Disjunction Ontology
Propositional Logic
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Disjunction Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/mathematical-logic-ontologies/propositional-logic/disjunction-ontology.html
FLOW DisjunctionOntology {
DOMAIN:
AI Core
-> Ontologies
-> Mathematical Ontologies
-> Mathematical Logic Ontologies
-> Propositional Logic
-> Disjunction Ontology
PURPOSE:
Represent logical disjunction as a machine-interpretable binary logical connective combining two propositions or formulas into a compound formula that is true, under classical propositional semantics, when at least one operand is true. The ontology models disjunction identity, notation, operands, arity, precedence, associativity, scope, inclusive and exclusive interpretations, truth functions, truth tables, Boolean algebra, proof rules, algebraic equivalences, normal forms, clauses, SAT reasoning, resolution, circuit mappings, natural-language formalisation, non-classical variants, ambiguity, validation, versioning and provenance. It enables AI systems to distinguish inclusive OR from exclusive OR, natural-language alternatives, set union, probability addition, programming operators and nondeterministic choice while preserving the exact semantics of the declared logical system.
ENTITY Disjunction {
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 DisjunctiveFormula {
TYPE: CompoundPropositionalFormula
STRUCTURE:
left_formula
OR
right_formula
}
ENTITY Disjunct {
TYPE: OperandFormula
ROLE:
member_ofdisjunction
}
DISJUNCTION_IDENTITY_MODEL {
canonical_identifier:
OR
arity:
2
classical_default:
inclusive
RULE:
disjunction_identity MUST be distinguished_fromsurface_symbol
}
LOGIC_CONTEXT_MODEL {
default:
classical_propositional_logic
truth_domain:
TRUE
FALSE
RULE:
disjunction_semantics MUST be logic_specific
}
SYMBOL_MODEL {
common:
∨
OR
|
||
RULE:
symbol MUST be resolved_usinglanguage_andnotation
}
ARITY_MODEL {
disjunction:
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:
source_order SHOULD remain_preserved
}
AST_MODEL {
node:
OR
children:
left_operand
right_operand
RULE:
child_count = 2
}
PRECEDENCE_MODEL {
common:
NOT_beforeAND
AND_beforeOR
OR_beforeIMPLIES
RULE:
actual_precedence MUST followdeclared_language
}
ASSOCIATIVITY_PARSE_MODEL {
common:
OR_semantically_associative
RULE:
parser_associativity MUST stillbe explicit
}
PARENTHESIS_MODEL {
examples:
(A OR B) AND C
A OR (B AND C)
RULE:
parentheses determine_scope
}
SCOPE_MODEL {
disjunction:
combines_exact_operand_subtrees
RULE:
scope MUST be resolved_beforeevaluation
}
CLASSICAL_TRUTH_FUNCTION_MODEL {
TT -> TRUE
TF -> TRUE
FT -> TRUE
FF -> FALSE
}
TRUTH_TABLE_MODEL {
rows:
A=TRUE B=TRUE -> A_OR_B=TRUE
A=TRUE B=FALSE -> A_OR_B=TRUE
A=FALSE B=TRUE -> A_OR_B=TRUE
A=FALSE B=FALSE -> A_OR_B=FALSE
}
TRUE_CONDITION_MODEL {
disjunction:
TRUE_ifatleastone_operand_TRUE
}
FALSE_CONDITION_MODEL {
disjunction:
FALSE_iffbothoperands_FALSE
}
INCLUSIVE_OR_MODEL {
A=TRUE
B=TRUE:
A_OR_B=TRUE
RULE:
classical_OR_isinclusive
}
EXCLUSIVE_OR_DISTINCTION_MODEL {
XOR:
TRUE_iffexactlyoneoperand_TRUE
RULE:
OR != XOR
}
COMMUTATIVITY_MODEL {
A OR B
equivalent_to
B OR A
}
ASSOCIATIVITY_MODEL {
