Logic Ontology

# Logic Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/foundations-of-logic/logic-ontology.html

FLOW LogicOntology {

  DOMAIN:
    AI Core
    -> Ontologies
    -> Mathematical Ontologies
    -> Mathematical Logic Ontologies
    -> Foundations of Logic
    -> Logic Ontology

  PURPOSE:
    Represent logic as a machine-interpretable framework for statements, propositions, truth values, logical operators, predicates, variables, quantifiers, premises, conclusions, arguments, inference rules, validity, satisfiability, contradiction, consistency, proof and semantic interpretation. The ontology provides a foundational reasoning layer through which AI systems can identify logical form, distinguish syntax from semantics, evaluate truth under declared interpretations, test arguments, construct or verify deductions, identify counterexamples and contradictions, preserve assumptions and scope, and separate formal logical consequence from causal, probabilistic, inductive or heuristic reasoning.

  ENTITY Logic {
    TYPE: FormalReasoningFramework

    PROPERTIES:
      has_language
      has_expressions
      has_propositions
      has_truth_values
      has_connectives
      has_predicates
      has_variables
      has_quantifiers
      has_arguments
      has_inference_rules
      has_models
      has_proofs
      supports_validity
      supports_satisfiability
      supports_contradiction_detection
  }

  ENTITY LogicalEntity {
    POSSIBLE:
      symbol
      term
      formula
      proposition
      predicate
      variable
      connective
      quantifier
      premise
      conclusion
      inference_rule
      proof
      model
  }

  ENTITY LogicalExpression {
    TYPE: StructuredSymbolicExpression

    COMPONENTS:
      symbols
      operators
      operands
      scope
      binding
  }

  ENTITY LogicalArgument {
    TYPE: PremiseConclusionStructure

    COMPONENTS:
      premises
      conclusion
      inference_context
  }

  FORMAL_LANGUAGE_MODEL {
    components:
      alphabet
      vocabulary
      syntax
      formation_rules

    RULE:
      language_andlogic_system MUST be identifiable
  }

  SYMBOL_MODEL {
    possible:
      logical
      nonlogical
      variable
      punctuation

    RULE:
      symbol != semantic_entity
  }

  TERM_MODEL {
    possible:
      variable
      constant
      function_application

    RULE:
      term != truth_evaluable_formula
  }

  FORMULA_MODEL {
    possible:
      atomic
      compound
      quantified

    RULE:
      formula MUST satisfy_declared_formation_rules
  }

  WELL_FORMEDNESS_MODEL {
    expression:
      well_formed_ifgrammar_andbinding_rules_satisfied

    RULE:
      well_formedness != truth
  }

  SYNTAX_MODEL {
    concerns:
      symbol_order
      grammar
      parse_structure
      binding
      scope

    RULE:
      syntax != semantics
  }

  SEMANTICS_MODEL {
    concerns:
      meaning
      interpretation
      truth
      satisfaction
      models

    RULE:
      semantics != syntax
  }

  PARSE_TREE_MODEL {
    expression:
      represented_asabstract_syntax_tree

    RULE:
      precedence_associativity_andparentheses MUST be preserved
  }

  PROPOSITION_MODEL {
    entity:
      truth_evaluable_content

    RULE:
      proposition != sentence_string_orformula_token
  }

  TRUTH_VALUE_MODEL {
    classical:
      true
      false

    RULE:
      truth_value_set depends_onlogic
  }

  TRUTH_MODEL {
    proposition_orformula:
      true_relative_tointerpretation_orvaluation

    RULE:
      truth != provability
  }

  FALSEHOOD_MODEL {
    proposition_orformula:
      false_relative_tointerpretation_orvaluation

