Conjunction Ontology
Propositional Logic
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Conjunction Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/propositional-logic/conjunction-ontology.html
FLOW ConjunctionOntology {
DOMAIN:
AI Core
-> Ontologies
-> Mathematical Ontologies
-> Mathematical Logic Ontologies
-> Propositional Logic
-> Conjunction Ontology
PURPOSE:
Represent logical conjunction as a machine-interpretable binary logical connective combining two propositions or formulas into a compound formula that is true, under classical propositional semantics, exactly when both operands are true. The ontology models conjunction identity, notation, operands, arity, precedence, associativity, scope, truth function, truth table, Boolean and set-theoretic mappings, introduction and elimination rules, algebraic laws, normal forms, literals and clauses, SAT constraints, circuit implementations, natural-language formalisation, non-classical variants, ambiguity, validation, versioning and provenance. It enables AI systems to reason explicitly about AND structures while preventing conjunction from being confused with temporal sequence, causal combination, arithmetic multiplication, set intersection, programming short-circuit operators, probabilistic joint events or natural-language coordination unless a declared mapping justifies the relation.
ENTITY Conjunction {
TYPE: BinaryLogicalConnective
PROPERTIES:
has_identifier
has_left_operand
has_right_operand
has_symbol
has_arity
has_truth_function
has_precedence
has_associativity
belongs_to_logic_system
may_have_inference_rules
may_have_equivalent_forms
has_version
has_provenance
}
ENTITY ConjunctiveFormula {
TYPE: CompoundPropositionalFormula
STRUCTURE:
left_formula
AND
right_formula
}
ENTITY Conjunct {
TYPE: OperandFormula
ROLE:
member_ofconjunction
}
CONJUNCTION_IDENTITY_MODEL {
canonical_identifier:
AND
arity:
2
RULE:
conjunction_identity MUST be distinguished_fromsurface_notation
}
LOGIC_CONTEXT_MODEL {
default:
classical_propositional_logic
truth_domain:
TRUE
FALSE
RULE:
conjunction_semantics MUST be logic_specific
}
SYMBOL_MODEL {
common:
∧
AND
&
&&
RULE:
symbol MUST be resolved_usinglanguage_andnotation_profile
}
ARITY_MODEL {
conjunction:
binary
RULE:
exactly_two_operands_required_inbinary_form
}
LEFT_OPERAND_MODEL {
operand:
well_formed_formula
}
RIGHT_OPERAND_MODEL {
operand:
well_formed_formula
}
OPERAND_ORDER_MODEL {
syntax:
left
right
classical_semantics:
commutative
RULE:
syntax_order SHOULD stillbe preserved_evenwhensemantically_commutative
}
AST_MODEL {
node:
AND
children:
left_operand
right_operand
RULE:
child_count = 2
}
PRECEDENCE_MODEL {
common:
NOT_beforeAND
AND_beforeOR
RULE:
actual_precedence MUST followdeclared_language
}
ASSOCIATIVITY_PARSE_MODEL {
common:
AND_isassociative_semantically
RULE:
parser_associativity_andsemantic_associativity MUST be distinguished
}
PARENTHESIS_MODEL {
examples:
(A AND B) OR C
A AND (B OR C)
RULE:
parentheses determine_scope
}
SCOPE_MODEL {
conjunction:
combines_exact_operand_subtrees
RULE:
scope MUST be resolved_beforeevaluation
}
CLASSICAL_TRUTH_FUNCTION_MODEL {
TT -> TRUE
TF -> FALSE
FT -> FALSE
FF -> FALSE
}
TRUTH_TABLE_MODEL {
rows:
A=TRUE B=TRUE -> A_AND_B=TRUE
A=TRUE B=FALSE -> A_AND_B=FALSE
A=FALSE B=TRUE -> A_AND_B=FALSE
A=FALSE B=FALSE -> A_AND_B=FALSE
