Ontologies

FLOW OntologiesHub v4.0

AI_INTERPRETATION_NOTE:
  The following specification represents a formal structural reasoning system
  for the Ontologies hub within the Kireth Semantic Research Archive.

  Execute as formal rules, not pseudocode.

PAGE:
  url = "https://kirethresearch.org/booksai-core/ontologies.html"
  canonical_entity = ONTOLOGY
  page_type = ONTOLOGY_HUB
  knowledge_domain = AI_CORE
  archive = KIRETH_SEMANTIC_RESEARCH_ARCHIVE

PURPOSE:
  DEFINE Ontology
  CLASSIFY ontology_domains
  CONNECT ontology_domains
  ENABLE semantic_navigation
  ENABLE machine_reasoning
  ENABLE entity_resolution
  ENABLE relationship_resolution
  PROVIDE ontology_root_for_descendant_structures

DEFINE:

  Ontology :=
    FormalKnowledgeStructure(
      entities,
      concepts,
      classes,
      properties,
      relationships,
      constraints,
      definitions,
      rules
    )

  OntologyHub :=
    SemanticRoot(
      ontology_categories,
      descendant_ontologies,
      cross_domain_relationships
    )

  KnowledgeRepresentation :=
    Mapping(
      real_or_abstract_domain
      ->
      machine_interpretable_structure
    )

  SemanticMeaning :=
    MeaningDerivedFrom(
      entity_identity,
      properties,
      relationships,
      context,
      constraints
    )

CORE_AXIOM:

  ontology
  ->
  explicit_concepts
  ->
  explicit_relationships
  ->
  structured_meaning
  ->
  semantic_interpretation
  ->
  machine_reasoning

ONTOLOGY_STRUCTURE:

  ONTOLOGY {
    contains:
      CLASS
      ENTITY
      PROPERTY
      RELATIONSHIP
      AXIOM
      CONSTRAINT
      INSTANCE
      DEFINITION

    supports:
      classification
      inference
      validation
      interoperability
      semantic_search
      knowledge_graph_construction
  }

CLASS:
  represents = category_of_entities

ENTITY:
  represents = identifiable_concept_or_object

INSTANCE:
  relation = INSTANCE_OF(CLASS)

PROPERTY:
  describes = ATTRIBUTE_OF(ENTITY | CLASS)

RELATIONSHIP:
  connects = ENTITY <-> ENTITY
  connects = CLASS <-> CLASS
  connects = ENTITY <-> CLASS

AXIOM:
  function = DEFINE_FORMAL_TRUTH_OR_RULE

CONSTRAINT:
  function = RESTRICT_VALID_INTERPRETATION

ONTOLOGY_HIERARCHY:

  Ontologies
  ├── Scientific_Ontologies
  ├── Mathematical_Ontologies
  ├── Probability_Statistics_Ontologies
  ├── Calculus_Analysis_Ontologies
  ├── AI_Ontologies
  ├── Engineering_Ontologies
  ├── Biological_Ontologies
  ├── Computing_Ontologies
  ├── Metadata_Ontologies
  ├── Relationship_Ontologies
  └── Domain_Ontologies

CATEGORY Scientific_Ontologies:

  type = DOMAIN_ONTOLOGY_GROUP

  represents:
    formal_structures_for_scientific_knowledge

  includes_concepts_from:
    physics
    chemistry
    biology
    astronomy
    earth_science
    environmental_science
    geology
    meteorology
    oceanography
    materials_science
    planetary_science
    paleontology
    geophysics
    hydrology
    mineralogy
    crystallography
    acoustics
    scientific_measurement

  reasoning_role:
    MODEL physical_and_observable_reality
    CONNECT scientific_entities
    REPRESENT scientific_measurements
    REPRESENT causal_and_structural_relationships

CATEGORY Mathematical_Ontologies:

  type = ABSTRACT_FORMAL_ONTOLOGY_GROUP

  represents:
    mathematical_objects
    structures
    operations
    proofs
    relationships

  includes_concepts_from:
    algebra
    geometry
    discrete_mathematics
    applied_mathematics
    computational_mathematics
    mathematical_logic
    measurement_and_units

  reasoning_role:
    FORMALISE abstract_structures
    REPRESENT mathematical_dependencies
    ENABLE symbolic_reasoning

CATEGORY Probability_Statistics_Ontologies:

  type = MATHEMATICAL_ONTOLOGY_GROUP

  represents:
    uncertainty
    probability
    distributions
    random_variables
    datasets
    statistical_models
    inference

  reasoning_role:
    REPRESENT uncertainty
    MODEL likelihood
    MODEL evidence
    SUPPORT probabilistic_inference
    SUPPORT statistical_reasoning