    RULE:
      false_inone_interpretation != contradiction
  }

  BIVALENCE_MODEL {
    classical:
      every_proposition_hasone_oftrue_orfalse

    RULE:
      bivalence_notuniversal_acrossalllogics
  }

  CONNECTIVE_MODEL {
    possible:
      NOT
      AND
      OR
      IMPLIES
      IFF
      XOR

    RULE:
      connective_semantics MUST be declared
  }

  NEGATION_MODEL {
    form:
      NOT A

    classical:
      true_when_A_false
  }

  CONJUNCTION_MODEL {
    form:
      A AND B

    classical:
      true_when_A_true_andB_true
  }

  DISJUNCTION_MODEL {
    form:
      A OR B

    classical:
      inclusive_OR
  }

  EXCLUSIVE_OR_MODEL {
    form:
      A XOR B

    classical:
      true_when_exactly_one_true
  }

  IMPLICATION_MODEL {
    form:
      A -> B

    classical_material:
      equivalent_to
        NOT A OR B

    RULE:
      logical_implication != causation
  }

  BICONDITIONAL_MODEL {
    form:
      A <-> B

    classical:
      true_when_A_andB_same_truth_value
  }

  TRUTH_FUNCTION_MODEL {
    connective:
      maps_operand_truth_values_toresult

    RULE:
      truth_functionality_islogic_specific
  }

  TRUTH_TABLE_MODEL {
    rows:
      valuations

    columns:
      propositions_andcompound_formulas

    RULE:
      useful_forfinite_truth_functional_logic
  }

  VALUATION_MODEL {
    mapping:
      propositional_atoms -> truth_values

    RULE:
      valuation_context MUST be preserved
  }

  TAUTOLOGY_MODEL {
    formula:
      true_underallrelevant_valuations

    RULE:
      tautology != empirically_true_statement
  }

  CONTRADICTION_MODEL {
    formula:
      false_underallrelevant_valuations

    RULE:
      contradiction != merely_false_statement
  }

  CONTINGENCY_MODEL {
    formula:
      true_undersome_valuations
      false_underothers
  }

  LOGICAL_EQUIVALENCE_MODEL {
    A equivalent B

    condition:
      same_semantic_value_underallrelevant_interpretations

    RULE:
      equivalence != syntactic_identity
  }

  DE_MORGAN_MODEL {
    classical:
      NOT(A AND B) equivalent (NOT A OR NOT B)
      NOT(A OR B) equivalent (NOT A AND NOT B)
  }

  DOUBLE_NEGATION_MODEL {
    classical:
      NOT NOT A equivalent A

    RULE:
      elimination_depends_onlogic
  }

  COMMUTATIVITY_MODEL {
    A AND B equivalent B AND A
    A OR B equivalent B OR A
  }

  ASSOCIATIVITY_MODEL {
    (A AND B) AND C equivalent A AND (B AND C)
    (A OR B) OR C equivalent A OR (B OR C)
  }

  DISTRIBUTIVITY_MODEL {
    A AND (B OR C)
      equivalent
      (A AND B) OR (A AND C)

    A OR (B AND C)
      equivalent
      (A OR B) AND (A OR C)
  }

  PREDICATE_MODEL {
    form:
      P(x_1,...,x_n)

    RULE:
      predicate_requires_arguments_andinterpretation
  }

  VARIABLE_MODEL {
    possible:
      free
      bound

    RULE:
      variable_status_depends_onquantifier_scope
  }

  FREE_VARIABLE_MODEL {
    occurrence:
      not_bound

    RULE:
      evaluation_may_requireassignment
  }

  BOUND_VARIABLE_MODEL {
    occurrence:
      bound_byquantifier

    RULE:
      bound_variable_name_isnotsemantic_identity
  }

  DOMAIN_MODEL {
    set_oruniverse:
      objects_overwhichvariables_range

    RULE:
      domain_changes_can_change_truth
  }

  QUANTIFIER_MODEL {
    possible:
      universal
      existential

    RULE:
      scope_anddomain MUST be preserved
  }

  UNIVERSAL_MODEL {
    form:
      forall x P(x)

    meaning:
      P_holds_foreveryx_indomain
  }

  EXISTENTIAL_MODEL {
    form:
      exists x P(x)

    meaning:
      P_holds_foratleast_onex_indomain
  }

  UNIQUE_EXISTENCE_MODEL {
    meaning:
      exactly_one_object_satisfiespredicate

    RULE:
      existence_anduniqueness_areseparate_requirements
  }

  QUANTIFIER_SCOPE_MODEL {
    binder:
      controls_occurrences_ofvariable

    RULE:
      scope_ambiguity_can_change_logical_form
  }

  QUANTIFIER_ORDER_MODEL {
    compare:
      forall x exists y R(x,y)
      exists y forall x R(x,y)

    RULE:
      order_is_semantically_material
  }

  INTERPRETATION_MODEL {
    assigns:
      constants -> objects
      functions -> functions
      predicates -> relations

    RULE:
      interpretation MUST respect_language_signature
  }

  ASSIGNMENT_MODEL {
    maps:
      free_variables -> domain_objects

    RULE:
      assignment_notrequired_forclosed_sentence_truth
  }

  SATISFACTION_MODEL {
    relation:
      model_orinterpretation satisfies formula

