Negation Ontology
Propositional Logic
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Negation Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/propositional-logic/negation-ontology.html
FLOW NegationOntology {
DOMAIN:
AI Core
-> Ontologies
-> Mathematical Ontologies
-> Mathematical Logic Ontologies
-> Propositional Logic
-> Negation Ontology
PURPOSE:
Represent logical negation as a machine-interpretable unary logical connective that transforms a proposition or formula according to the semantics of an explicitly identified logical system. In classical propositional logic, negation reverses the two classical truth values: TRUE becomes FALSE and FALSE becomes TRUE. The ontology models negation identity, notation, operand scope, syntax-tree structure, truth function, truth tables, literals, complementarity, double negation, De Morgan transformations, normal forms, contradiction, excluded middle, inference rules, SAT and resolution usage, Boolean algebra mappings, natural-language negation, non-classical variants, ambiguity, versioning and provenance. It prevents logical negation from being confused with absence, uncertainty, database null, negation as failure, numerical sign reversal, set complement, linguistic denial, opposition or empirical falsification unless an explicit mapping is declared.
ENTITY Negation {
TYPE: UnaryLogicalConnective
PROPERTIES:
has_identifier
has_symbol
has_operand
has_scope
has_truth_function
has_precedence
belongs_to_logic_system
may_form_negative_literal
may_have_equivalent_transformations
may_have_inference_rules
has_version
has_provenance
}
ENTITY NegatedFormula {
TYPE: CompoundFormula
COMPONENTS:
negation_operator
operand_formula
}
ENTITY NegativeLiteral {
TYPE: Literal
STRUCTURE:
NOT atomic_proposition
}
NEGATION_IDENTITY_MODEL {
canonical_identifier:
NOT
arity:
1
RULE:
negation_identity MUST be distinguished_fromsurface_symbol
}
LOGIC_CONTEXT_MODEL {
default:
classical_propositional_logic
RULE:
negation_semantics MUST be logic_specific
}
SYMBOL_MODEL {
common:
¬
~
!
NOT
RULE:
symbol_mapping MUST use_declared_notation
}
PREFIX_OPERATOR_MODEL {
structure:
NOT A
RULE:
negation_precedes_itsoperand
}
ARITY_MODEL {
negation:
unary
RULE:
exactly_one_operand_required
}
OPERAND_MODEL {
operand:
well_formed_formula
RULE:
operand_formula_identifier SHOULD be preserved
}
SCOPE_MODEL {
negation:
applies_toexact_operand_subtree
RULE:
scope MUST be resolved_beforesemantic_evaluation
}
PARENTHESIS_MODEL {
examples:
NOT(A AND B)
(NOT A) AND B
RULE:
parentheses_canchange_negation_scope_andmeaning
}
PRECEDENCE_MODEL {
classical_common:
NOT_has_higher_precedence_thanbinary_connectives
RULE:
actual_precedence MUST followlanguage_profile
}
AST_MODEL {
node:
NEGATION
child:
operand_AST
RULE:
child_count = 1
}
CLASSICAL_TRUTH_FUNCTION_MODEL {
input_TRUE:
output_FALSE
input_FALSE:
output_TRUE
}
TRUTH_TABLE_MODEL {
rows:
A=TRUE -> NOT_A=FALSE
A=FALSE -> NOT_A=TRUE
}
INVOLUTION_MODEL {
classical:
NOT(NOT A) equivalent_to A
RULE:
involution_islogic_specific
}
DOUBLE_NEGATION_MODEL {
expression:
¬¬A
classical_equivalence:
A
RULE:
double_negation_elimination_notuniversallyvalid_inalllogics
}
DOUBLE_NEGATION_INTRODUCTION_MODEL {
classical_andintuitionistic_standard:
A -> NOT NOT A
RULE:
distinguish_introduction_fromelimination
}
DOUBLE_NEGATION_ELIMINATION_MODEL {
classical:
NOT NOT A -> A
RULE:
notgenerally_derivable_inintuitionistic_logic
}
LITERAL_MODEL {
positive:
p
negative:
NOT p
RULE:
negative_literal_operand MUST beatomic
}
COMPLEMENTARY_LITERAL_MODEL {
pair:
p
NOT p
