Truth Value Ontology

# Truth Value Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/propositional-logic/truth-value-ontology.html

FLOW TruthValueOntology {

  DOMAIN:
    AI Core
    -> Ontologies
    -> Mathematical Ontologies
    -> Mathematical Logic Ontologies
    -> Propositional Logic
    -> Truth Value Ontology

  PURPOSE:
    Represent truth values as machine-interpretable semantic values assigned to propositions and formulas under explicitly declared logical systems, valuations, interpretations or models. In classical propositional logic the canonical truth-value domain is {TRUE, FALSE}, with compound formula values determined recursively by truth-functional connectives. The ontology also distinguishes classical truth values from numeric encodings, probability, confidence, fuzzy membership, unknown or unassigned states, database null values, solver statuses and non-classical many-valued semantics. It enables AI systems to evaluate formulas, construct truth tables, test satisfiability and validity, preserve valuation context, compare semantic equivalence and avoid treating uncertainty, absence of information or computational failure as logical falsehood.

  ENTITY TruthValue {
    TYPE: LogicalSemanticValue

    PROPERTIES:
      has_identifier
      belongs_to_truth_domain
      belongs_to_logic_system
      may_be_assigned_to_proposition
      may_be_computed_for_formula
      may_have_encoding
      has_semantic_context
      has_version
      has_provenance
  }

  ENTITY ClassicalTruthValue {
    TYPE: TruthValue

    POSSIBLE:
      TRUE
      FALSE
  }

  ENTITY TruthAssignment {
    TYPE: ValuationMapping

    COMPONENTS:
      proposition_identifier
      truth_value
      valuation_identifier
  }

  ENTITY TruthDomain {
    TYPE: LogicSpecificSemanticDomain

    COMPONENTS:
      allowed_truth_values
      designated_values
      connective_operations
  }

  TRUTH_VALUE_IDENTITY_MODEL {
    fields:
      truth_value_identifier
      canonical_name
      logic_system
      truth_domain
      version

    RULE:
      truth_value_identity MUST be logic_specific
  }

  CLASSICAL_TRUTH_DOMAIN_MODEL {
    domain:
      TRUE
      FALSE

    cardinality:
      2

    RULE:
      classical_truth_domain MUST not_be silentlyextended
  }

  TRUE_MODEL {
    canonical:
      TRUE

    Boolean_encoding:
      1_when_declared

    RULE:
      TRUE != numeric_one_byidentity
  }

  FALSE_MODEL {
    canonical:
      FALSE

    Boolean_encoding:
      0_when_declared

    RULE:
      FALSE != numeric_zero_byidentity
  }

  BOOLEAN_ENCODING_MODEL {
    mapping:
      TRUE -> 1
      FALSE -> 0

    RULE:
      encoding_isrepresentational_notsemantic_identity
  }

  SYMBOLIC_ENCODING_MODEL {
    TRUE_aliases:
      T
      ⊤
      true

    FALSE_aliases:
      F
      ⊥
      false

    RULE:
      alias_meaning MUST be notation_context_specific
  }

  TRUTH_CONSTANT_MODEL {
    top:
      formula_constant_evaluating_TRUE

    bottom:
      formula_constant_evaluating_FALSE

    RULE:
      truth_constant_symbol != truth_value_entity
  }

  PROPOSITION_TRUTH_MODEL {
    proposition:
      receives_truth_value_under valuation_orinterpretation

    RULE:
      truth_value_assignment_requires_context
  }

  FORMULA_TRUTH_MODEL {
    compound_formula:
      truth_value_computed_recursively_fromsubformula_values

    RULE:
      connective_semantics MUST be declared
  }

  VALUATION_MODEL {
    mapping:
      propositional_variables -> classical_truth_values

    RULE:
      valuation_uniquely_extends_toallformulas_underclassical_truth_functions
  }

  VALUATION_CONTEXT_MODEL {
    fields:
      valuation_identifier
      formula_set
      atom_mapping
      logic_system

    RULE:
      truth_value MUST remainlinked_tovaluation_whencontextual
  }

  COMPLETE_VALUATION_MODEL {
    valuation:
      assigns_allrelevant_atoms

    RULE:
      everyformula_hasdeterminate_classical_value
  }

  PARTIAL_VALUATION_MODEL {
    valuation:
      assigns_subset_ofatoms

    RULE:
      unresolved_formula_value != FALSE
  }

  UNASSIGNED_STATE_MODEL {
    state:
      no_truth_value_currentlysupplied

    RULE:
      UNASSIGNED != FALSE
      UNASSIGNED != UNKNOWN_truth_value_unlesslogic_definesit
  }

  UNKNOWN_STATUS_MODEL {
    status:
      semantic_orcomputational_result_notdetermined

    RULE:
      UNKNOWN != FALSE
      UNKNOWN != third_truth_value_unlesslogic_explicitlydefinesit
  }