}
TRUE_CONDITION_MODEL {
conjunction:
TRUE_iff_allbinary_operands_TRUE
}
FALSE_CONDITION_MODEL {
conjunction:
FALSE_ifatleastone_operand_FALSE
}
SHORT_SEMANTIC_RULE_MODEL {
IF left=FALSE OR right=FALSE
THEN conjunction=FALSE
IF left=TRUE AND right=TRUE
THEN conjunction=TRUE
}
COMMUTATIVITY_MODEL {
A AND B
equivalent_to
B AND A
RULE:
classical_conjunction_commutative
}
ASSOCIATIVITY_MODEL {
(A AND B) AND C
equivalent_to
A AND (B AND C)
RULE:
permits_flattening_underclassical_semantics
}
IDEMPOTENCE_MODEL {
A AND A
equivalent_to
A
}
IDENTITY_MODEL {
A AND TRUE
equivalent_to
A
}
DOMINATION_MODEL {
A AND FALSE
equivalent_to
FALSE
}
COMPLEMENT_MODEL {
A AND NOT A
equivalent_to
FALSE
}
ABSORPTION_MODEL {
A AND (A OR B)
equivalent_to
A
}
DISTRIBUTIVITY_OVER_OR_MODEL {
A AND (B OR C)
equivalent_to
(A AND B) OR (A AND C)
}
OR_DISTRIBUTIVITY_OVER_AND_MODEL {
A OR (B AND C)
equivalent_to
(A OR B) AND (A OR C)
RULE:
relationship_relevant_toCNF_conversion
}
DE_MORGAN_MODEL {
NOT(A AND B)
equivalent_to
NOT A OR NOT B
}
NEGATED_DISJUNCTION_MODEL {
NOT A AND NOT B
equivalent_to
NOT(A OR B)
}
IMPLICATION_RELATION_MODEL {
A AND B:
entails_A
entails_B
RULE:
conjunction_isstronger_than_eachconjunct_underclassical entailment
}
CONJUNCT_ENTAILMENT_MODEL {
A AND B entails A
A AND B entails B
}
CONJUNCTION_INTRODUCTION_SEMANTIC_MODEL {
if:
Gamma entails A
AND Gamma entails B
then:
Gamma entails A AND B
}
CONJUNCTION_INTRODUCTION_PROOF_MODEL {
premises:
A
B
conclusion:
A AND B
RULE:
proof_context_anddependencies MUST be preserved
}
CONJUNCTION_ELIMINATION_LEFT_MODEL {
premise:
A AND B
conclusion:
A
}
CONJUNCTION_ELIMINATION_RIGHT_MODEL {
premise:
A AND B
conclusion:
B
}
SIMPLIFICATION_RULE_MODEL {
aliases:
conjunction_elimination
RULE:
extraction_ofconjunct_isvalid_instandard_classical_andintuitionistic_systems
}
ADJUNCTION_RULE_MODEL {
aliases:
conjunction_introduction
premises:
A
B
conclusion:
A AND B
}
NATURAL_DEDUCTION_MODEL {
introduction:
fromA_andB_incontext inferA_AND_B
elimination:
fromA_AND_B inferA
fromA_AND_B inferB
RULE:
proof_system MUST be identified
}
SEQUENT_RIGHT_RULE_MODEL {
representative:
Gamma |- A
Gamma |- B
therefore Gamma |- A AND B
RULE:
exact_context_handling depends_oncalculus
}
SEQUENT_LEFT_RULE_MODEL {
representative:
Gamma,A,B |- C
therefore Gamma,A_AND_B |- C
RULE:
exact_rule_variant MUST be identified
}
CONJUNCTION_AS_MEET_MODEL {
Boolean_order:
conjunction = meet
RULE:
order_structure MUST be declared
}
BOOLEAN_ALGEBRA_MODEL {
AND:
Boolean_multiplication_or meet
identities:
A_AND_1=A
A_AND_0=0
A_AND_A=A
}
BOOLEAN_MULTIPLICATION_DISTINCTION_MODEL {
encoding:
1*1=1
otherwise=0
RULE:
arithmetic_multiplication_mapping_isBoolean_encoding_notidentity
}
SET_INTERSECTION_MODEL {
undercharacteristic_mapping:
A AND B corresponds_toset_intersection
RULE:
logical_conjunction != set_intersection_byidentity
}
EVENT_INTERSECTION_DISTINCTION_MODEL {
events:
A_intersection_B
proposition:
"A occurs AND B occurs"
RULE:
event_intersection_andlogical_conjunction_arelinked_butdifferent_entity_types
}
PROBABILITY_DISTINCTION_MODEL {
P(A AND B):
joint_probability
RULE:
P(A_AND_B) generally_not_equal P(A)*P(B)_withoutindependence
}
CAUSAL_DISTINCTION_MODEL {
A AND B:
joint_truth_condition
RULE:
conjunction_doesnotassertcausal_relation_betweenA_andB
}