(A OR B) OR C
equivalent_to
A OR (B OR C)
}
IDEMPOTENCE_MODEL {
A OR A
equivalent_to
A
}
IDENTITY_MODEL {
A OR FALSE
equivalent_to
A
}
DOMINATION_MODEL {
A OR TRUE
equivalent_to
TRUE
}
COMPLEMENT_MODEL {
A OR NOT A
equivalent_to
TRUE
}
ABSORPTION_MODEL {
A OR (A AND B)
equivalent_to
A
}
DISTRIBUTIVITY_OVER_AND_MODEL {
A OR (B AND C)
equivalent_to
(A OR B) AND (A OR C)
}
AND_DISTRIBUTIVITY_OVER_OR_MODEL {
A AND (B OR C)
equivalent_to
(A AND B) OR (A AND C)
}
DE_MORGAN_MODEL {
NOT(A OR B)
equivalent_to
NOT A AND NOT B
}
NEGATED_CONJUNCTION_MODEL {
NOT A OR NOT B
equivalent_to
NOT(A AND B)
}
IMPLICATION_LINK_MODEL {
A -> B
equivalent_to
NOT A OR B
RULE:
material_implication_mapping_isclassical
}
DISJUNCTIVE_SYLLOGISM_MODEL {
premises:
A OR B
NOT A
conclusion:
B
RULE:
exact_validity depends_onlogic
}
DISJUNCTION_INTRODUCTION_LEFT_MODEL {
premise:
A
conclusion:
A OR B
}
DISJUNCTION_INTRODUCTION_RIGHT_MODEL {
premise:
B
conclusion:
A OR B
}
DISJUNCTION_ELIMINATION_MODEL {
premises:
A OR B
derivation_ofC_fromA
derivation_ofC_fromB
conclusion:
C
RULE:
case_assumptions MUST be tracked_anddischarged
}
PROOF_BY_CASES_MODEL {
cases:
A
B
premise:
A OR B
requirement:
derive_sameconclusion_fromeachcase
RULE:
disjunction_elimination_formalises_case_reasoning
}
NATURAL_DEDUCTION_MODEL {
introduction:
inferA_OR_B_fromA
inferA_OR_B_fromB
elimination:
proof_bycases
RULE:
proof_system MUST be identified
}
SEQUENT_RIGHT_RULE_MODEL {
possible_classical:
Gamma |- A,Delta
therefore Gamma |- A_OR_B,Delta
RULE:
exact_rule depends_onsequent_calculus
}
SEQUENT_LEFT_RULE_MODEL {
representative:
Gamma,A |- C
Gamma,B |- C
therefore Gamma,A_OR_B |- C
RULE:
context_structure MUST be preserved
}
BOOLEAN_ALGEBRA_MODEL {
OR:
join_orBoolean_sum
identities:
A_OR_0=A
A_OR_1=1
A_OR_A=A
}
BOOLEAN_ADDITION_DISTINCTION_MODEL {
Boolean_OR:
1_OR_1=1
arithmetic_addition:
1+1=2
RULE:
Boolean_sum != arithmetic_addition
}
SET_UNION_MODEL {
undercharacteristic_mapping:
OR corresponds_tounion
RULE:
logical_disjunction != set_union_byidentity
}
EVENT_UNION_MODEL {
event:
A_union_B
proposition:
A_occurs_OR_B_occurs
RULE:
event_union_andlogical_OR_arelinked_butdifferent_entity_types
}
PROBABILITY_DISTINCTION_MODEL {
P(A OR B):
P(A)+P(B)-P(A AND B)
RULE:
probability_combination != logical_OR_truth_function
}
MUTUALLY_EXCLUSIVE_EVENT_MODEL {
if:
A_andB_cannotbothoccur
then:
P(A OR B)=P(A)+P(B)
RULE:
mutual_exclusivity_isprobabilistic_orsemantic_condition_notdefinition_ofOR
}
CAUSAL_DISTINCTION_MODEL {
A OR B:
alternative_truth_condition
RULE:
disjunction_doesnotassertcausal_relation
}
TEMPORAL_DISTINCTION_MODEL {
A OR B:
atleastsone_true_insemantic_context
RULE:
OR_doesnotencodebefore_after
}
PROGRAMMING_OR_MODEL {
possible:
logical_OR
short_circuit_OR
RULE:
programming_operator MAY includeevaluation_strategy
}
SHORT_CIRCUIT_OR_MODEL {
if_left_true:
right_operand_maynotbeevaluated
RULE:
evaluation_strategy != truth_function
}
BITWISE_OR_DISTINCTION_MODEL {
bit_vectors:
componentwise_OR
RULE:
bitwise_OR != propositional_disjunction_withoutBoolean mapping
}
DATABASE_OR_MODEL {
SQL:
mayoperate_withTRUE_FALSE_UNKNOWN
RULE:
SQL_OR != classical_OR_whenNULL_present
}