  INDETERMINATE_DISTINCTION_MODEL {
    indeterminate:
      mayrepresentsemantic_state_inparticular_nonclassical_logic

    RULE:
      indeterminate != computational_unknown_withoutdefinition
  }

  TRUTH_FUNCTION_MODEL {
    function:
      truth_values^n -> truth_value

    RULE:
      connective_truth_function MUST be total_understandard_classical_logic
  }

  NEGATION_TRUTH_MODEL {
    NOT TRUE = FALSE
    NOT FALSE = TRUE
  }

  CONJUNCTION_TRUTH_MODEL {
    TRUE AND TRUE = TRUE
    TRUE AND FALSE = FALSE
    FALSE AND TRUE = FALSE
    FALSE AND FALSE = FALSE
  }

  DISJUNCTION_TRUTH_MODEL {
    TRUE OR TRUE = TRUE
    TRUE OR FALSE = TRUE
    FALSE OR TRUE = TRUE
    FALSE OR FALSE = FALSE

    RULE:
      OR_isinclusive_underclassical_default
  }

  XOR_TRUTH_MODEL {
    TRUE XOR TRUE = FALSE
    TRUE XOR FALSE = TRUE
    FALSE XOR TRUE = TRUE
    FALSE XOR FALSE = FALSE
  }

  IMPLICATION_TRUTH_MODEL {
    TRUE -> TRUE = TRUE
    TRUE -> FALSE = FALSE
    FALSE -> TRUE = TRUE
    FALSE -> FALSE = TRUE

    RULE:
      material_implication_truth_function != causal_semantics
  }

  BICONDITIONAL_TRUTH_MODEL {
    TRUE <-> TRUE = TRUE
    TRUE <-> FALSE = FALSE
    FALSE <-> TRUE = FALSE
    FALSE <-> FALSE = TRUE
  }

  NAND_TRUTH_MODEL {
    result:
      NOT(A AND B)
  }

  NOR_TRUTH_MODEL {
    result:
      NOT(A OR B)
  }

  TRUTH_TABLE_MODEL {
    rows:
      valuations

    cells:
      truth_values

    RULE:
      truth_table_requires_stable_atom_androw_order
  }

  TRUTH_TABLE_CELL_MODEL {
    fields:
      formula_oratom
      valuation
      truth_value
  }

  TRUTH_VECTOR_MODEL {
    formula:
      ordered_sequence_oftruth_values_overallvaluations

    RULE:
      valuation_order MUST be preserved
  }

  SEMANTIC_EQUIVALENCE_MODEL {
    formulas_A_B:
      equivalent_iftruth_values_equal_foreveryvaluation

    RULE:
      same_singlevaluation_value_doesnotestablish_equivalence
  }

  TAUTOLOGY_MODEL {
    formula:
      truth_vector_allTRUE

    RULE:
      tautology == classical_propositional_validity
  }

  CONTRADICTION_MODEL {
    formula:
      truth_vector_allFALSE

    RULE:
      contradiction != formula_false_underonevaluation
  }

  CONTINGENCY_MODEL {
    formula:
      truth_vector_containsTRUE_andFALSE
  }

  SATISFIABILITY_MODEL {
    formula:
      satisfiable_ifatleastoneTRUE_entry_intruthvector

    RULE:
      satisfiable != valid
  }

  UNSATISFIABILITY_MODEL {
    formula:
      noTRUE_valuation

    RULE:
      unsatisfiable == contradiction_underclassical_propositional_logic
  }

  VALIDITY_MODEL {
    formula:
      allvaluations_produceTRUE

    RULE:
      validity != current_truth_value
  }

  FALSIFIABILITY_MODEL {
    formula:
      atleastonevaluation_producesFALSE

    RULE:
      falsifiable != false_underallvaluations
  }

  MODEL_MODEL {
    valuation:
      model_offormula_whenformula_value_TRUE

    RULE:
      truth_value_isrelative_tomodel_orvaluation_context
  }

  COUNTERMODEL_MODEL {
    valuation:
      formula_value_FALSE

    role:
      refutes_validity_claim
  }

  ENTAILMENT_MODEL {
    Gamma entails A:
      no_valuation_whereallGamma_TRUE_andA_FALSE

    RULE:
      truth_preservation_relation != single_formula_truth_value
  }

  PREMISE_TRUTH_MODEL {
    premise:
      may_beTRUE_orFALSE_undervaluation

    RULE:
      argument_validity_doesnotrequireallvaluations_makepremisesTRUE
  }

  CONCLUSION_TRUTH_MODEL {
    conclusion:
      evaluated_under samevaluation_as premises