TEMPORAL_DISTINCTION_MODEL {
A AND B:
bothtrue_underrelevantsemantic_context
RULE:
conjunction_doesnotencode_before_after_or simultaneity_withouttemporal semantics
}
SEQUENCE_DISTINCTION_MODEL {
natural_language:
"A and then B"
RULE:
"and then" contains_temporal_order_notcaptured_bypureconjunction
}
PROGRAMMING_AND_MODEL {
possible:
logical_AND_operator
short_circuit_AND
RULE:
programming_semantics MAY includeevaluation_order_andtruthiness
}
SHORT_CIRCUIT_AND_MODEL {
if_left_false:
right_operand_maynotbeevaluated
RULE:
evaluation_strategy != classical_truth_function
}
BITWISE_AND_DISTINCTION_MODEL {
bit_vectors:
componentwise_AND
RULE:
bitwise_AND != propositional_conjunction_withoutBoolean mapping
}
DATABASE_AND_MODEL {
SQL:
mayoperate_underthree_valued_TRUE_FALSE_UNKNOWN_semantics
RULE:
SQL_AND != classical_AND_whenNULL_present
}
MULTIARY_CONJUNCTION_MODEL {
form:
AND(A_1,...,A_n)
true_iff:
everyoperand_TRUE
RULE:
n_ary_extension SHOULD be linked_toiterated_binary_AND
}
EMPTY_CONJUNCTION_MODEL {
zero_operands:
TRUE_understandard_algebraic_convention
RULE:
convention MUST be declared
}
SINGLETON_CONJUNCTION_MODEL {
one_operand:
equivalent_tooperand
}
FLATTENING_MODEL {
nested:
A AND (B AND C)
flattened:
AND(A,B,C)
RULE:
valid_whenassociativity_available
}
CONJUNCT_SET_MODEL {
flattened_conjunction:
collection_ofconjuncts
RULE:
set_representation_losesduplicates_andorder
onlysafe_whenidempotence_commutativity_associativity_apply
}
DUPLICATE_CONJUNCT_MODEL {
A AND A:
simplify_toA_underidempotence
}
TRUE_CONJUNCT_MODEL {
A AND TRUE:
removeTRUE_underidentity
}
FALSE_CONJUNCT_MODEL {
A AND FALSE:
simplify_entireconjunction_toFALSE
}
CONTRADICTORY_CONJUNCTS_MODEL {
contains:
A
NOT A
result:
FALSE_underclassical_semantics
}
CNF_MODEL {
top_level:
conjunction_ofclauses
RULE:
conjunction_isouter_combiner_inCNF
}
CLAUSE_SET_MODEL {
CNF:
C_1 AND ... AND C_n
RULE:
allclauses_mustbeTRUE_forsatisfaction
}
CNF_SAT_MODEL {
valuation:
satisfiesCNF_iff_satisfieseveryclause
}
DNF_MODEL {
conjunction:
combinesliterals_insideeachterm
}
DNF_TERM_MODEL {
term:
conjunction_ofliterals
RULE:
oneTRUE_term_suffices_forDNF_TRUE
}
MINTERM_MODEL {
conjunction:
includes_eachvariable_once_positive_ornegative
RULE:
minterm_TRUE_onexactlyonecompletevaluation
}
CONJUNCTION_OF_PREMISES_MODEL {
finite_Gamma:
A_1 AND ... AND A_n
RULE:
canencodefinite_premise_set_forsemantic_tests
}
ENTAILMENT_REDUCTION_MODEL {
Gamma entails C:
conjunction(Gamma) -> C_isvalid
forfiniteGamma
RULE:
emptyGamma_conjunction = TRUE_understandard convention
}
SAT_CONSTRAINT_MODEL {
conjunction:
allcomponent_constraints_mustbesatisfied
}
CONSTRAINT_PROPAGATION_MODEL {
A_AND_B_TRUE:
requiresA_TRUE
requiresB_TRUE
RULE:
backward_propagation_fromTRUE_conjunction_isvalid
}
FALSE_CONJUNCTION_DIAGNOSTIC_MODEL {
A_AND_B_FALSE:
atleastoneoperand_FALSE
RULE:
doesnotidentifywhichoperand_withoutadditionalinformation
}
TSEITIN_ENCODING_MODEL {
auxiliary:
z <-> (A AND B)
CNF_constraints:
NOT z OR A
NOT z OR B
z OR NOT A OR NOT B
RULE:
exactliteral_notation MAY vary
}
CIRCUIT_MODEL {
conjunction:
AND_gate
inputs:
operands
output:
conjunction_truth_value
}
AND_GATE_MODEL {
output_high:
iff_allBoolean_inputs_high_underdeclared encoding
RULE:
physical_signal_levels != truth_values
}
BDD_MODEL {
conjunction:
Boolean_apply_operation_betweenBDD_A_andBDD_B