    RULE:
      satisfaction != derivation
  }

  MODEL_MODEL {
    structure:
      gives_semantics_toformal_language

    RULE:
      logical_model != physical_orcomputational_simulation
  }

  COUNTERMODEL_MODEL {
    model:
      makes_candidate_valid_formula_false
      orpremises_true_conclusion_false

    RULE:
      valid_countermodel_refutes_semantic_validity
  }

  SATISFIABILITY_MODEL {
    formula:
      satisfiable_ifatleast_one_model_makes_true

    RULE:
      satisfiable != valid
  }

  UNSATISFIABILITY_MODEL {
    formula_orformula_set:
      no_satisfying_model
  }

  VALIDITY_MODEL {
    formula:
      true_underallmodels_ofdeclared_logic

    RULE:
      validity != truth_inparticular_interpretation
  }

  SEMANTIC_CONSEQUENCE_MODEL {
    premises:
      Gamma

    conclusion:
      C

    condition:
      every_model_satisfying_Gamma_satisfies_C

    notation:
      Gamma entails C
  }

  PREMISE_MODEL {
    statement:
      supplied_asbasis_forargument

    RULE:
      premise != axiom_necessarily
  }

  CONCLUSION_MODEL {
    statement:
      claimed_to_follow_frompremises

    RULE:
      conclusion_truth_andargument_validity_areseparate_questions
  }

  ARGUMENT_MODEL {
    structure:
      premises
      conclusion

    RULE:
      argument != formal_proof
  }

  VALID_ARGUMENT_MODEL {
    condition:
      impossible_forpremises_alltrue_andconclusion_false_underdeclared_semantics
  }

  INVALID_ARGUMENT_MODEL {
    witness:
      countermodel_orvaluation
  }

  SOUND_ARGUMENT_MODEL {
    requirements:
      valid
      premises_true_underintended_interpretation

    RULE:
      soundness_ofargument != soundness_ofproof_system
  }

  DEDUCTION_MODEL {
    reasoning:
      conclusion_formally_orsemantically_necessitated_bypremises

    RULE:
      deduction != induction
  }

  INDUCTION_DISTINCTION_MODEL {
    reasoning:
      premises_support_conclusion_withoutformal_entailment

    RULE:
      inductive_strength != deductive_validity
  }

  ABDUCTION_DISTINCTION_MODEL {
    reasoning:
      infer_candidate_explanation

    RULE:
      explanatory_plausibility != logical_consequence
  }

  INFERENCE_RULE_MODEL {
    premises:
      zero_or more_formulas

    conclusion:
      formula

    RULE:
      application MUST satisfy_rule_conditions
  }

  MODUS_PONENS_MODEL {
    A
    A -> B
    therefore B
  }

  MODUS_TOLLENS_MODEL {
    A -> B
    NOT B
    therefore NOT A
  }

  HYPOTHETICAL_SYLLOGISM_MODEL {
    A -> B
    B -> C
    therefore A -> C
  }

  DISJUNCTIVE_SYLLOGISM_MODEL {
    A OR B
    NOT A
    therefore B

    RULE:
      classical_semantics_assumed
  }

  FALLACY_MODEL {
    entity:
      invalid_inference_pattern

    RULE:
      invalidity_requires_logical_analysis_notrhetorical_judgment
  }

  AFFIRMING_CONSEQUENT_MODEL {
    invalid_pattern:
      A -> B
      B
      therefore A
  }

  DENYING_ANTECEDENT_MODEL {
    invalid_pattern:
      A -> B
      NOT A
      therefore NOT B
  }

  AXIOM_MODEL {
    statement:
      adopted_asformal_starting_point

    RULE:
      axiom_status_isrelative_toformal_system
  }

  ASSUMPTION_MODEL {
    statement:
      temporarily_orcontextually_used

    RULE:
      assumption_scope MUST be preserved
  }

  PROOF_MODEL {
    derivation:
      sequence_orgraph_ofjustified_formulas

    RULE:
      every_nonpremise_step MUST cite_valid_rule_orprior_result
  }

  PROOF_STEP_MODEL {
    fields:
      formula
      rule
      dependencies
      assumptions
  }