    RULE:
      validity_test_requires_search_forTRUE_premises_FALSE_conclusion
  }

  DESIGNATED_VALUE_MODEL {
    many_valued_logic:
      subset_oftruth_values_countedasdesignated

    classical:
      TRUE_designated

    RULE:
      designated != TRUE_bydefinition_acrossalllogics
  }

  UNDESIGNATED_VALUE_MODEL {
    many_valued_logic:
      truth_value_notdesignated

    classical:
      FALSE_undesignated

    RULE:
      designatedness_islogic_specific
  }

  BIVALENCE_MODEL {
    principle:
      everyproposition_hasexactlyoneofTRUE_orFALSE

    RULE:
      bivalence_isclassical_principle_notuniversal
  }

  EXCLUDED_MIDDLE_MODEL {
    formula:
      A OR NOT A

    classical_value:
      TRUE_underallvaluations

    RULE:
      status_differs_inintuitionistic_semantics
  }

  NONCONTRADICTION_MODEL {
    formula:
      NOT(A AND NOT A)

    classical_value:
      TRUE_underallvaluations
  }

  DOUBLE_NEGATION_MODEL {
    classical:
      truth_value_ofNOT_NOT_A_equals_truth_value_ofA
  }

  COMPLEMENT_MODEL {
    A:
      complement_truth_value_givenbynegation
  }

  TRUTH_ORDER_MODEL {
    Boolean_order:
      FALSE <= TRUE

    RULE:
      order_isalgebraic_structure_nottemporal_orprobabilistic_order
  }

  BOOLEAN_ALGEBRA_MODEL {
    carrier:
      {FALSE,TRUE}

    operations:
      AND
      OR
      NOT

    RULE:
      Boolean_algebra_representation_preserves_classical_truth_functions
  }

  MEET_MODEL {
    Boolean:
      A_meet_B = A_AND_B
  }

  JOIN_MODEL {
    Boolean:
      A_join_B = A_OR_B
  }

  COMPLEMENT_OPERATION_MODEL {
    Boolean:
      complement(A) = NOT_A
  }

  IDENTITY_ELEMENTS_MODEL {
    AND_identity:
      TRUE

    OR_identity:
      FALSE
  }

  ABSORBING_ELEMENTS_MODEL {
    AND_absorbing:
      FALSE

    OR_absorbing:
      TRUE
  }

  NUMERIC_DISTINCTION_MODEL {
    truth_value:
      semantic_logical_value

    number:
      arithmetic_entity

    RULE:
      TRUE_andFALSE_are_notnumbers_unlessencoded
  }

  PROBABILITY_DISTINCTION_MODEL {
    truth_value:
      value_underparticularvaluation_orworld

    probability:
      measure_ofuncertainty_orfrequency_overevents_orworlds

    RULE:
      probability_1 != TRUE_bysemantic_identity
      probability_0 != FALSE_bysemantic_identity
  }

  CONFIDENCE_DISTINCTION_MODEL {
    truth_value:
      logical_semantics

    confidence:
      degree_ofsupport_forclaim_orinterpretation

    RULE:
      confidence_0_to1 != truth_value
  }

  FUZZY_TRUTH_DISTINCTION_MODEL {
    fuzzy_truth:
      graded_value_in[0,1]_orotherlattice

    classical_truth:
      TRUE_orFALSE

    RULE:
      fuzzy_degree != probability
      fuzzy_degree != classical_truth_withoutthreshold_rule
  }

  MEMBERSHIP_DISTINCTION_MODEL {
    fuzzy_membership:
      degree_ofset_membership

    RULE:
      membership_degree != classical_truth_value_necessarily
  }

  DATABASE_NULL_DISTINCTION_MODEL {
    NULL:
      missing_orunknown_database_value

    RULE:
      NULL != FALSE
      SQL_three_valued_logic_requires_separate_semantics
  }

  PROGRAMMING_BOOLEAN_MODEL {
    Boolean:
      runtime_data_type_withtrue_false_values

    RULE:
      programming_boolean_correspondence_tological_truth_requiresdeclared_interpretation
  }

  BIT_MODEL {
    bit:
      0_or1_information_unit

    RULE:
      bit != truth_value_withoutencoding
  }

  DIGITAL_SIGNAL_MODEL {
    signal:
      physical_orabstract_low_high_state

    RULE:
      signal_level != truth_value_withoutlogic_encoding
  }

  SENSOR_STATE_DISTINCTION_MODEL {
    measurement:
      observed_state_orvalue

    logical_truth:
      semantic_evaluation_ofproposition_aboutmeasurement

    RULE:
      sensor_reading != truth_value
  }

  FACT_DISTINCTION_MODEL {
    fact:
      proposition_taken_orverified_astrue_aboutdomain

    truth_value:
      semantic_value

    RULE:
      truth_value_entity != proposition_itself
  }

  PROPOSITION_DISTINCTION_MODEL {
    proposition:
      truth_bearer

    truth_value:
      value_assigned_totruth_bearer

    RULE:
      proposition != truth_value
  }

  FORMULA_DISTINCTION_MODEL {
    formula:
      syntactic_expression

    truth_value:
      semantic_evaluation

    RULE:
      syntax != semantic_value
  }

  ASSERTION_DISTINCTION_MODEL {
    assertion:
      act_orrecord_ofclaimingproposition