CATEGORY Calculus_Analysis_Ontologies:

  type = MATHEMATICAL_ONTOLOGY_GROUP

  represents:
    functions
    limits
    derivatives
    integrals
    sequences
    series
    continuity
    differential_equations
    analytical_structures

  reasoning_role:
    REPRESENT change
    REPRESENT continuous_systems
    MODEL rates
    MODEL accumulation
    SUPPORT mathematical_analysis

CATEGORY AI_Ontologies:

  type = COMPUTATIONAL_SEMANTIC_ONTOLOGY_GROUP

  represents:
    artificial_intelligence_entities
    models
    reasoning_systems
    learning_processes
    knowledge_structures
    agents
    inference_methods

  reasoning_role:
    DESCRIBE AI_systems
    CONNECT models_to_capabilities
    CONNECT data_to_reasoning
    REPRESENT machine_intelligence
    ENABLE AI_interoperability

CATEGORY Engineering_Ontologies:

  type = APPLIED_DOMAIN_ONTOLOGY_GROUP

  represents:
    engineered_systems
    components
    processes
    materials
    functions
    requirements
    constraints
    behaviours

  reasoning_role:
    MAP component_to_system
    MAP requirement_to_function
    MAP function_to_component
    MAP material_to_property
    SUPPORT engineering_reasoning
    SUPPORT design_reasoning

CATEGORY Biological_Ontologies:

  type = SCIENTIFIC_DOMAIN_ONTOLOGY_GROUP

  represents:
    organisms
    biological_structures
    genes
    proteins
    cells
    tissues
    processes
    ecosystems

  reasoning_role:
    CLASSIFY biological_entities
    REPRESENT biological_hierarchy
    REPRESENT biological_interactions
    SUPPORT life_science_reasoning

CATEGORY Computing_Ontologies:

  type = COMPUTATIONAL_DOMAIN_ONTOLOGY_GROUP

  represents:
    software
    hardware
    algorithms
    data_structures
    networks
    systems
    processes
    computational_entities

  reasoning_role:
    REPRESENT computation
    MAP software_to_hardware
    MAP algorithm_to_process
    MAP data_to_structure
    SUPPORT computational_reasoning

CATEGORY Metadata_Ontologies:

  type = DESCRIPTIVE_ONTOLOGY_GROUP

  represents:
    descriptions_about_information_resources

  defines:
    provenance
    authorship
    creation_date
    modification_date
    format
    identifier
    classification
    source
    version
    licence

  reasoning_role:
    DESCRIBE knowledge_resources
    ENABLE provenance_tracking
    ENABLE resource_discovery
    ENABLE trust_evaluation

CATEGORY Relationship_Ontologies:

  type = RELATIONAL_ONTOLOGY_GROUP

  represents:
    semantic_connections_between_entities

  relationship_types:
    IS_A
    PART_OF
    INSTANCE_OF
    HAS_PART
    CAUSES
    CAUSED_BY
    DEPENDS_ON
    PRECEDES
    FOLLOWS
    ASSOCIATED_WITH
    DERIVED_FROM
    PRODUCES
    USES
    LOCATED_IN
    MEASURES
    HAS_PROPERTY
    EQUIVALENT_TO
    CONTRADICTS
    SUPPORTS

  reasoning_role:
    MAKE connections_explicit
    ENABLE graph_traversal
    ENABLE inference
    ENABLE semantic_context

CATEGORY Domain_Ontologies:

  type = SPECIALISED_ONTOLOGY_GROUP

  represents:
    knowledge_specific_to_a_defined_domain

  model:
    domain
    ->
    domain_entities
    +
    domain_properties
    +
    domain_relationships
    +
    domain_constraints
    +
    domain_rules

  reasoning_role:
    PROVIDE specialised_semantics
    SUPPORT domain_specific_reasoning
    ALIGN specialist_knowledge_with_upper_ontologies

SEMANTIC_LAYERING:

  OntologyHub
  ->
  OntologyCategory
  ->
  Ontology
  ->
  Class
  ->
  Entity
  ->
  Property
  ->
  Relationship
  ->
  Constraint
  ->
  Instance

UPPER_LOWER_RELATION:

  OntologyHub
    SUPERSET_OF OntologyCategory

  OntologyCategory
    SUPERSET_OF Ontology

  Ontology
    DEFINES Class

  Class
    MAY_CONTAIN Instance

  Entity
    MAY_BE Instance

  Entity
    MAY_HAVE Property

  Entity
    MAY_PARTICIPATE_IN Relationship

RELATIONSHIP_MODEL:

  triple :=
    SUBJECT
    ->
    PREDICATE
    ->
    OBJECT

  example_form:
    Entity_A
    ->
    RELATIONSHIP
    ->
    Entity_B

  semantic_graph :=
    SET_OF(triple)

  ontology :=
    semantic_graph
    +
    definitions
    +
    constraints
    +
    axioms