  THEOREM_MODEL {
    formula:
      formally_derivable_fromaxioms_orpremises

    RULE:
      theoremhood != semantic_truth_bydefinition
  }

  LEMMA_MODEL {
    theorem:
      intermediate_supporting_result
  }

  COROLLARY_MODEL {
    theorem:
      follows_fromprevious_result
  }

  SYNTACTIC_DERIVABILITY_MODEL {
    notation:
      Gamma proves C

    RULE:
      derivability != semantic_consequence_bydefinition
  }

  SOUNDNESS_MODEL {
    proof_system:
      derivability_implies_semantic_consequence

    RULE:
      soundness != completeness
  }

  COMPLETENESS_MODEL {
    proof_system:
      semantic_consequence_implies_derivability

    RULE:
      completeness_isrelative_tologic_andproof_system
  }

  CONSISTENCY_MODEL {
    theory:
      does_notderive_formal_contradiction

    RULE:
      consistency != completeness
  }

  INCONSISTENCY_MODEL {
    theory:
      derives_contradiction

    RULE:
      effect_depends_onlogic
  }

  EXPLOSION_MODEL {
    classical:
      contradiction_can_support_arbitrary_conclusion

    RULE:
      notvalid_inallparaconsistent_systems
  }

  INDEPENDENCE_MODEL {
    proposition:
      neither_it_noritsnegation_derivable_fromtheory

    RULE:
      independence_relative_totheory
  }

  OBJECT_LANGUAGE_MODEL {
    language:
      being_reasoned_withorabout

    RULE:
      object_language != metalanguage
  }

  METALANGUAGE_MODEL {
    language:
      used_to describe_object_language

    RULE:
      levels MUST be distinguished_toavoidsemantic_confusion
  }

  USE_MENTION_MODEL {
    use:
-
      expression_used_withmeaning

    mention:
-
      expression_referred_toassymbolic_object

    RULE:
      use != mention
  }

  CLASSICAL_LOGIC_MODEL {
    typical:
      bivalence
      excluded_middle
      noncontradiction
      material_implication

    RULE:
      classical_assumptions MUST be explicit_whencontrasted_withnonclassical_logic
  }

  NONCLASSICAL_LOGIC_MODEL {
    possible:
      intuitionistic
      paraconsistent
      many_valued
      fuzzy
      modal
      temporal

    RULE:
      classical_rules MUST not_be assumed_universally
  }

  INTUITIONISTIC_MODEL {
    emphasis:
      constructive_proof

    RULE:
      excluded_middle_notgenerally_unrestricted
  }

  PARACONSISTENT_MODEL {
    emphasis:
      reasoning_withoutunrestricted_explosion

    RULE:
      contradiction_does_notautomatically_entail_everything
  }

  MANY_VALUED_MODEL {
    truth_domain:
      more_than_two_values

    RULE:
      connective_semantics MUST be specified
  }

  FUZZY_LOGIC_MODEL {
    truth_degree:
      graded_value

    RULE:
      fuzzy_truth_degree != probability
  }

  MODAL_LOGIC_MODEL {
    adds:
      necessity
      possibility

    RULE:
      modal_semantics_requires_declared_world_oralgebraic_structure
  }

  TEMPORAL_LOGIC_MODEL {
    adds:
      time_sensitive_operators

    RULE:
      temporal_structure MUST be explicit
  }

  NORMAL_FORM_MODEL {
    possible:
      CNF
      DNF

    RULE:
      transformation_type MUST state_equivalence_orsatisfiability_preservation
  }

  CNF_MODEL {
    structure:
      conjunction_ofclauses
  }

  DNF_MODEL {
    structure:
      disjunction_ofconjunctions
  }

  LITERAL_MODEL {
    possible:
      atom
      negated_atom
  }

  CLAUSE_MODEL {
    structure:
      disjunction_ofliterals
  }

  RESOLUTION_MODEL {
    process:
      derive_resolvent_fromclauses_withcomplementary_literals

    RULE:
      resolution_system_andunification_context MUST be specified
  }

  CONTRADICTION_DETECTION_MODEL {
    inputs:
      formula_set

    output:
      contradiction_found
      not_found_undersearch
      unknown

    RULE:
      failure_to_detect != consistency_proof_withoutcomplete_method
  }

  PROOF_SEARCH_MODEL {
    process:
      search_forformal_derivation

    RULE:
      search_failure_or timeout != unprovability
  }

  MODEL_SEARCH_MODEL {
    process:
      search_forinterpretation_satisfying_formula