RULE:
bothrefer_tosame_atomic_variable
}
COMPLEMENT_MODEL {
Boolean:
NOT mapsvalue_toBoolean_complement
}
CONTRADICTION_MODEL {
formula:
A AND NOT A
classical:
always_FALSE
}
EXCLUDED_MIDDLE_MODEL {
formula:
A OR NOT A
classical:
always_TRUE
RULE:
classical_validity_notuniversal_acrosslogics
}
NONCONTRADICTION_MODEL {
formula:
NOT(A AND NOT A)
classical:
always_TRUE
}
DE_MORGAN_MODEL {
NOT(A AND B)
equivalent_to
NOT A OR NOT B
NOT(A OR B)
equivalent_to
NOT A AND NOT B
RULE:
transformation_semantics MUST be logic_specific
}
IMPLICATION_NEGATION_MODEL {
NOT(A -> B)
classical_equivalent_to
A AND NOT B
}
BICONDITIONAL_NEGATION_MODEL {
NOT(A <-> B)
classical_equivalent_to
A XOR B
}
XOR_NEGATION_MODEL {
NOT(A XOR B)
classical_equivalent_to
A <-> B
}
NAND_MODEL {
definition:
NOT(A AND B)
}
NOR_MODEL {
definition:
NOT(A OR B)
}
NEGATION_NORMAL_FORM_MODEL {
abbreviation:
NNF
requirement:
negation_occurs_onlydirectly_beforeatomic_propositions
RULE:
compound_negations_must_be pushed_inward
}
NNF_TRANSFORMATION_MODEL {
process:
eliminate_implication_andbiconditional
push_negations_usingDeMorgan
eliminate_double_negation
RULE:
classical_orappropriate_logic_context MUST be identified
}
CNF_MODEL {
negative_literals:
permitted_insideclauses
RULE:
NOT_shouldapply_toatoms_instandard_CNF
}
DNF_MODEL {
negative_literals:
permitted_insideterms
RULE:
NOT_shouldapply_toatoms_instandard_DNF
}
SAT_MODEL {
negative_literal:
representsvariable_assignedFALSE_forliteral_toevaluateTRUE
RULE:
literal_truth_andvariable_truth MUST be distinguished
}
NEGATIVE_LITERAL_EVALUATION_MODEL {
if p=TRUE:
NOT_p=FALSE
if p=FALSE:
NOT_p=TRUE
}
UNIT_NEGATIVE_LITERAL_MODEL {
clause:
NOT p
implication:
p_must_beFALSE_tosatisfyclause
}
RESOLUTION_MODEL {
complementary_pair:
p
NOT p
RULE:
resolution_requires_sameunderlying_variable
}
TAUTOLOGICAL_CLAUSE_MODEL {
clause:
p OR NOT p
classical:
always_TRUE
}
CONTRADICTORY_TERM_MODEL {
term:
p AND NOT p
classical:
always_FALSE
}
BOOLEAN_ALGEBRA_MODEL {
NOT:
complement_operation
laws:
complement_of_TRUE = FALSE
complement_of_FALSE = TRUE
complement_of_complement_A = A
}
SET_COMPLEMENT_MAPPING_MODEL {
undercharacteristic_set_mapping:
NOT corresponds_tocomplement
RULE:
set_complement != logical_negation_byidentity
}
BITWISE_NOT_DISTINCTION_MODEL {
bitwise_NOT:
flips_eachbit_inbitvector
RULE:
bitwise_NOT != logical_negation_withoutBoolean_single_bit_mapping
}
PROGRAMMING_NOT_MODEL {
operator:
maymaptruthy_falsy_values_toBoolean_result
RULE:
programming_language_semantics MUST be declared
}
NUMERIC_NEGATION_DISTINCTION_MODEL {
arithmetic:
-x
logical:
NOT A
RULE:
unary_minus != logical_negation
}
NATURAL_LANGUAGE_NEGATION_MODEL {
cues:
not
no
never
neither
it_is_not_the_case_that
RULE:
linguistic_negation_scope MUST be resolved
}
SENTENTIAL_NEGATION_MODEL {
source:
"It is not the case that A"
formal:
NOT A
}
CONSTITUENT_NEGATION_MODEL {
source:
negation_applies_topart_ofsentence
RULE:
mayrequiremorethanpropositional_atom_negation
}
NEGATIVE_PREFIX_DISTINCTION_MODEL {
examples:
unhappy
impossible
nonzero
RULE:
lexical_negative_prefix != logical_NOT_automatically
}
DENIAL_MODEL {
speech_act:
rejects_orcontradicts_priorclaim
RULE:
denial != formal_negation_withoutpropositional_mapping
}
OPPOSITION_MODEL {
concepts:
may_becontraries_oropposites
RULE:
opposite_concept != logical_complement_necessarily
}
CONTRARY_MODEL {
A_andB:
cannotbothbetrue_butmaybothbefalse
RULE:
contrary != contradiction
}
CONTRADICTORY_RELATION_MODEL {
A_andNOT_A:
exactlyone_true_underclassical_bivalence
RULE:
relation_islogic_specific
