE {
    Caption,
    Headers,
    RelevantRows,
    Units,
    ParentContext
};

SplittingTableWithoutHeaders MAY_DESTROY MeaningOfCellValues;

KnowledgeGraph MAY_MAP TableRowsToEntitiesAndColumnsToProperties;

Example:
    RowEntity
    -> ColumnProperty
    -> CellValue;

Table MAY_BE TransformedInto {
    CSV,
    JSON,
    RDF,
    DatabaseRows,
    DataFrame
};

Transformation SHOULD_PRESERVE {
    Headers,
    Datatypes,
    Units,
    Provenance
};

MetadataRepository MAY_STORE TableStructuralMetadata;

MetadataRegistry MAY_REGISTER TablePropertiesAndStructuralTypes;

HTML MAY_REPRESENT TableUsing {
    table,
    caption,
    thead,
    tbody,
    tfoot,
    tr,
    th,
    td
};

HTMLHeaderAssociations MAY_USE scopeHeadersOrStructuralPosition;

Accessibility MAY_REQUIRE {
    CaptionOrAccessibleName,
    CorrectHeaderCells,
    HeaderAssociations,
    LogicalReadingOrder
};

ScreenReaders MAY_NAVIGATE TableUsing HeaderRelationships;

ComplexTables MAY_REQUIRE ExplicitHeaderAssociations;

XML MAY_REPRESENT TablesUsing DomainSpecificTableSchemas;

Markdown MAY_REPRESENT SimpleTables
BUT MayNotRepresentComplexSpansOrHeaderStructures;

PDFTableStructure MAY_REQUIRE TaggedContentForReliableExtractionAndAccessibility;

TableInteroperability MAY_REQUIRE {
    StableIdentifiers,
    ExplicitHeaders,
    Datatypes,
    Units,
    SharedStructuralSemantics
};

TableAccessControl MAY_APPLY_TO {
    Table,
    Row,
    Column,
    Cell
};

RestrictedCell MUST_NOT_BE ExposedToUnauthorisedConsumer;

TableSecurity MAY_INCLUDE {
    InputValidation,
    FormulaInjectionProtection,
    AccessControl,
    ProvenanceIntegrity,
    ChangeAuthorisation
};

MachineReadableTable SHOULD_PRESERVE {
    TableIdentifier,
    Caption,
    Rows,
    Columns,
    HeaderAssociations,
    CellValues,
    Datatypes,
    Units,
    Version,
    Provenance
};

# ---------- SEMANTIC REASONING ----------
IF ResourceComponentOrganisesRelatedValuesIntoRowsColumnsAndCells
THEN TableClassification := supported;

IF HeaderCellLabelsColumn
THEN DataCellsInApplicableColumn INHERIT HeaderContext;

IF HeaderCellLabelsRow
THEN DataCellsInApplicableRow INHERIT HeaderContext;

IF CellSpansMultipleColumns
THEN HeaderAndPositionResolution MUST_ACCOUNT_FOR Span;

IF TableIdentifierStableAcrossCaptionChange
THEN ExistingMachineLinks MAY_REMAIN Valid;

IF RowOrColumnReordered
THEN CoordinateBasedReferences SHOULD_BE Revalidated;

IF TableChunkExcludesRequiredHeaders
THEN SemanticInterpretability SHOULD_DECREASE;

IF LayoutGridHasNoTabularDataSemantics
THEN It SHOULD_NOT_BE ClassifiedAsDataTable;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "table" ~= "data table" WHEN tabular_data_context;
    "table identifier" ~= "table ID";
    "table caption" ~= "table title or caption" WHEN descriptive_context;
    "header cell" ~= "table heading cell";
    "data cell" ~= "table value cell";
    "row header" ~= "row heading";
    "column header" ~= "column heading";
    "table grid" ~= "logical tabular matrix";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_PARENT_RESOURCE(q) ->
    IDENTIFY_TABLE(q) ->
    RESOLVE_TABLE_IDENTIFIER(q) ->
    IDENTIFY_CAPTION_AND_SCHEMA(q) ->
    IDENTIFY_ROWS_COLUMNS_AND_CELLS(q) ->
    IDENTIFY_HEADERS_AND_ASSOCIATIONS(q) ->
    IDENTIFY_SPANS_DATATYPES_AND_UNITS(q) ->
    IDENTIFY_VERSION_AND_PROVENANCE(q) ->
    VALIDATE_TABLE_STRUCTURE(q) ->
    SCORE_CONFIDENCE(q) ->
    RETURN_RELEVANT_TABLE_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        table_structure_consistency,
        header_resolution_strength,
        datatype_consistency,
        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: Table;
    ontology: TableOntology;
    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_table:
        identify_parent_resource
        -> detect_or_receive_table
        -> assign_table_identifier
        -> capture_caption
        -> identify_rows_columns_and_cells
        -> resolve_headers_and_spans
        -> infer_datatypes_and_units
        -> attach_provenance
        -> validate
        -> integrate;

    table_revision:
        preserve_previous_version
        -> apply_structure_or_value_changes
        -> preserve_identifier_where_identity_continues
        -> revalidate_grid_headers_and_datatypes
        -> update_index
        -> recompute_confidence
        -> regenerate_flow_hash;

    row_column_revision:
        identify_affected_cells
        -> update_positions_and_references
        -> preserve_stable_identifiers
        -> revalidate_header_associations
        -> integrate;

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

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + TableEntity
    + StructuralEntity
    + MetadataEntity
    + Table
    + TableGrid
    + TableValidation
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
TableOntology
    -> IdentifyParentResourceAndTableBoundary
    -> AssignStableTableIdentifier
    -> CaptureCaptionAndTableSchema
    -> DetectRowsColumnsCellsAndGroups
    -> ResolveHeaderAssociationsAndCellSpans
    -> IdentifyDatatypesUnitsAndKeys
    -> ValidateGridStructureAndAccessibility
    -> StoreAndVersionTableMetadata
    -> IndexForStructuredAndSemanticSearch
    -> PreserveHeadersAndContextForRAG
    -> SupportTransformationToMachineReadableData
    -> MaintainCrossVersionTableAndCellReferences
    -> MaintainReliableTabularStructureKnowledge;

END FLOW