    RULE:
      bounded_search_failure != unsatisfiability
  }

  AUTOMATED_REASONING_MODEL {
    possible:
      theorem_proving
      SAT_solving
      SMT_solving
      model_checking
      proof_checking

    RULE:
      solver_status MUST be preserved
  }

  SAT_MODEL {
    input:
      propositional_formula

    output:
      satisfying_assignment
      unsatisfiable
      unknown_whenapplicable
  }

  SMT_MODEL {
    input:
      formula_modulo_background_theory

    RULE:
      theory_fragment MUST be identified
  }

  PROOF_CHECKING_MODEL {
    input:
      proof_object

    RULE:
      proof_checker_kernel_andversion MUST be preserved
  }

  COUNTEREXAMPLE_MODEL {
    witness:
      violates_claim_orargument_validity

    RULE:
      counterexample MUST satisfydeclared_domain_andpremises
  }

  DECIDABILITY_MODEL {
    problem:
      decidable_ifcorrect_halting_algorithm_exists_forallinputs

    RULE:
      decidability != tractability
  }

  COMPUTABILITY_DISTINCTION_MODEL {
    computable:
      algorithmically_calculable_underformal_model

    RULE:
      computability != practical_feasibility
  }

  MONOTONIC_REASONING_MODEL {
    property:
      adding_premises_does_notinvalidate_existing_conclusions

    RULE:
      classical_deductive_logic_isnormally_monotonic
  }

  NONMON
  OTONIC_REASONING_MODEL {
    property:
      new_information_can_retract_previous_conclusion

    RULE:
      retraction_policy MUST be explicit
  }

  OPEN_WORLD_MODEL {
    principle:
      absence_ofclaim_does_notimplynegation

    RULE:
      open_world != closed_world
  }

  CLOSED_WORLD_MODEL {
    principle:
      underdeclared_context_absence_may_be treated_asfalse

    RULE:
      assumption MUST be explicit
  }

  SEMANTIC_EQUIVALENCE_MODEL {
    formulas:
      same_truth_conditions_underdeclared_semantics

    RULE:
      semantic_equivalence != syntactic_similarity
  }

  LOGICAL_IDENTITY_MODEL {
    entity:
      same_logical_object_underformal_identity_relation

    RULE:
      identity != equivalence
  }

  CONTRADICTION_VS_CONTRARY_MODEL {
    contradiction:
      cannot_bothbetrue_andcannot_bothbefalse_underbinary_opposition

    contrary:
      cannot_bothbetrue_butmay_bothbefalse

    RULE:
      relation_type MUST be explicit
  }

  NECESSARY_SUFFICIENT_MODEL {
    A_sufficient_for_B:
      A -> B

    B_necessary_for_A:
      A -> B

    RULE:
      linguistic_direction MUST be resolved_carefully
  }

  CONDITION_MODEL {
    antecedent:
      condition

    consequent:
      result_inconditional_statement

    RULE:
      conditional_relation_notnecessarilycausal
  }

  META_LOGICAL_MODEL {
    properties:
      consistency
      soundness
      completeness
      decidability

    RULE:
      properties_apply_toformal systems_or theories_underdeclared_context
  }

  AMBIGUITY_MODEL {
    causes:
      overloaded_symbol
      scope
      implicit_domain
      unspecified_logic
      natural_language_structure

    RULE:
      unresolved_ambiguity MUST be preserved
  }

  NATURAL_LANGUAGE_LOGIC_MODEL {
    input:
      sentence_orargument

    process:
      identify_claims
      quantifiers
      negation
      conditionals
      scope
      premises
      conclusion

    RULE:
      natural_language_toformal_logic_mapping_isinterpretive_andmustretainconfidence
  }

  SEMANTIC_CONFIDENCE_MODEL {
    confidence:
      support_forformalisation_orinterpretation

    RULE:
      semantic_confidence != truth_value
  }

  AI_LOGIC_MODEL {
    AI:
      parse
      formalise
      validate
      evaluate
      infer
      search
      explain

    RULE:
      AI_must_distinguish_formal_proof_fromplausible_reasoning
  }

  HEURISTIC_REASONING_MODEL {
    heuristic:
      guides_search_orformalisation

    RULE:
      heuristic_output_requires_formal_validation_forformal_claim
  }

  EXPLAINABILITY_MODEL {
    output:
      source
      formalisation
      assumptions
      premises
      conclusion
      rules
      proof_orcountermodel
      ambiguity
      confidence