RULE:
variable_order MUST be shared_orreconciled
}
TRUTH_VECTOR_MODEL {
A_AND_B:
pointwise_AND_oftruth_vectors_A_B
RULE:
commonvaluation_order REQUIRED
}
SEMANTIC_EQUIVALENCE_MODEL {
conjunction_formulas:
equivalent_iftruth_vectors_identical
RULE:
syntactic_reordering MAY preserveequivalence
}
SATISFIABILITY_MODEL {
A_AND_B:
satisfiable_iffexistsvaluation_satisfyingboth
RULE:
satisfiability_ofA_andB_individually_doesnotguarantee_joint_satisfiability
}
UNSATISFIABILITY_MODEL {
conjunction:
unsatisfiable_ifno_common_model
}
VALIDITY_MODEL {
A_AND_B:
valid_iffA_valid_andB_valid_underclassical semantics
}
MODEL_INTERSECTION_MODEL {
Models(A_AND_B):
Models(A) intersection Models(B)
RULE:
semantic_model_sets_intersect
}
COUNTERMODEL_MODEL {
A_AND_B_false:
valuation_whereA_false_orB_false
RULE:
onecountermodel_refutesvalidity
}
CONSISTENCY_MODEL {
conjunction_ofpremises:
consistent_ifjointly_satisfiable
}
CONTRADICTION_DETECTION_MODEL {
conjunction:
detectincompatible_conjuncts
RULE:
syntactic_A_andNOT_A_isonecase_notallsemantic_inconsistency
}
SUBSUMPTION_MODEL {
if A entails B:
A AND B equivalent_to A
RULE:
entailment_context MUST be established
}
REDUNDANT_CONJUNCT_MODEL {
conjunct_B:
redundant_ifotherconjuncts_entailB
RULE:
redundancy != duplicate_only
}
CONJUNCTION_SIMPLIFICATION_MODEL {
operations:
flatten
removeTRUE
collapseFALSE
remove_duplicates
detectcomplements
removeentailed_conjuncts_whenproven
RULE:
eachsimplification MUST preserveequivalence
}
FACTORISATION_MODEL {
(A AND B) OR (A AND C):
equivalent_to
A AND (B OR C)
RULE:
distributive_factorisation_classical
}
NATURAL_LANGUAGE_CONJUNCTION_MODEL {
cues:
and
both
as_well_as
together_with
RULE:
natural_language_coordination != logical_conjunction_automatically
}
BOTH_AND_MODEL {
phrase:
both A and B
candidate_formalisation:
A AND B
}
COMMA_AND_MODEL {
coordinated_claims:
mayimplyconjunction
RULE:
discourse_structure MUST be parsed
}
CONJUNCTION_SCOPE_AMBIGUITY_MODEL {
example:
A AND B OR C
candidates:
(A AND B) OR C
A AND (B OR C)
RULE:
usegrammar_parentheses_orpreserveambiguity
}
DISTRIBUTIVE_LANGUAGE_AMBIGUITY_MODEL {
plural_subject_predicate:
mayhavecollective_ordistributive_reading
RULE:
propositional_AND MAY beinsufficient_forfullsemantic representation
}
COLLECTIVE_DISTINCTION_MODEL {
"A and B jointly perform X":
maydescribe_collective_relation
RULE:
notnecessarily conjunction_ofindependent propositions
}
CONCESSIVE_AND_MODEL {
natural_language:
"A and yet B"
RULE:
logical_core_maybeconjunction_butdiscourse_relation_additional
}
TEMPORAL_AND_MODEL {
natural_language:
"A and then B"
RULE:
temporal_order MUST notbelost
}
CAUSAL_AND_MODEL {
natural_language:
"A and therefore B"
RULE:
conjunction_alone_doesnotencodeinference_orcausation
}
FORMALISATION_MODEL {
source:
natural_language_coordination
target:
candidate_conjunction_formula
metadata:
operand_spans
scope
discourse_relation
confidence
RULE:
preserveoriginal_text_andinterpretive_choices
}
FORMALISATION_CONFIDENCE_MODEL {
confidence:
support_forAND_mapping_andoperand_scope
RULE:
confidence != truth
}
INTUITIONISTIC_CONJUNCTION_MODEL {
proof_meaning
:
proof_ofA_AND_B_contains_proof_ofA_andproof_ofB
RULE:
conjunction_isconstructively_well_behaved
}
PARACONSISTENT_CONJUNCTION_MODEL {
conjunction:
maycombineinconsistent_information