}
ABSENCE_DISTINCTION_MODEL {
absence_ofevidence_orproperty_record:
noassertion
RULE:
absence != NOT A
}
UNKNOWN_DISTINCTION_MODEL {
unknown:
truth_notdetermined
RULE:
unknown != NOT A
}
NULL_DISTINCTION_MODEL {
database_NULL:
missing_orunknownvalue
RULE:
NULL != FALSE
NULL != logical_negation
}
OPEN_WORLD_MODEL {
failure_tofind_A:
doesnotentail_NOT_A
RULE:
absence_ofassertion != negated_assertion
}
CLOSED_WORLD_MODEL {
failure_tofind_A:
maypermitinfer_NOT_A_underdeclared policy
RULE:
closed_world_assumption MUST be explicit
}
NEGATION_AS_FAILURE_MODEL {
logic_programming:
not_A_maymeanfailure_toprove_A
RULE:
negation_as_failure != classical_negation
}
STRONG_NEGATION_MODEL {
explicit:
formal_negative_assertion
RULE:
strong_negation_anddefault_negation MUST be distinguished
}
DEFAULT_NEGATION_MODEL {
operational:
absence_ofproof_orbelief
RULE:
default_negation_isnonmonotonic_andcontextual
}
EPISTEMIC_NEGATION_DISTINCTION_MODEL {
"not known A":
NOT(KNOWS A)
notnecessarily
KNOWS(NOT A)
RULE:
negation_scope_overepistemic_operator_issemanticallymaterial
}
MODAL_NEGATION_MODEL {
examples:
NOT box A
NOT diamond A
RULE:
interaction_withmodal_operators depends_onsemantics
}
TEMPORAL_NEGATION_MODEL {
examples:
NOT always A
NOT eventually A
RULE:
temporal_dualities requiredeclared temporal_logic
}
QUANTIFIER_NEGATION_DISTINCTION_MODEL {
first_order:
NOT forall x P(x)
equivalent_to exists x NOT P(x)
NOT exists x P(x)
equivalent_to forall x NOT P(x)
RULE:
outsidebasic_propositional_scope_butimportant_crossdomain_mapping
}
INTUITIONISTIC_NEGATION_MODEL {
common_definition:
NOT A as A -> bottom
RULE:
classical_double_negation_elimination_andexcluded_middle_notgenerallyvalid
}
PARACONSISTENT_NEGATION_MODEL {
semantics:
A_andNOT_A_maybothbe supported_withoutexplosion
RULE:
classical_contradiction_rules MUST not_be assumed
}
MANY_VALUED_NEGATION_MODEL {
truth_domain:
morethan2_values
operation:
logic_specific
RULE:
truth_function MUST be explicitlydefined
}
FUZZY_NEGATION_MODEL {
common_standard:
NOT x = 1-x
alternatives:
othernegators
RULE:
fuzzy_negation != classical_NOT_withoutBoolean restriction
}
THREE_VALUED_NEGATION_MODEL {
truth_values:
logic_specific_three_values
RULE:
UNKNOWN_orindeterminate_mapping depends_onchosen_logic
}
FOUR_VALUED_NEGATION_MODEL {
truth_states:
logic_specific
RULE:
operation MUST be declared
}
NEGATION_POLARITY_MODEL {
occurrence:
negation_changespolarity_ofoperand
RULE:
recursive_polarity_analysis MUST considerconnective_context
}
ODD_EVEN_NEGATION_MODEL {
atom:
underodd_number_ofNOTs -> negative_polarity
undereven_number_ofNOTs -> positive_polarity
RULE:
simplified_rule_assumesdirect_negation_chain
}
NEGATION_DEPTH_MODEL {
formula:
maximum_nested_negation_count
RULE:
depth_isstructural_measure
}
NEGATION_COUNT_MODEL {
formula:
number_ofNOT_occurrences
RULE:
count != semantic_complexity_necessarily
}
NEGATION_SIMPLIFICATION_MODEL {
rules:
NOT TRUE -> FALSE
NOT FALSE -> TRUE
NOT NOT A -> A_inclassical_context
RULE:
simplification MUST preservedeclared semantics
}
CONSTANT_FOLDING_MODEL {
input:
NOT truth_constant
output:
opposite_truth_constant
}
FORMULA_RESTRICTION_MODEL {
if A_assigned:
NOT A_evaluates_tooppositevalue
RULE:
restriction_context MUST be preserved
}
SHANNON_LINK_MODEL {
formula:
NOT phi
cofactors:
NOT(phi[p:=TRUE])
NOT(phi[p:=FALSE])
RULE:
negation_commutes_withsubstitution
}
BDD_MODEL {
negated_function:
mayberepresented_bycomplemented_edges_orterminal_swap
RULE:
BDD_implementation_semantics MUST be explicit
}
CIRCUIT_MODEL {
NOT:
inverter_gate