    RULE:
      assertion != TRUE
  }

  BELIEF_DISTINCTION_MODEL {
    belief:
      agent_attitude_towardproposition

    RULE:
      belief != truth_value
  }

  KNOWLEDGE_DISTINCTION_MODEL {
    knowledge:
      epistemic_relation_orstate

    RULE:
      knowledge != truth_value
  }

  EVIDENCE_DISTINCTION_MODEL {
    evidence:
      supports_orunderminesproposition

    RULE:
      evidence_strength != truth_value
  }

  SOLVER_STATUS_DISTINCTION_MODEL {
    SAT:
      formula_hassatisfyingvaluation

    UNSAT:
      formula_hasnone

    UNKNOWN:
      solver_didnotdetermine

    RULE:
      SAT_UNSAT_UNKNOWN_areproblemstatuses_notformula_truth_values
  }

  SAT_ASSIGNMENT_MODEL {
    satisfying_valuation:
      formula_truth_value_TRUE

    RULE:
      assignment_iswitness_nottruth_value_entity
  }

  UNSAT_CERTIFICATE_MODEL {
    certificate:
      evidence_noTRUE_valuation_exists

    RULE:
      certificate != FALSE_truth_value
  }

  MODEL_CHECKER_STATUS_MODEL {
    possible:
      holds
      violated
      unknown

    RULE:
      status_must_be mapped_toformal property_semantics_beforetruth_value_assignment
  }

  THREE_VALUED_LOGIC_MODEL {
    truth_domain:
      three_values

    RULE:
      third_value_identity_andconnective_tables MUST be explicitlydefined
  }

  KLEENE_THREE_VALUED_MODEL {
    possible_values:
      TRUE
      UNKNOWN
      FALSE

    RULE:
      exact_strong_orweak_Kleene_semantics MUST be identified
  }

  LUKASIEWICZ_THREE_VALUED_MODEL {
    truth_domain:
      three_values

    RULE:
      connective_tables differ_fromKleene_logic
  }

  MANY_VALUED_LOGIC_MODEL {
    truth_domain:
      more_than_two_values

    RULE:
      truth_values_anddesignated_set MUST be explicit
  }

  FINITE_MANY_VALUED_MODEL {
    domain:
      finite_set_oftruth_values

    RULE:
      connective_truth_tables MAY be explicitlyenumerated
  }

  INFINITE_MANY_VALUED_MODEL {
    domain:
      infinite_orcontinuous_truth_values

    RULE:
      operations MUST be mathematicallydefined
  }

  INTUITIONISTIC_TRUTH_MODEL {
    semantics:
      oftenKripke_orproof_theoretic_notclassical_two_valued_truth_table

    RULE:
      classical_truth_table_equivalences MUST not_be assumed
  }

  PARACONSISTENT_TRUTH_MODEL {
    semantics:
      mayrepresentboth_true_andfalse_information_orothernonclassical states

    RULE:
      contradiction_doesnotnecessarilycauseexplosion
  }

  FOUR_VALUED_MODEL {
    possible_information_states:
      true_only
      false_only
      both
      neither

    RULE:
      exact_logic_anddesignated_values MUST be declared
  }

  MODAL_TRUTH_MODEL {
    formula_truth:
      mayberelative_toworld_inmodel

    RULE:
      world_identifier MUST be preserved
  }

  TEMPORAL_TRUTH_MODEL {
    formula_truth:
      mayberelative_totime_orstate

    RULE:
      temporal_index MUST be preserved
  }

  CONTEXTUAL_TRUTH_MODEL {
    truth:
      relative_todeclared_semantic_context_whenlogic_requires

    RULE:
      context_dependence != subjective_truth
  }

  WORLD_INDEX_MODEL {
    fields:
      model_identifier
      world_identifier

    RULE:
      modal_truth_value_withoutworld MAY be incomplete
  }

  TIME_INDEX_MODEL {
    fields:
      trace_identifier
      time_orstate_identifier

    RULE:
      temporal_truth_value_withoutindex MAY be incomplete
  }

  TRUTH_PERSISTENCE_MODEL {
    intuitionistic_Kripke:
      truth_maybemonotone_alongaccessibility

    RULE:
      property_islogic_specific
  }

  SUPERVALUATION_MODEL {
    partial_orvague_semantics:
      supertrue_iftrue_underalladmissible_precisifications
      superfalse_iffalse_underall