RULE:
A_AND_NOT_A_doesnotnecessarilyentailarbitraryB
}
MANY_VALUED_CONJUNCTION_MODEL {
truth_domain:
morethan2values
operation:
logic_specific
RULE:
classical_AND_table MUST notbeassumed
}
FUZZY_CONJUNCTION_MODEL {
operation:
t_norm
examples:
minimum
product
Lukasiewicz_t_norm
RULE:
fuzzy_conjunction_semantics MUST identifyt_norm
}
THREE_VALUED_CONJUNCTION_MODEL {
truth_domain:
threevalues
RULE:
truth_table depends_onchosenlogic
}
SQL_CONJUNCTION_MODEL {
values:
TRUE
FALSE
UNKNOWN
RULE:
SQL_three_valued_AND MUST be separatelymodelled
}
RESOURCE_SENSITIVE_CONJUNCTION_MODEL {
linear_logic:
multiple_conjunction_likeoperators
RULE:
additive_andmultiplicative_conjunction MUST be distinguished
}
LINEAR_LOGIC_TENSOR_DISTINCTION_MODEL {
tensor:
multiplicative_conjunction
with:
additive_conjunction
RULE:
neither_isidentical_toclassical_AND_withouttranslation
}
MODAL_SCOPE_MODEL {
compare:
box(A AND B)
boxA AND boxB
RULE:
equivalence_depends_onmodal semantics
}
TEMPORAL_SCOPE_MODEL {
compare:
always(A AND B)
alwaysA AND alwaysB
RULE:
temporal_logic_semantics MUST be declared
}
QUANTIFIER_SCOPE_MODEL {
predicate_logic:
forallx(P(x) AND Q(x))
RULE:
conjunction_interacts_withquantifier_scope
}
ERROR_MODEL {
possible:
missing_operand
extra_operand_inbinarysyntax
scope_error
symbol_collision
incorrect_truth_function
invalid_simplification
RULE:
error SHOULD identifylogic_andformula_position
}
AMBIGUITY_MODEL {
possible:
symbol
operand_scope
natural_language_coordination
collective_reading
nonclassical_semantics
RULE:
unresolved_ambiguity MUST be preserved
}
VALIDATION_MODEL {
checks:
conjunction_identifier
logic_system
arity
operands
scope
AST
truth_function
equivalence_rules
inference_rules
semantic_context
RULE:
validation MUST be logic_specific
}
EXPLAINABILITY_MODEL {
output:
operands
AND_operator
operand_truth_values
result
equivalent_forms
inference_rules
semantic_context
RULE:
explanation SHOULD exposewhyboth_operands_are_required_forTRUE
}
VERSION_MODEL {
versioned:
conjunction_semantics
logic_system
notation
proof_rules
ontology
RULE:
historical_formula_results MUST preserveversions
}
PROVENANCE_MODEL {
fields:
source
formula
parser
logic_system
transformation
proof
version
agent
RULE:
conjunction_record MUST remainprovenance_linked
}
INTEROPERABILITY_MODEL {
exchange:
canonical_AND_identifier
left_operand_AST
right_operand_AST
symbol
truth_function
logic_system
version
provenance
RULE:
plain_word_and_isnotlossless
}
KNOWLEDGE_GRAPH_MODEL {
nodes:
conjunction
conjunct
formula
truth_value
proof_rule
clause
circuit_gate
edges:
HAS_CONJUNCT
COMBINES
ENTAILS
EQUIVALENT_TO
DERIVED_BY
IMPLEMENTED_BY
SATISFIED_BY
RULE:
logical_semantic_proof_andimplementation_edges MUST be typed
}
RELATIONSHIPS {
Conjunction -> IS_A -> BinaryLogicalConnective
Conjunction -> HAS_LEFT_OPERAND -> Formula
Conjunction -> HAS_RIGHT_OPERAND -> Formula
ConjunctiveFormula -> CONTAINS -> Conjunct
Conjunction -> HAS_TRUTH_FUNCTION -> ClassicalAND
Conjunction -> MAY_HAVE -> IntroductionRule
Conjunction -> MAY_HAVE -> EliminationRule
Conjunction -> MAY_MAP_TO -> ANDGate
CNF -> COMBINES -> ClausesByConjunction
}
SEMANTIC_EQUIVALENCE {
"conjunction" ~= binary_logical_connective_true_exactly_whenbothoperands_true_underclassical_semantics
"conjunct" ~= operand_formula_withinconjunction