RULE:
gate_signal_semantics requireBoolean encoding
}
INVERTER_MODEL {
input_high:
output_low
input_low:
output_high
RULE:
physical_signal_levels != logical_truth_values
}
PROOF_RULE_MODEL {
negation:
mayhaveintroduction_elimination_orclassical_rules
RULE:
proof_rules MUST be proof_system_specific
}
NEGATION_INTRODUCTION_MODEL {
natural_deduction:
assume_A
derive_bottom
discharge_A
infer_NOT_A
}
NEGATION_ELIMINATION_MODEL {
A
NOT_A
infer_bottom
RULE:
exact_rule depends_onformal system
}
CLASSICAL_REDUCTIO_MODEL {
assume_NOT_A
derive_bottom
infer_A
RULE:
classical_principle
}
MODUS_TOLLENS_MODEL {
A -> B
NOT B
therefore NOT A
RULE:
valid_classically_andinmanyotherlogics_underappropriate implication
}
CONTRAPOSITION_MODEL {
A -> B
equivalent_classically_to
NOT B -> NOT A
RULE:
equivalence_notuniversal_acrosslogics
}
RESOLUTION_REFUTATION_MODEL {
negated_goal:
added_to premises
process:
deriveempty_clause
RULE:
negation_ofgoal MUST be correctlyformed
}
PROOF_BY_CONTRADICTION_MODEL {
goal:
A
assume:
NOT A
derive:
contradiction
RULE:
infer_A_onlywhenlogic_supportsreductio
}
SEMANTIC_ENTAILMENT_MODEL {
Gamma entails NOT A:
everymodel_ofGamma_makesA_FALSE_underclassical semantics
}
SATISFIABILITY_RELATION_MODEL {
NOT A_satisfiable:
iff A_falsifiable_underclassical semantics
}
VALIDITY_RELATION_MODEL {
NOT A_valid:
iff A_unsatisfiable_underclassical semantics
}
CONTRADICTION_RELATION_MODEL {
NOT A_contradiction:
iff A_tautology_underclassical semantics
}
TAUTOLOGY_RELATION_MODEL {
NOT A_tautology:
iff A_contradiction_underclassical semantics
}
COMPLEMENT_TRUTH_VECTOR_MODEL {
truth_vector_NOT_A:
pointwise_complement_oftruth_vector_A
}
SEMANTIC_EQUIVALENCE_MODEL {
NOT_A_equivalent_NOT_B:
iff A_equivalent_B_underclassical semantics
RULE:
equivalence_requirescommonvaluation_mapping
}
NEGATION_HASH_MODEL {
semantic:
derivefromcomplemented_truth_vector_orcanonical_AST
RULE:
hash_method MUST be explicit
}
NATURAL_LANGUAGE_FORMALISATION_MODEL {
input:
text_withnegation
process:
identifynegationcue
identifyscope
identifyatom_orcompound_operand
constructNOT_formula
RULE:
preserveoriginal_text_andconfidence
}
NEGATION_SCOPE_AMBIGUITY_MODEL {
example:
"It is not true that A and B"
candidates:
NOT(A AND B)
(NOT A) AND B_iflinguisticallysupported
RULE:
preservecandidate_parses_whenunresolved
}
NEGATIVE_QUANTIFIER_LANGUAGE_MODEL {
examples:
nobody
nothing
never
RULE:
mayrequirepredicate_logic_notpropositional_atom_negation
}
NEGATIVE_CONCORD_MODEL {
language:
multiple_negative_forms_mayexpresssingle_semantic_negation
RULE:
surface_negative_count != logical_negation_count
}
DOUBLE_NEGATIVE_LANGUAGE_MODEL {
natural_language:
mayexpressaffirmation_emphasis_orotherpragmaticmeaning
RULE:
do_not mechanicallyapplyclassical_double_negation_withoutsemantic parsing
}
FORMALISATION
_CONFIDENCE_MODEL {
confidence:
support_foridentified_negation_scope_andoperand
RULE:
confidence != truth_value
}
AMBIGUITY_MODEL {
possible:
scope
symbol
logic_system
natural_language
strong_vsdefault_negation
unknown_vsfalse
RULE:
ambiguity MUST be resolved_orpreserved
}
ERROR_MODEL {
possible:
missing_operand
malformed_scope
invalid_symbol
unsupported_nonclassical_semantics
incorrect_double_negation_reduction
RULE:
error SHOULD identifysource_andlogic_context
}
VALIDATION_MODEL {
checks:
negation_identifier
logic_system
symbol
arity
operand
scope
truth_function
transformation_rules
proof_rules
nonclassical_semantics
RULE:
validation MUST useexact_logic_version
}
EXPLAINABILITY_MODEL {
output:
source_formula
negated_operand
scope