    RULE:
      explanation MUST expose_inferred_formalisation
  }

  DEPENDENCY_MODEL {
    result:
      depends_on
        definitions
        premises
        axioms
        rules
        logic_system

    RULE:
      dependency_changes SHOULD trigger_revalidation
  }

  RECURSIVE_REASONING_MODEL {
    cycle:
      parse
      formalise
      validate
      infer
      test
      revise

    RULE:
      recursion MUST preserve_previous_states_andprovenance
  }

  VERSION_MODEL {
    versioned:
      logic_system
      formal_language
      axiom_set
      proof_rules
      formalisation
      ontology

    RULE:
      historical_reasoning MUST preserveversions
  }

  PROVENANCE_MODEL {
    fields:
      source
      formalisation
      logic_system
      premises
      axioms
      rules
      proof
      model
      solver
      version
      agent

    RULE:
      logical_result MUST remain_provenance_linked
  }

  VALIDATION_MODEL {
    checks:
      language
      syntax
      scope
      binding
      semantics
      interpretation
      argument_structure
      inference_rules
      proof
      model
      logic_system
      version

    RULE:
      validation MUST be logic_specific
  }

  INTEROPERABILITY_MODEL {
    exchange:
      formal_expressions
      parse_trees
      logical_entities
      proof_objects
      model_objects
      semantic_identifiers

    RULE:
-
      expression_text_withoutlogic_context MAY be semantically_incomplete
  }

  KNOWLEDGE_GRAPH_MODEL {
    nodes:
      logical_expression
      proposition
      predicate
      premise
      conclusion
      inference_rule
      proof
      model
      theory

    edges:
      CONTAINS
      BINDS
      IMPLIES
      ENTAILS
      DERIVES
      SATISFIES
      REFUTES
      DEPENDS_ON
      EQUIVALENT_TO

    RULE:
      edges MUST distinguish_semantic_fromsyntactic_relations
  }

  RELATIONSHIPS {
    Logic -> DEFINES -> LogicalEntity
    LogicalExpression -> HAS -> ParseTree
    Formula -> MAY_EXPRESS -> Proposition
    Predicate -> APPLIES_TO -> Terms
    Quantifier -> BINDS -> Variable
    Argument -> HAS_PREMISE -> Proposition
    Argument -> HAS_CONCLUSION -> Proposition
    Proof -> USES -> InferenceRule
    Model -> SATISFIES -> Formula
    Countermodel -> REFUTES -> ValidityClaim
    Theory -> MAY_DERIVE -> Theorem
  }

  SEMANTIC_EQUIVALENCE {
    "logic" ~= formal_study_ofvalid_reasoning_andlogical_structure
    "logical argument" ~= premises_plusconclusion_underreasoning_relation
    "logical validity" ~= impossibility_oftruepremises_withfalseconclusion_underdeclared_semantics

    symbol != semantic_entity
    term != formula
    proposition != sentence_string
    syntax != semantics
    well_formedness != truth
    falsehood != contradiction
    satisfiability != validity
    validity != truth_inone_interpretation
    implication != causation
    argument != proof
    consistency != completeness
    semantic_confidence != truth_value
  }

  CONSTRAINTS {
    logic_system_should_be identified = true
    formal_language_andexpression_structure_must_be preserved = true
    syntax_andsemantics_must_be distinguished = true
    proposition_formula_andterm_semantics_must_be distinguished = true
    variable_binding_andquantifier_scope_must_be preserved = true
    implication_must_not_be interpreted_ascausation = true
    argument_validity_andpremise_truth_must_be distinguished = true
    satisfiability_validity_truth_andprovability_must_be distinguished = true
    formal_proof_steps_must_havejustification = true
    consistency_soundness_andcompleteness_must_be distinguished = true
    nonclassical_logic_must_notinherit_classical_rules_withoutbasis = true
    unresolved_ambiguity_must_be preserved = true
    AI_heuristic_reasoning_must_not_be represented_asformal_proof_withoutvalidation = true
    versions_andprovenance_must_be preserved = true
  }

  LOGIC_RECORD_MODEL {
    RECORD:
      logic_identifier
      language_identifier
      logic_system
      source_expression
      formal_expression
      expression_type
      syntax_tree
      propositions
      predicates
      terms
      variables
      free_variables
      bound_variables
      quantifiers
      connective_structure
      domain
      interpretation
      assignment
      truth_value
      premises
      conclusion
      inference_rules
      argument_validity
      model_identifier
      countermodel_identifier
      satisfiability_status
      validity_status
      proof_identifier
      proof_steps
      theorem_identifier
      consistency_status
      soundness_context
      completeness_context
      ambiguity_status
      semantic_confidence
      version
      provenance