"conjunction introduction" ~= inference_fromA_andB_toA_AND_B
conjunction != arithmetic_multiplication
conjunction != set_intersection_byidentity
conjunction != probability_product
conjunction != causation
conjunction != temporal_sequence
logical_AND != programming_short_circuit_AND
logical_AND != bitwise_AND
logical_AND != SQL_AND_withNULL_withoutmapping
natural_language_and != logical_conjunction_necessarily
joint_satisfiability != individual_satisfiability
semantic_confidence != truth_value
}
CONSTRAINTS {
canonical_conjunction_identifier_must_be preserved = true
logic_system_andversion_must_be identified = true
binary_conjunction_must_haveexactly_two_operands = true
operand_ASTs_andscope_must_be preserved = true
classical_conjunction_true_iffbothoperands_true = true
commutativity_associativity_idempotence_identity_anddomination_rules_must_be logic_specific = true
conjunction_introduction_andelimination_rules_must_preserveproof_context = true
conjunction_must_not_be interpreted_ascausal_or temporal_order = true
programming_bitwise_SQL_andprobabilistic_AND_semantics_must_be distinguished = true
natural_language_coordination_ambiguity_must_be preserved = true
nonclassical_conjunction_must_defineitsown_semantics = true
provenance_must_be preserved = true
}
CONJUNCTION_RECORD_MODEL {
RECORD:
conjunction_identifier
logic_system_identifier
logic_version
notation_profile
symbol
left_operand_identifier
right_operand_identifier
left_operand_AST
right_operand_AST
scope
truth_function
truth_vector
commutative_status
associative_status
idempotent_status
equivalent_forms
CNF_role
DNF_role
SAT_constraint_role
introduction_rule
elimination_rules
circuit_mapping
natural_language_source
discourse_relation
ambiguity_status
formalisation_confidence
version
provenance
RULE:
conjunction_record MUST support_reconstruction_ofoperands_scope_truth_semantics_proof_rules_andprovenance
}
REASONING_RULES {
IF conjunction_expression_received
THEN identifylogic_andnotation
resolvecanonical_AND
parseleft_andright_operands
validatescope_andarity
IF classical_operand_values_available
THEN returnTRUE_onlyifbothTRUE
elseFALSE
IF conjunction_nested
AND associativity_supported
THEN mayflatten_whilepreservingoriginal_AST_lineage
IF simplification_requested
THEN applyidentity_domination_idempotence_complement_absorption_orentailed_conjunct_rules_onlywhenvalidated
IF conjunction_used_inproof
THEN applyintroduction_orelimination_rules_underidentified_proof_system
IF conjunction_used_asSAT_constraint
THEN requireallspecified_conjuncts_satisfied
preserveconflict_orwitness_information
IF natural_language_and_received
THEN identifyoperand_spans
detecttemporal_causal_collective_concessive_orordinarycoordination
maptoAND_onlywhenappropriate
preserveconfidence
IF nonclassical_logic_selected
THEN loadlogic_specific_conjunction_operation_andproof_rules
IF semantics_orlogic_version_changes
THEN preservehistorical_record
revalidatecurrent_equivalences_proofs_andSAT_encodings
}
VALIDATION {
CHECK conjunction_identifier
CHECK logic_system
CHECK logic_version
CHECK symbol
CHECK arity
CHECK left_operand
CHECK right_operand
CHECK AST
CHECK scope
CHECK truth_function
CHECK truth_vector
CHECK commutativity
CHECK associativity
CHECK idempotence
CHECK identity
CHECK domination
CHECK complement
CHECK De_Morgan_relation