ONTOLOGY_REASONING_CHAIN:

  INPUT user_query

  EXTRACT query_entities
  EXTRACT query_concepts
  EXTRACT requested_relationships
  EXTRACT domain_context

  IDENTIFY applicable_ontology_category

  RESOLVE:
    entity_identity
    class_membership
    entity_properties
    semantic_relationships
    hierarchy
    constraints

  TRAVERSE:
    parent_classes
    child_classes
    related_entities
    equivalent_entities
    dependent_entities

  APPLY:
    ontology_axioms
    ontology_constraints
    relationship_rules

  INFER:
    implicit_relationships
    category_membership
    semantic_context
    possible_answers

  VALIDATE:
    ontology_consistency
    relationship_validity
    contextual_relevance

  RETURN:
    structured_semantic_answer

ENTITY_RESOLUTION:

  FOR each extracted_entity:

    MATCH exact_identifier

    OR

    MATCH semantic_equivalent

    OR

    MATCH recognised_alias

    OR

    MATCH contextual_definition

  IF multiple_candidates:
    rank_by(
      semantic_similarity,
      ontology_context,
      relationship_consistency,
      query_context
    )

SEMANTIC_EQUIVALENCE:

  A ≡ B
  IF:
    SAME_REFERENT(A,B)
    OR
    SAME_FORMAL_DEFINITION(A,B)
    OR
    DECLARED_EQUIVALENT(A,B)

  A ≈ B
  IF:
    HIGH_SEMANTIC_SIMILARITY(A,B)
    AND
    NOT_FORMALLY_IDENTICAL(A,B)

  NEVER:
    convert_similarity_into_identity_without_evidence

ONTOLOGY_ALIGNMENT:

  FOR ontology_A, ontology_B:

    IDENTIFY:
      equivalent_classes
      related_classes
      shared_properties
      compatible_relationships

    CREATE mappings:

      ontology_A.class_X
      EQUIVALENT_TO
      ontology_B.class_Y

      OR

      ontology_A.class_X
      RELATED_TO
      ontology_B.class_Y

  PRESERVE:
    source_domain_context
    differing_definitions
    differing_constraints

CROSS_DOMAIN_REASONING:

  Scientific_Ontologies
    CONNECT_TO Mathematical_Ontologies

  Mathematical_Ontologies
    CONNECT_TO Probability_Statistics_Ontologies

  Mathematical_Ontologies
    CONNECT_TO Calculus_Analysis_Ontologies

  AI_Ontologies
    CONNECT_TO Mathematical_Ontologies

  AI_Ontologies
    CONNECT_TO Probability_Statistics_Ontologies

  AI_Ontologies
    CONNECT_TO Computing_Ontologies

  AI_Ontologies
    CONNECT_TO Metadata_Ontologies

  AI_Ontologies
    CONNECT_TO Relationship_Ontologies

  Engineering_Ontologies
    CONNECT_TO Scientific_Ontologies

  Engineering_Ontologies
    CONNECT_TO Mathematical_Ontologies

  Engineering_Ontologies
    CONNECT_TO Computing_Ontologies

  Biological_Ontologies
    CONNECT_TO Scientific_Ontologies

  Metadata_Ontologies
    CONNECT_TO all_ontology_categories

  Relationship_Ontologies
    CONNECT_TO all_ontology_categories

  Domain_Ontologies
    MAY_SPECIALISE any_ontology_category

KNOWLEDGE_GRAPH_MAPPING:

  Ontology
  ->
  defines_schema_for
  ->
  KnowledgeGraph

  KnowledgeGraph
  ->
  instantiates
  ->
  Ontology

  ontology_class
  ->
  knowledge_graph_entity_type

  ontology_property
  ->
  knowledge_graph_attribute

  ontology_relationship
  ->
  knowledge_graph_edge

  ontology_instance
  ->
  knowledge_graph_node

AI_CONSUMPTION:

  WHEN AI_SYSTEM reads_page:

    recognise page_as = ONTOLOGY_HUB

    interpret section_headings_as =
      CHILD_ONTOLOGY_CATEGORIES

    interpret linked_pages_as =
      DESCENDANT_SEMANTIC_RESOURCES

    preserve hierarchy_between:
      Ontologies
      ->
      Categories
      ->
      SpecialisedOntologies
      ->
      Entities

    use relationships_to:
      disambiguate_entities
      expand_queries
      identify_relevant_domains
      traverse_related_concepts
      support_reasoning