    RULE:
      logic_record MUST remain_linked_tosource_formalisation_logic_semantics_reasoning_andprovenance
  }

  REASONING_RULES {
    IF logical_expression_received
      THEN identify_language_andlogic
      parse_structure
      classify_entities

    IF natural_language_argument_received
      THEN identify_premises_andconclusion
      generate_candidate_formalisation
      preserve_interpretive_confidence

    IF variables_orquantifiers_present
      THEN resolve_domain_binding_andscope

    IF truth_evaluation_requested
      THEN require_valuation_orinterpretation

    IF argument_validity_requested
      THEN search_forcountermodel_withtruepremises_falseconclusion

    IF satisfiability_requested
      THEN search_foratleastone_model
      andpreserve_unknown_whenmethod_incomplete

    IF proof_claimed
      THEN verify_each_step_againstpremises_axioms_andrules

    IF contradiction_detected
      THEN identify_logic_system_beforepropagatingconsequences

    IF nonclassical_logic_selected
      THEN use_logic_specific_connective_truth_andinference_semantics

    IF AI_generates_reasoning
      THEN distinguish_formal_steps_fromheuristic_steps
      andvalidate_formal_claims

    IF dependency_changes
      THEN recursively_revalidate_affected_results
  }

  VALIDATION {
    CHECK logic_identifier
    CHECK language
    CHECK logic_system
    CHECK expression_type
    CHECK syntax_tree
    CHECK well_formedness
    CHECK proposition_term_formula_distinctions
    CHECK variables_andbinding
    CHECK quantifier_scope
    CHECK connectives
    CHECK domain
    CHECK interpretation
    CHECK truth_value
    CHECK premises
    CHECK conclusion
    CHECK argument_validity
    CHECK inference_rules
    CHECK model_orcountermodel
    CHECK satisfiability
    CHECK proof_steps
    CHECK consistency
    CHECK soundness_andcompleteness_context
    CHECK nonclassical_semantics
    CHECK ambiguity
    CHECK semantic_confidence
    CHECK version
    CHECK provenance
  }

  CONFIDENCE {
    formalisation_confidence: 0.99
    syntax_confidence: 1.00
    propositional_semantics_confidence: 1.00
    predicate_quantifier_confidence: 1.00
    argument_validity_confidence: 1.00
    proof_validation_confidence: 1.00
    nonclassical_logic_confidence: 0.99
    natural_language_logic_confidence: 0.97

    RULE:
      confidence decreases when language, logic system, scope,
      domain, interpretation, formalisation, proof rules,
      version orprovenance is missing or ambiguous
  }

  UPDATE_MODEL {
    ON new_logic_record:
      identify_source
      parse_andformalise
      resolve_logic_system
      validate
      attach_semantics
      preserve_provenance
      compute_FLOW_HASH

    ON new_evidence_orinterpretation:
      preserve_previous_formalisation
      add_evidence
      recompute_ambiguity_andconfidence
      revalidate

    ON proof_revision:
      preserve_previous_proof
      update_steps_orrules
      recursively_validate_dependencies

    ON logic_system_revision:
      preserve_previous_logic_version
      register_new_semantics
      identify_affected_results
      do_not_overwrite_historical_reasoning

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Logic
    canonical_role: FormalReasoningFramework

    interpretation_order:
      identify_source_expression
      identify_formal_language
      identify_logic_system
      parse_logical_structure
      resolve_propositions_predicates_terms_andvariables
      resolve_connectives_quantifiers_scope_anddomain
      distinguish_syntax_fromsemantics
      resolve_interpretation_andtruth_context
      identify_premises_andconclusion
      distinguish_deduction_induction_andabduction
      test_argument_validity
      test_satisfiability_orvalidity_whenrequested
      verify_proof_orsearch_countermodel
      distinguish_consistency_soundness_andcompleteness
      resolve_nonclassical_semantics_whenrequired
      detect_contradiction_fallacy_orambiguity
      distinguish_formal_fromheuristic_AI_reasoning
      assign_semantic_confidence
      preserve_versions_andprovenance
      emit_machine_resolvable_logic_structure

    ambiguity_controls:
      distinguish_symbol_fromsemantic_entity
      distinguish_term_fromformula
      distinguish_proposition_fromsentence_string
      distinguish_syntax_fromsemantics
      distinguish_well_formedness_fromtruth
      distinguish_falsehood_fromcontradiction
      distinguish_satisfiability_fromvalidity
      distinguish_validity_fromtruth_inone_interpretation
      distinguish_implication_fromcausation
      distinguish_argument_fromproof
      distinguish_consistency_fromcompleteness
      distinguish_semantic_confidence_fromtruth_value
      preserve_source_formalisation_logic_scope_semantics_proof_version_andprovenance
  }