input_truth_value
output_truth_value
equivalent_forms
proof_context
RULE:
explanation MUST distinguishlogical_negation_fromothernegative_relations
}
VERSION_MODEL {
versioned:
logic_system
negation_semantics
notation
proof_rules
ontology
RULE:
historical_negation_results MUST preserveversions
}
PROVENANCE_MODEL {
fields:
source
formalisation
parser
logic_system
transformation
proof
version
agent
RULE:
negation_record MUST remainprovenance_linked
}
INTEROPERABILITY_MODEL {
exchange:
canonical_negation_identifier
symbol
operand_AST
scope
truth_function
logic_system
version
provenance
RULE:
symbol_withoutoperand_scope_isnotlossless
}
KNOWLEDGE_GRAPH_MODEL {
nodes:
negation
formula
atom
literal
truth_value
proof_rule
edges:
NEGATES
HAS_OPERAND
COMPLEMENT_OF
EQUIVALENT_TO
DERIVED_BY
TRANSFORMS_TO
RULE:
syntactic_semantic_andproof_relations MUST be typed
}
RELATIONSHIPS {
Negation -> IS_A -> UnaryLogicalConnective
Negation -> HAS_OPERAND -> Formula
NegatedFormula -> CONTAINS -> Negation
NegativeLiteral -> NEGATES -> AtomicProposition
Negation -> MAPS -> TruthValueToComplement
DoubleNegation -> MAY_REDUCE_TO -> OperandFormula
Negation -> MAY_HAVE -> IntroductionRule
Negation -> MAY_HAVE -> EliminationRule
}
SEMANTIC_EQUIVALENCE {
"negation" ~= unary_logical_operator_expressinglogical_not_underdeclared_semantics
"negative literal" ~= negation_ofatomic_proposition
"classical negation" ~= Boolean_complement_truth_function
negation != absence
negation != unknown
negation != database_NULL
negation != numerical_negative_sign
negation != set_complement_byidentity
negation != negation_as_failure
negation != opposite_concept
contradiction != contrary
double_negation_elimination != universally_valid_rule
logical_NOT != bitwise_NOT
semantic_confidence != truth_value
}
CONSTRAINTS {
canonical_negation_identifier_must_be preserved = true
logic_system_andversion_must_be identified = true
negation_must_haveexactly_one_operand = true
operand_scope_must_be explicit = true
classical_negation_truth_function_must_mapTRUE_toFALSE_andFALSE_toTRUE = true
negative_literal_andnegated_compound_formula_must_be distinguished = true
double_negation_elimination_must_not_be applied_outside_supporting_logic = true
De_Morgan_andothertransformations_must_be logic_specific = true
negation_must_not_be interpreted_asabsence_unknown_orNULL = true
strong_default_andnegation_as_failure_must_be distinguished = true
natural_language_negation_scope_must_be preserved = true
nonclassical_negation_must_defineitsown_semantics = true
provenance_must_be preserved = true
}
NEGATION_RECORD_MODEL {
RECORD:
negation_identifier
logic_system_identifier
logic_version
notation_profile
symbol
operand_formula_identifier
operand_AST
scope
input_truth_value
output_truth_value
literal_status
polarity
negation_depth
equivalent_forms
NNF_transformation
proof_rule_identifiers
SAT_literal_mapping
natural_language_source
strong_or_default_status
ambiguity_status
formalisation_confidence
version
provenance
RULE:
negation_record MUST support_reconstruction_ofoperator_operand_scope_semantics_transformations_andprovenance
}
REASONING_RULES {
IF negation_expression_received
THEN identifylogic_andnotation
resolveNOT_operator
parseexact_operand_scope
validatearity
IF classical_truth_value_available
THEN returnBoolean_complement
IF nested_negation_detected
THEN countnegation_depth
simplifydouble_negation_onlywhenlogic_supports
IF negation_applies_tocompound_AND_orOR
THEN DeMorgan_transformation_maybeoffered_orapplied_underdeclaredlogic
IF negative_literal_inSAT