    RULE:
      supertruth != classical_truth_withoutsemantic_mapping
  }

  GAP_MODEL {
    truth_value_gap:
      proposition_receivesneitherclassical_TRUE_norFALSE_underparticularsemantics

    RULE:
      gap != unknown_computation
  }

  GLUT_MODEL {
    truth_value_glut:
      proposition_mayreceivebothtrue_andfalse_status

    RULE:
      glut_semantics requiresnonclassical_logic
  }

  TRUTH_VALUE_LATTICE_MODEL {
    truth_values:
      organised_byorder_orlattice

    RULE:
      ordering_semantics MUST be explicit
  }

  INFORMATION_ORDER_MODEL {
    values:
      ordered_byinformation_content

    RULE:
      information_order != truth_order
  }

  TRUTH_ORDER_DISTINCTION_MODEL {
    values:
      ordered_bydegree_orlogical_truth_relation

    RULE:
      multiple_orders MAY coexist_inbilattice
  }

  BILATTICE_MODEL {
    structure:
      truth_order
      knowledge_orinformation_order

    RULE:
      orders MUST be separatelyrepresented
  }

  DESIGNATEDNESS_MODEL {
    truth_value:
      maybedesignated_forvalidity

    RULE:
      validity_inmanyvaluedlogic oftenusesdesignatedness_not
necessarilysingle_TRUE
  }

  CLASSICAL_VALIDITY_LINK_MODEL {
    valid_formula:
      evaluates_TRUE_underallvaluations

    RULE:
      direct_TRUE_link_isclassical_specific
  }

  NONCLASSICAL_VALIDITY_LINK_MODEL {
    valid_formula:
      receivesdesignated_value_underallmodels_orvaluations_asdefined

    RULE:
      validity_rule MUST identifydesignated_values
  }

  TRUTH_PRESERVATION_MODEL {
    inference:
      preservesdesignated_truth_frompremises_toconclusion

    RULE:
      preservation_definition depends_onlogic
  }

  SEMANTIC_CONSEQUENCE_MODEL {
    relation:
      everymodel_wherepremises_designated_makesconclusion_designated

    RULE:
      classical_TRUE_preservation_isaspecial_case
  }

  TRUTH_VALUE_TRANSFORMATION_MODEL {
    source_logic:
      L1

    target_logic:
      L2

    mapping:
      truth_values_L1 -> truth_values_L2

    RULE:
      mapping MAY belossy_andmustdeclarepreservedproperties
  }

  BINARY_COLLAPSE_MODEL {
    many_valued_toBoolean:
      threshold_or designatedness_mapping

    RULE:
      collapse_isinterpretive_notidentity
  }

  THRESHOLD_MODEL {
    graded_value:
      mapped_toBoolean_usingthreshold

    RULE:
      threshold MUST be explicit
  }

  TRUTH_VALUE_SERIALISATION_MODEL {
    possible:
      TRUE_FALSE
      T_F
      1_0
      typed_JSON
      RDF_identifier

    RULE:
      serialisation MUST preservecanonical_truth_value_identifier
  }

  JSON_BOOLEAN_MODEL {
    values:
      true
      false

    RULE:
      JSON_boolean_isdata_representation_andrequiressemantic_mapping_tological_truth
  }

  RDF_LITERAL_MODEL {
    value:
      mayencodeBoolean

    RULE:
      datatype_andlexical_form MUST be preserved
  }

  ONTOLOGY_ASSERTION_MODEL {
    proposition:
      mayhaveasserted_truth_status

    RULE:
      assertion_status != formal_truth_value_withoutsemantic regime
  }

  OPEN_WORLD_DISTINCTION_MODEL {
    absent_statement:
      notknown_true

    RULE:
      absence_doesnotimplyFALSE
  }

  CLOSED_WORLD_DISTINCTION_MODEL {
    absent_statement:
      maybetreated_FALSE_underdeclared policy

    RULE:
      closed_world_assumption MUST be explicit
  }

  NEGATION_AS_FAILURE_MODEL {
    failure_toprove:
      mayyieldoperational_negation_inlogic_programming

    RULE:
      failure_toprove != classical_FALSE_withoutdeclared semantics
  }

  DEFAULT_REASONING_DISTINCTION_MODEL {
    default_conclusion:
      defeasible

    RULE:
      default_status != immutable_truth_value
  }

  REVISION_MODEL {
    assignment:
      maychange_whenvaluation_context_changes

    RULE:
      changed_assignment_doesnotmeantruth_value_definition_changed
  }

  IMMUTABILITY_MODEL {
    canonical_TRUE_FALSE:
      semantic identities_stable_withinlogic_version

    RULE:
      contextual_assignment_changes_areseparate
  }

  TRUTH_VALUE_PROVENANCE_MODEL {
    fields:
      source_formula
      valuation
      interpretation
      model
      computation
      solver
      logic_version
      agent