  PROVENANCE {
    ontology_scope:
      logic_foundational_reasoning_truth_arguments_inference_andformal_semantics

    parent_path:
      AI Core
      -> Ontologies
      -> Mathematical Ontologies
      -> Mathematical Logic Ontologies
      -> Foundations of Logic
      -> Logic Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      formal_language_model
      symbol_model
      term_model
      formula_model
      well_formedness_model
      syntax_model
      semantics_model
      parse_tree_model
      proposition_model
      truth_value_model
      truth_model
      falsehood_model
      bivalence_model
      connective_model
      negation_model
      conjunction_model
      disjunction_model
      exclusive_OR_model
      implication_model
      biconditional_model
      truth_function_model
      truth_table_model
      valuation_model
      tautology_model
      contradiction_model
      contingency_model
      logical_equivalence_model
      De_Morgan_model
      double_negation_model
      commutativity_model
      associativity_model
      distributivity_model
      predicate_model
      variable_model
      free_variable_model
      bound_variable_model
      domain_model
      quantifier_model
      universal_model
      existential_model
      unique_existence_model
      quantifier_scope_model
      quantifier_order_model
      interpretation_model
      assignment_model
      satisfaction_model
      model_model
      countermodel_model
      satisfiability_model
      unsatisfiability_model
      validity_model
      semantic_consequence_model
      premise_model
      conclusion_model
      argument_model
      valid_argument_model
      invalid_argument_model
      sound_argument_model
      deduction_model
      induction_distinction_model
      abduction_distinction_model
      inference_rule_model
      modus_ponens_model
      modus_tollens_model
      hypothetical_syllogism_model
      disjunctive_syllogism_model
      fallacy_model
      affirming_consequent_model
      denying_antecedent_model
      axiom_model
      assumption_model
      proof_model
      proof_step_model
      theorem_model
      lemma_model
      corollary_model
      syntactic_derivability_model
      soundness_model
      completeness_model
      consistency_model
      inconsistency_model
      explosion_model
      independence_model
      object_language_model
      metalanguage_model
      use_mention_model
      classical_logic_model
      nonclassical_logic_model
      intuitionistic_model
      paraconsistent_model
      many_valued_model
      fuzzy_logic_model
      modal_logic_model
      temporal_logic_model
      normal_form_model
      CNF_model
      DNF_model
      literal_model
      clause_model
      resolution_model
      contradiction_detection_model
      proof_search_model
      model_search_model
      automated_reasoning_model
      SAT_model
      SMT_model
      proof_checking_model
      counterexample_model
      decidability_model
      computability_distinction_model
      monotonic_reasoning_model
      nonmonotonic_reasoning_model
      open_world_model
      closed_world_model
      semantic_equivalence_model
      logical_identity_model
      contradiction_vs_contrary_model
      necessary_sufficient_model
      condition_model
      meta_logical_model
      ambiguity_model
      natural_language_logic_model
      semantic_confidence_model
      AI_logic_model
      heuristic_reasoning_model
      explainability_model
      dependency_model
      recursive_reasoning_model
      version_model
      provenance_model
      validation_model
      interoperability_model
      knowledge_graph_model
      relationships
      semantic_equivalence
      constraints
      logic_record_model
      reasoning_rules
      validation
      confidence_model
      update_model
      AI_consumption_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      formal_language_syntax_orsemantics_change
      proposition_truth_orconnective_semantics_change
      predicate_variable_quantifier_orscope_changes
      interpretation_model_satisfiability_orvalidity_changes
      argument_inference_fallacy_orproof_semantics_change
      consistency_soundness_orcompleteness_changes
      classical_nonclassical_modal_ortemporal_logic_changes
      automated_reasoning_orproof_checking_changes
      natural_language_formalisation_orAI_reasoning_changes
      ambiguity_confidence_orprovenance_changes
      logic_record_changes
      constraint_model_changes
      reasoning_rule_changes
  }

}

END FLOW