CHECK CNF_DNF_role
CHECK SAT_constraint
CHECK introduction_rule
CHECK elimination_rules
CHECK circuit_mapping
CHECK natural_language_mapping
CHECK nonclassical_semantics
CHECK ambiguity
CHECK formalisation_confidence
CHECK version
CHECK provenance
}
CONFIDENCE {
conjunction_identity_confidence: 1.00
operand_scope_confidence: 1.00
classical_truth_function_confidence: 1.00
equivalence_rule_confidence: 1.00
proof_rule_confidence: 1.00
SAT_constraint_confidence: 1.00
natural_language_conjunction_confidence: 0.95
nonclassical_semantics_confidence: 0.98
RULE:
confidence decreases when logic, notation, operand scope,
natural-language discourse relation, proof system,
nonclassical operation, version orprovenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_conjunction:
assign_orresolve_identifier
attachlogic_andnotation
parseoperands
validateclassical_orlogic_specific_semantics
preserveprovenance
compute_FLOW_HASH
ON simplification_ortransformation:
preserve_source_formula
applyvalidated_rule
recordtarget_andsemantic_basis
ON proof_usage:
attachproof_context_rule_anddependencies
preserveverification_status
ON semantic_revision:
preserveprevious_conjunction_definition
registernewversion
revalidateequivalences_anddependentartifacts
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Conjunction
canonical_role: BinaryLogicalConnective
interpretation_order:
identify_logic_system
identify_AND_symbol_orlinguisticcue
resolvecanonical_conjunction_identifier
parseleft_andright_operand_ASTs
resolveprecedence_parentheses_andscope
validatebinary_arity
resolveclassical_orlogic_specific_truth_function
evaluateunderprovidedvaluation
identifyalgebraic_equivalences_andDeMorgan_relation
identifyCNF_DNF_andSAT_roles
resolveintroduction_andelimination_rules
distinguishlogical_AND_fromprogramming_bitwise_SQL_probability_set_andcausal_relations
resolve_natural_language_coordination_anddiscourse_relation
detectambiguity
assignsemantic_confidence
preserveversions_andprovenance
emit_machine_resolvable_conjunction_structure
ambiguity_controls:
distinguish_conjunction_fromarithmetic_multiplication
distinguish_conjunction_fromset_intersection_byidentity
distinguish_conjunction_fromprobability_product
distinguish_conjunction_fromcausation
distinguish_conjunction_fromtemporal_sequence
distinguish_logical_AND_fromprogramming_short_circuit_AND
distinguish_logical_AND_frombitwise_AND
distinguish_logical_AND_fromSQL_AND_withNULL_withoutmapping
distinguish_natural_language_and_fromlogical_conjunction_necessarily
distinguish_joint_satisfiability_fromindividual_satisfiability
distinguish_semantic_confidence_fromtruth_value
preserve_logic_operands_AST_scope_truth_function_rules_version_andprovenance
}
PROVENANCE {
ontology_scope:
conjunction_AND_truth_function_equivalences_proof_rules_SAT_constraints_natural_language_andAI_interpretation
parent_path:
AI Core
-> Ontologies
-> Mathematical Ontologies
-> Mathematical Logic Ontologies
-> Propositional Logic
-> Conjunction Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
conjunction_identity_model
logic_context_model
symbol_model
arity_model
left_operand_model
right_operand_model
operand_order_model
AST_model
precedence_model
associativity_parse_model
parenthesis_model
scope_model
classical_truth_function_model
truth_table_model
true_condition_model