    RULE:
      computed_truth_value SHOULD retain_derivation_context
  }

  EXPLAINABILITY_MODEL {
    output:
      formula
      valuation
      subformula_values
      connective_operations
      final_truth_value

    RULE:
      explanation SHOULD expose_bottom_up_evaluation
  }

  COMPUTATION_TRACE_MODEL {
    nodes:
      subformulas

    values:
      truth_values

    RULE:
      trace MUST align_withAST
  }

  CACHING_MODEL {
    subformula_value:
      maybecached_forvaluation

    RULE:
      cache_key MUST includeformula_valuation_logic_version
  }

  TRUTH_VALUE_HASH_MODEL {
    input:
      canonical_truth_value_identifier
      logic_system
      version

    RULE:
      hash MUST notdepend_onlyondisplay_alias
  }

  AMBIGUITY_MODEL {
    possible:
      truth_domain_unspecified
      numeric_encoding_confusion
      unknown_vs_false_confusion
      fuzzy_vsprobability_confusion
      solver_status_confusion

    RULE:
      ambiguity MUST be resolved_orpreserved
  }

  SEMANTIC_CONFIDENCE_MODEL {
    confidence:
      support_fortruth_value_interpretation_orcomputed_assignment

    RULE:
      semantic_confidence != truth_value
  }

  VALIDATION_MODEL {
    checks:
      truth_domain
      logic_system
      canonical_value
      encoding
      valuation
      formula
      connective_semantics
      contextual_indices
      designatedness
      provenance

    RULE:
      validation MUST useexact_logic_semantics
  }

  INTEROPERABILITY_MODEL {
    exchange:
      canonical_truth_value_identifier
      logic_system
      truth_domain
      designated_status
      encoding
      valuation_context
      world_or time_index
      provenance

    RULE:
      bare_0_or1_isnotlossless_truth_value_exchange
  }

  KNOWLEDGE_GRAPH_MODEL {
    nodes:
      truth_value
      proposition
      formula
      valuation
      truth_domain
      logic_system

    edges:
      ASSIGNED_TO
      COMPUTED_FOR
      BELONGS_TO
      DESIGNATED_IN
      ENCODED_AS
      DERIVED_FROM

    RULE:
      semantic_value_andencoding_nodes MUST be distinguished
  }

  RELATIONSHIPS {
    TruthValue -> BELONGS_TO -> TruthDomain
    TruthDomain -> BELONGS_TO -> LogicSystem
    Valuation -> ASSIGNS -> TruthValue
    TruthValue -> MAY_EVALUATE -> Proposition
    Formula -> HAS_VALUE_UNDER -> Valuation
    TruthValue -> MAY_BE_ENCODED_AS -> BooleanOrSymbolicEncoding
    DesignatedValue -> IS_MEMBER_OF -> TruthDomain
  }

  SEMANTIC_EQUIVALENCE {
    "truth value" ~= semantic_value_assigned_toformula_orproposition_underdeclared_logic
    "classical truth value" ~= TRUE_orFALSE_underclassical_two_valued_semantics
    "valuation" ~= mapping_frompropositional_variables_totruth_values

    truth_value != proposition
    truth_value != formula
    TRUE != numeric_one_byidentity
    FALSE != numeric_zero_byidentity
    unassigned != FALSE
    unknown != FALSE
    probability != truth_value
    confidence != truth_value
    fuzzy_degree != classical_truth
    database_NULL != FALSE
    solver_status != truth_value
    designated_value != TRUE_bydefinition_acrossalllogics
    semantic_confidence != truth_value
  }

  CONSTRAINTS {
    truth_value_identifier_logic_system_anddomain_must_be preserved = true
    classical_truth_domain_must_contain_exactly_TRUE_andFALSE = true
    numeric_symbolic_anddata_encodings_must_be distinguished_fromsemantic_identity = true
    truth_value_assignments_must_preserve_valuation_orinterpretation_context = true
    unassigned_unknown_andFALSE_must_be distinguished = true
    proposition_formula_andtruth_value_must_be distinguished = true
    probability_confidence_fuzzy_membership_andtruth_value_must_be distinguished = true
    nonclassical_truth_domains_must_define_values_connectives_anddesignatedness = true
    modal_or temporal_truth_values_must_preserve_world_or time_index_whenrequired = true
    solver_statuses_must_not_be interpreted_astruth_values_withoutmapping = true
    open_world_absence_must_not_be interpreted_asFALSE = true
    semantic_confidence_must_not_be interpreted_astruth_value = true
    versions_andprovenance_must_be preserved = true
  }

  TRUTH_VALUE_RECORD_MODEL {
    RECORD:
      truth_value_identifier
      canonical_name
      logic_system_identifier
      logic_version
      truth_domain_identifier
      designated_status
      symbolic_aliases
      numeric_encoding
      data_encoding
      proposition_identifier
      formula_identifier
      valuation_identifier
      assignment_status
      world_identifier
      time_orstate_identifier
      computation_trace
      connective_semantics
      satisfiability_context
      validity_context
      solver_status
      confidence
      ambiguity_status
      version
      provenance