THEN map_toopposite_truth_requirement_ofunderlyingvariable
IF natural_language_negation_received
THEN identifycue_andsemantic_scope
distinguishsentential_constituent_lexical_anddefault_negation
preserveambiguity_andconfidence
IF absence_unknown_NULL_orfailedproof_encountered
THEN do_notmap_toNOT_A_withoutdeclaredclosed_world_orothersemantic rule
IF nonclassical_logic_selected
THEN loadlogic_specific_negation_operation_andproof_rules
IF negation_semantics_orlogic_version_changes
THEN preservehistorical_records
revalidatecurrent_transformations_andproofs
}
VALIDATION {
CHECK negation_identifier
CHECK logic_system
CHECK logic_version
CHECK symbol
CHECK arity
CHECK operand
CHECK operand_AST
CHECK scope
CHECK truth_function
CHECK literal_status
CHECK polarity
CHECK double_negation
CHECK De_Morgan_transformations
CHECK NNF_status
CHECK SAT_literal_mapping
CHECK proof_rules
CHECK strong_default_NAF_distinctions
CHECK natural_language_scope
CHECK nonclassical_semantics
CHECK ambiguity
CHECK formalisation_confidence
CHECK version
CHECK provenance
}
CONFIDENCE {
negation_identity_confidence: 1.00
operand_scope_confidence: 1.00
classical_truth_function_confidence: 1.00
equivalence_transformation_confidence: 1.00
SAT_literal_confidence: 1.00
proof_rule_confidence: 0.99
natural_language_negation_confidence: 0.95
nonclassical_semantics_confidence: 0.98
RULE:
confidence decreases when logic, notation, operand scope,
natural-language context, negation type, proof system,
version orprovenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_negation_expression:
assign_orresolve_negation_identifier
attachlogic_andnotation
parseoperand_scope
validate_semantics
preserveprovenance
compute_FLOW_HASH
ON transformation:
preserve_source_formula
applyvalidated_negation_rule
recordtarget_andlogic_context
ON semantic_revision:
preserveprevious_negation_definition
registernewlogic_version
revalidateequivalences_anddependentproofs
recompute_FLOW_HASH
ON natural_language_revision:
preserveoriginal_formalisation
attachnewcandidate_mapping_andconfidence
}
AI_CONSUMPTION {
canonical_entity: Negation
canonical_role: UnaryLogicalConnective
interpretation_order:
identify_logic_system
identify_negation_symbol_orlinguisticcue
resolvecanonical_NOT_identifier
identifyexact_operand_andAST_scope
validateunary_arity
resolveclassical_orlogic_specific_truth_function
identifynegative_literal_status
computecomplement_truth_value_whenvaluationavailable
detectdouble_negation_andDeMorgan_opportunities
distinguishnegation_fromabsence_unknown_NULL_andfailure_toprove
distinguishlogical_NOT_fromnumeric_bitwise_programming_andset_operations
resolveproof_rules_andSAT_literal_role
resolve_natural_language_negation_scope
identifystrong_default_or nonclassical_negation_whenapplicable
detectambiguity
assignsemantic_confidence
preserveversions_andprovenance
emit_machine_resolvable_negation_structure
ambiguity_controls:
distinguish_negation_fromabsence
distinguish_negation_fromunknown
distinguish_negation_fromdatabase_NULL
distinguish_negation_fromnumerical_negative_sign
distinguish_negation_fromset_complement_byidentity
distinguish_negation_fromnegation_as_failure
distinguish_negation_fromopposite_concept
distinguish_contradiction_fromcontrary
distinguish_double_negation_elimination_fromuniversally_valid_rule
distinguish_logical_NOT_frombitwise_NOT
distinguish_semantic_confidence_fromtruth_value
preserve_logic_symbol_operand_scope_semantics_proof_rules_version_andprovenance
}
PROVENANCE {
ontology_scope:
logical_negation_truth_complement_literals_transformations_proof_rules_nonclassical_semantics_andAI_interpretation
parent_path:
AI Core
-> Ontologies
-> Mathematical Ontologies
-> Mathematical Logic Ontologies
-> Propositional Logic
-> Negation Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
negation_identity_model
logic_context_model
symbol_model
prefix_operator_model
arity_model
operand_model
scope_model
parenthesis_model
precedence_model
AST_model
classical_truth_function_model
truth_table_model
involution_model
double_negation_model
double_negation_introduction_model
double_negation_elimination_model
literal_model
complementary_literal_model
complement_model
contradiction_model
excluded_middle_model
noncontradiction_model
De_Morgan_model
implication_negation_model
biconditional_negation_model
XOR_negation_model
NAND_model
NOR_model
negation_normal_form_model
NNF_transformation_model
CNF_model
DNF_model
SAT_model
negative_literal_evaluation_model
unit_negative_literal_model
resolution_model
tautological_clause_model
contradictory_term_model
Boolean_algebra_model
set_complement_mapping_model
bitwise_NOT_distinction_model
programming_NOT_model
numeric_negation_distinction_model
natural_language_negation_model
sentential_negation_model
constituent_negation_model
negative_prefix_distinction_model
denial_model
opposition_model
contrary_model
contradictory_relation_model
absence_distinction_model
unknown_distinction_model
NULL_distinction_model
open_world_model
closed_world_model
negation_as_failure_model
strong_negation_model
default_negation_model
epistemic_negation_distinction_model
modal_negation_model
temporal_negation_model
quantifier_negation_distinction_model
intuitionistic_negation_model
paraconsistent_negation_model
many_valued_negation_model
fuzzy_negation_model
three_valued_negation_model
four_valued_negation_model
negation_polarity_model
odd_even_negation_model
negation_depth_model
negation_count_model
negation_simplification_model
constant_folding_model
formula_restriction_model
Shannon_link_model
BDD_model
circuit_model
inverter_model
proof_rule_model
negation_introduction_model
negation_elimination_model
classical_reductio_model
modus_tollens_model
contraposition_model
resolution_refutation_model
proof_by_contradiction_model
semantic_entailment_model
satisfiability_relation_model
validity_relation_model
contradiction_relation_model
tautology_relation_model
complement_truth_vector_model
semantic_equivalence_model
negation_hash_model
natural_language_formalisation_model
negation_scope_ambiguity_model
negative_quantifier_language_model
negative_concord_model
double_negative_language_model
formalisation_confidence_model
ambiguity_model
error_model
validation_model
explainability_model
version_model
provenance_model
interoperability_model
knowledge_graph_model
relationships
semantic_equivalence
constraints
negation_record_model
reasoning_rules
validation
confidence_model
update_model
AI_consumption_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
negation_identity_logic_system_orsymbol_mapping_changes
operand_scope_precedence_orAST_semantics_change
classical_truth_function_ortruth_table_changes
double_negation_DeMorgan_normal_form_orSAT_semantics_change
proof_rule_resolution_orcontradiction_reasoning_changes
nonclassical_intuitionistic_paraconsistent_manyvalued_orfuzzy_negation_changes
open_closed_world_strong_default_ornegation_asfailure_semantics_change
natural_language_negation_scope_orformalisation_changes
negation_record_changes
constraint_model_changes
reasoning_rule_changes
version_orprovenance_changes
}
}
END FLOW