false_condition_model
short_semantic_rule_model
commutativity_model
associativity_model
idempotence_model
identity_model
domination_model
complement_model
absorption_model
distributivity_over_OR_model
OR_distributivity_over_AND_model
De_Morgan_model
negated_disjunction_model
implication_relation_model
conjunct_entailment_model
conjunction_introduction_semantic_model
conjunction_introduction_proof_model
conjunction_elimination_left_model
conjunction_elimination_right_model
simplification_rule_model
adjunction_rule_model
natural_deduction_model
sequent_right_rule_model
sequent_left_rule_model
conjunction_as_meet_model
Boolean_algebra_model
Boolean_multiplication_distinction_model
set_intersection_model
event_intersection_distinction_model
probability_distinction_model
causal_distinction_model
temporal_distinction_model
sequence_distinction_model
programming_AND_model
short_circuit_AND_model
bitwise_AND_distinction_model
database_AND_model
multiary_conjunction_model
empty_conjunction_model
singleton_conjunction_model
flattening_model
conjunct_set_model
duplicate_conjunct_model
true_conjunct_model
false_conjunct_model
contradictory_conjuncts_model
CNF_model
clause_set_model
CNF_SAT_model
DNF_model
DNF_term_model
minterm_model
conjunction_of_premises_model
entailment_reduction_model
SAT_constraint_model
constraint_propagation_model
false_conjunction_diagnostic_model
Tseitin_encoding_model
circuit_model
AND_gate_model
BDD_model
truth_vector_model
semantic_equivalence_model
satisfiability_model
unsatisfiability_model
validity_model
model_intersection_model
countermodel_model
consistency_model
contradiction_detection_model
subsumption_model
redundant_conjunct_model
conjunction_simplification_model
factorisation_model
natural_language_conjunction_model
both_AND_model
comma_AND_model
conjunction_scope_ambiguity_model
distributive_language_ambiguity_model
collective_distinction_model
concessive_AND_model
temporal_AND_model
causal_AND_model
formalisation_model
formalisation_confidence_model
intuitionistic_conjunction_model
paraconsistent_conjunction_model
many_valued_conjunction_model
fuzzy_conjunction_model
three_valued_conjunction_model
SQL_conjunction_model
resource_sensitive_conjunction_model
linear_logic_tensor_distinction_model
modal_scope_model
temporal_scope_model
quantifier_scope_model
error_model
ambiguity_model
validation_model
explainability_model
version_model
provenance_model
interoperability_model
knowledge_graph_model
relationships
semantic_equivalence
constraints
conjunction_record_model
reasoning_rules
validation
confidence_model
update_model
AI_consumption_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
conjunction_identity_logic_system_orsymbol_mapping_changes
operand_arity_scope_precedence_orAST_changes
classical_truth_function_ortruth_table_changes
commutativity_associativity_idempotence_distribution_orDeMorgan_changes
proof_rule_entailment_orsemantic_relation_changes
CNF_DNF_SAT_Tseitin_BDD_orcircuit_semantics_change
programming_bitwise_SQL_probability_set_temporal_orcausal_distinctions_change
natural_language_conjunction_orformalisation_changes
nonclassical_intuitionistic_paraconsistent_manyvalued_orfuzzy_conjunction_changes
conjunction_record_changes
constraint_model_changes
reasoning_rule_changes
version_orprovenance_changes
}
}
END FLOW