    RULE:
      truth_value_record MUST support_reconstruction_ofsemantic_domain_assignment_context_encoding_andprovenance
  }

  REASONING_RULES {
    IF truth_value_received
      THEN identify_logic_system_andtruth_domain
      resolvecanonical_value_andencoding

    IF classical_propositional_context
      THEN permitonlyTRUE_orFALSE_astruth_values
      whilepreservingUNASSIGNED_orUNKNOWN_asstatuses_nottruth_values

    IF formula_evaluation_requested
      THEN resolvevaluation
      evaluateAST_bottom_up
      preserve_subformula_trace

    IF partial_valuation
      AND formula_notdetermined
      THEN returnUNRESOLVED_status
      notFALSE

    IF validity_requested
      THEN evaluate_allvaluations_oruseequivalent_complete_method
      andrequireTRUE_foreveryvaluation_inclassical_context

    IF satisfiability_requested
      THEN requireatleastonevaluation_withTRUE

    IF nonclassical_logic_selected
      THEN loaddeclared_truth_domain_connective_operations_anddesignated_values
      anddo_notreuseclassicaltables_withoutbasis

    IF numeric_probability_confidence_fuzzy_orNULL_value_encountered
      THEN identifysemantic_type_beforemapping_totruth

    IF solver_returnsUNKNOWN_timeout_orresource_limit
      THEN preservecomputational_status
      anddo_notassignFALSE

    IF truth_domain_orlogic_version_changes
      THEN preservehistorical_truth_records
      andrecompute_current_semantics_onlyundernewversion
  }

  VALIDATION {
    CHECK truth_value_identifier
    CHECK canonical_name
    CHECK logic_system
    CHECK logic_version
    CHECK truth_domain
    CHECK designated_status
    CHECK symbolic_encoding
    CHECK numeric_encoding
    CHECK proposition_formula_distinction
    CHECK valuation
    CHECK assignment_status
    CHECK unassigned_unknown_false_distinction
    CHECK connective_truth_functions
    CHECK truth_table
    CHECK satisfiability
    CHECK validity
    CHECK world_index
    CHECK temporal_index
    CHECK nonclassical_semantics
    CHECK probability_confidence_fuzzy_distinctions
    CHECK solver_status
    CHECK ambiguity
    CHECK semantic_confidence
    CHECK version
    CHECK provenance
  }

  CONFIDENCE {
    classical_truth_semantics_confidence: 1.00
    valuation_confidence: 1.00
    truth_function_confidence: 1.00
    encoding_resolution_confidence: 0.99
    nonclassical_truth_domain_confidence: 0.98
    contextual_index_confidence: 0.99
    solver_status_distinction_confidence: 1.00
    provenance_confidence: 1.00

    RULE:
      confidence decreases when logic system, truth domain,
      valuation, encoding, designatedness, world or time context,
      version orprovenance is missing or ambiguous
  }

  UPDATE_MODEL {
    ON new_truth_value_record:
      resolve_logic_anddomain
      assigncanonical_identifier
      validateencoding
      attachcontext
      preserveprovenance
      compute_FLOW_HASH

    ON new_formula_evaluation:
      preserveformula_andvaluation
      compute_subformula_values
      attachfinal_truth_value
      storetrace

    ON new_nonclassical_domain:
      registertruth_values
      registerdesignated_set
      registerconnective_operations
      validateinternal_semantics

    ON encoding_revision:
      preserveprevious_mapping
      registernewencoding_version
      do_notchangecanonical_semantic_identity

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: TruthValue
    canonical_role: LogicalSemanticValue

    interpretation_order:
      identify_logic_system
      identify_truth_domain
      resolve_canonical_truth_value
      distinguish_semantic_value_fromencoding
      identify_proposition_orformula
      identify_valuation_orinterpretation_context
      resolve_assignment_status
      distinguishTRUE_FALSE_UNASSIGNED_andUNKNOWN
      evaluatecompound_formula_whenrequired
      preserve_truth_table_orcomputation_trace
      determine_satisfiability_orvalidity_context
      resolve_designatedness_innonclassical_logic
      preserve_world_or time_index_whenrequired
      distinguish_probability_confidence_fuzzy_NULL_andsolver_statuses
      detect_ambiguity
      assign_semantic_confidence
      preserve_versions_andprovenance
      emit_machine_resolvable_truth_value_structure

    ambiguity_controls:
      distinguish_truth_value_fromproposition
      distinguish_truth_value_fromformula
      distinguish_TRUE_fromnumeric_one_byidentity
      distinguish_FALSE_fromnumeric_zero_byidentity
      distinguish_unassigned_fromFALSE
      distinguish_unknown_fromFALSE
      distinguish_probability_fromtruth_value
      distinguish_confidence_fromtruth_value
      distinguish_fuzzy_degree_fromclassical_truth
      distinguish_database_NULL_fromFALSE
      distinguish_solver_status_fromtruth_value
      distinguish_designated_value_fromTRUE_bydefinition_acrossalllogics
      distinguish_semantic_confidence_fromtruth_value
      preserve_logic_domain_valuation_encoding_context_version_andprovenance
  }