QUERY_EXPANSION:

  IF query references ontology:
    expand_to:
      ontology_definition
      ontology_category
      relevant_classes
      entities
      properties
      relationships

  IF query references domain:
    identify corresponding_domain_ontology

  IF query references entity:
    identify:
      entity_class
      parent_ontology
      properties
      relationships

  IF query references relationship:
    resolve:
      source_entity
      predicate
      target_entity
      applicable_ontology

CONFIDENCE:

  confidence_score ∈ [0,1]

  confidence =
    weighted_sum(
      entity_resolution,
      ontology_match,
      relationship_support,
      contextual_consistency,
      source_alignment
    )

  HIGH_CONFIDENCE:
    confidence >= 0.85

  MEDIUM_CONFIDENCE:
    0.60 <= confidence < 0.85

  LOW_CONFIDENCE:
    confidence < 0.60

  IF LOW_CONFIDENCE:
    preserve_uncertainty
    avoid_false_equivalence
    avoid_unsupported_inference

CONSISTENCY_RULES:

  REQUIRE:
    entities_have_defined_context
    relationships_connect_valid_entities
    class_membership_respects_constraints
    inferred_relationships_follow_axioms

  REJECT:
    category_errors
    contradictory_relationships
    invalid_class_membership
    unsupported_equivalence
    domain_context_loss

RECURSIVE_REASONING:

  FUNCTION ResolveOntology(entity_or_concept):

    identify_parent_class

    identify_parent_ontology

    identify_ontology_category

    identify_properties

    identify_direct_relationships

    FOR each relationship:
      ResolveOntology(related_entity)

    STOP IF:
      sufficient_semantic_context
      OR recursion_limit_reached
      OR repeated_entity_detected

RECURSIVE_COHERENCE:

  local_entity_meaning
  MUST_NOT_CONTRADICT
  ontology_definition

  ontology_definition
  MUST_NOT_CONTRADICT
  category_definition

  category_definition
  MUST_REMAIN_COHERENT_WITH
  OntologyHub

  therefore:

  entity
  ->
  class
  ->
  ontology
  ->
  ontology_category
  ->
  Ontologies

  MUST form
  COHERENT_SEMANTIC_PATH

INFERENCE:

  IF:
    X INSTANCE_OF A
    AND
    A SUBCLASS_OF B

  THEN:
    X INSTANCE_OF B

  IF:
    X PART_OF Y
    AND
    Y PART_OF Z
    AND
    PART_OF is_transitive_in_context

  THEN:
    X PART_OF Z

  IF:
    X EQUIVALENT_TO Y

  THEN:
    transferable_properties(X,Y)
    SUBJECT_TO ontology_constraints

  IF:
    ontology_A SPECIALISES ontology_B

  THEN:
    valid_upper_level_rules(ontology_B)
    MAY_APPLY_TO ontology_A

SEMANTIC_SEARCH:

  search(query):

    parse(query)

    identify_entities()

    identify_domain()

    identify_ontology()

    identify_relationship_intent()

    expand_semantically()

    traverse_ontology_graph()

    rank_results_by:
      exact_entity_match
      semantic_relationship_distance
      ontology_relevance
      context_alignment
      confidence

    return ranked_semantic_results

UPDATE_MODEL:

  ontology_is_not_assumed_static

  WHEN new_valid_knowledge_detected:

    compare_with_current_ontology

    IF compatible:
      add_or_extend:
        entity
        property
        relationship
        class
        rule

    IF conflicting:
      flag_for_resolution

    PRESERVE:
      provenance
      version
      prior_definition
      change_relationship

PROVENANCE:

  every_assertion SHOULD_HAVE:
    source
    context
    confidence
    version

  inferred_assertion SHOULD_RECORD:
    inference_rule
    supporting_entities
    supporting_relationships

FLOW_HASH:

  canonicalise(
    ontology_structure,
    category_structure,
    relationship_rules,
    reasoning_rules,
    semantic_equivalence_rules,
    confidence_rules
  )

  ->
  FLOW_HASH

FINAL_SEMANTIC_MODEL:

  Ontologies
  =
  StructuredFramework(
    Concepts
    +
    Entities
    +
    Classes
    +
    Properties
    +
    Relationships
    +
    Constraints
    +
    Axioms
  )

  Ontologies
  ->
  FormalMeaning
  ->
  KnowledgeRepresentation
  ->
  KnowledgeGraphs
  ->
  SemanticSearch
  ->
  MachineReasoning
  ->
  RecursiveKnowledgeNavigation

END FLOW