  PROVENANCE {
    ontology_scope:
      truth_values_classical_semantics_valuations_nonclassical_domains_encodings_andAI_truth_interpretation

    parent_path:
      AI Core
      -> Ontologies
      -> Mathematical Ontologies
      -> Mathematical Logic Ontologies
      -> Propositional Logic
      -> Truth Value Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      truth_value_identity_model
      classical_truth_domain_model
      true_model
      false_model
      Boolean_encoding_model
      symbolic_encoding_model
      truth_constant_model
      proposition_truth_model
      formula_truth_model
      valuation_model
      valuation_context_model
      complete_valuation_model
      partial_valuation_model
      unassigned_state_model
      unknown_status_model
      indeterminate_distinction_model
      truth_function_model
      negation_truth_model
      conjunction_truth_model
      disjunction_truth_model
      XOR_truth_model
      implication_truth_model
      biconditional_truth_model
      NAND_truth_model
      NOR_truth_model
      truth_table_model
      truth_table_cell_model
      truth_vector_model
      semantic_equivalence_model
      tautology_model
      contradiction_model
      contingency_model
      satisfiability_model
      unsatisfiability_model
      validity_model
      falsifiability_model
      model_model
      countermodel_model
      entailment_model
      premise_truth_model
      conclusion_truth_model
      designated_value_model
      undesignated_value_model
      bivalence_model
      excluded_middle_model
      noncontradiction_model
      double_negation_model
      complement_model
      truth_order_model
      Boolean_algebra_model
      meet_model
      join_model
      complement_operation_model
      identity_elements_model
      absorbing_elements_model
      numeric_distinction_model
      probability_distinction_model
      confidence_distinction_model
      fuzzy_truth_distinction_model
      membership_distinction_model
      database_NULL_distinction_model
      programming_Boolean_model
      bit_model
      digital_signal_model
      sensor_state_distinction_model
      fact_distinction_model
      proposition_distinction_model
      formula_distinction_model
      assertion_distinction_model
      belief_distinction_model
      knowledge_distinction_model
      evidence_distinction_model
      solver_status_distinction_model
      SAT_assignment_model
      UNSAT_certificate_model
      model_checker_status_model
      three_valued_logic_model
      Kleene_three_valued_model
      Lukasiewicz_three_valued_model
      many_valued_logic_model
      finite_many_valued_model
      infinite_many_valued_model
      intuitionistic_truth_model
      paraconsistent_truth_model
      four_valued_model
      modal_truth_model
      temporal_truth_model
      contextual_truth_model
      world_index_model
      time_index_model
      truth_persistence_model
      supervaluation_model
      gap_model
      glut_model
      truth_value_lattice_model
      information_order_model
      truth_order_distinction_model
      bilattice_model
      designatedness_model
      classical_validity_link_model
      nonclassical_validity_link_model
      truth_preservation_model
      semantic_consequence_model
      truth_value_transformation_model
      binary_collapse_model
      threshold_model
      truth_value_serialisation_model
      JSON_Boolean_model
      RDF_literal_model
      ontology_assertion_model
      open_world_distinction_model
      closed_world_distinction_model
      negation_as_failure_model
      default_reasoning_distinction_model
      revision_model
      immutability_model
      truth_value_provenance_model
      explainability_model
      computation_trace_model
      caching_model
      truth_value_hash_model
      ambiguity_model
      semantic_confidence_model
      validation_model
      interoperability_model
      knowledge_graph_model
      relationships
      semantic_equivalence
      constraints
      truth_value_record_model
      reasoning_rules
      validation
      confidence_model
      update_model
      AI_consumption_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      truth_value_identity_logic_system_ordomain_changes
      classical_TRUE_FALSE_orencoding_semantics_change
      valuation_truth_function_truth_table_orsemantic_equivalence_changes
      satisfiability_validity_entailment_orcountermodel_semantics_change
      designatedness_many_valued_fuzzy_paraconsistent_orintuitionistic_semantics_change
      modal_temporal_world_orcontext_index_semantics_change
      probability_confidence_NULL_solver_status_oropen_world_distinctions_change
      truth_value_serialisation_interoperability_orprovenance_changes
      truth_value_record_changes
      constraint_model_changes
      reasoning_rule_changes
      version_changes
  }

}

END FLOW