MULTIARY_DISJUNCTION_MODEL {
form:
OR(A_1,...,A_n)
true_iff:
atleastoneoperand_TRUE
RULE:
n_ary_extension SHOULD be linked_toiterated_binary_OR
}
EMPTY_DISJUNCTION_MODEL {
zero_operands:
FALSE_understandard_algebraic_convention
RULE:
convention MUST be declared
}
SINGLETON_DISJUNCTION_MODEL {
one_operand:
equivalent_tooperand
}
FLATTENING_MODEL {
nested:
A OR (B OR C)
flattened:
OR(A,B,C)
RULE:
valid_whenassociativity_supported
}
DISJUNCT_SET_MODEL {
flattened_disjunction:
collection_ofdisjuncts
RULE:
set_representation_safe_onlywhencommutativity_associativity_idempotence_apply
}
DUPLICATE_DISJUNCT_MODEL {
A OR A:
simplify_toA
}
FALSE_DISJUNCT_MODEL {
A OR FALSE:
removeFALSE
}
TRUE_DISJUNCT_MODEL {
A OR TRUE:
simplify_entireformula_toTRUE
}
COMPLEMENTARY_DISJUNCTS_MODEL {
contains:
A
NOT A
result:
TRUE_underclassical_semantics
}
CNF_MODEL {
clause:
disjunction_ofliterals
RULE:
OR_isinner_combiner_withineachclause
}
CLAUSE_MODEL {
structure:
L_1 OR ... OR L_n
true_if:
atleastone_literal_TRUE
}
EMPTY_CLAUSE_MODEL {
zero_literals:
FALSE
RULE:
empty_clause_representscontradiction_inCNF
}
UNIT_CLAUSE_MODEL {
one_literal:
disjunction_ofsingleliteral_equivalent_toliteral
}
TAUTOLOGICAL_CLAUSE_MODEL {
contains:
p
NOT p
result:
TRUE
}
CLAUSE_SUBSUMPTION_MODEL {
if:
literals(C) subset literals(D)
then:
D_isredundant_inCNF_containingC
RULE:
set_based_clause_semantics assumed
}
DNF_MODEL {
top_level:
disjunction_ofconjunctive_terms
}
DNF_TERM_SELECTION_MODEL {
formula:
TRUE_ifatleastone_term_TRUE
}
CANONICAL_DNF_MODEL {
construction:
OR_ofminterms_corresponding_toTRUE_truth_table_rows
}
SAT_MODEL {
disjunctive_clause:
satisfied_ifatleastone_literal_TRUE
}
SAT_CLAUSE_MODEL {
clause:
disjunction_ofliterals
RULE:
clause_unsatisfied_onlyifallliterals_FALSE
}
UNIT_PROPAGATION_LINK_MODEL {
clause:
allbutone_literal_FALSE
result:
remaining_literal_mustbeTRUE
}
RESOLUTION_MODEL {
premises:
C OR p
D OR NOT p
resolvent:
C OR D
RULE:
complementary_literals MUST shareunderlyingvariable
}
RESOLUTION_CLAUSE_MODEL {
OR:
fundamental_clause_combiner
RULE:
resolution_operates_onsets_orsequences_ofliterals_underdeclared representation
}
TSEITIN_ENCODING_MODEL {
auxiliary:
z <-> (A OR B)
CNF_constraints:
z OR NOT A
z OR NOT B
NOT z OR A OR B
RULE:
encoding_isclassically_equisatisfiable_withsource_whencombinedappropriately
}
BDD_MODEL {
disjunction:
Boolean_apply_OR_toBDD_A_andBDD_B
RULE:
variable_order MUST be compatible
}
CIRCUIT_MODEL {
disjunction:
OR_gate
}
OR_GATE_MODEL {
output_high:
ifatleastoneBoolean_input_high
RULE:
physical_signal_encoding MUST be declared
}
TRUTH_VECTOR_MODEL {
A_OR_B:
pointwise_OR_oftruth_vectors_A_B
RULE:
commonvaluation_order REQUIRED
}
SEMANTIC_EQUIVALENCE_MODEL {
disjunction_formulas:
equivalent_iftruth_vectors_identical
}
SATISFIABILITY_MODEL {
A_OR_B:
satisfiable_ifA_satisfiable_orB_satisfiable
RULE:
classical semantics
}
UNSATISFIABILITY_MODEL {
A_OR_B:
unsatisfiable_iffA_unsatisfiable_andB_unsatisfiable
}
VALIDITY_MODEL {
A_OR_B:
may_bevalid_evenifneitherA_norB_individuallyvalid
example:
A OR NOT A
RULE:
validity_requiresallvaluations
}
MODEL_UNION_MODEL {
Models(A_OR_B):
Models(A) union Models(B)
}
COUNTERMODEL_MODEL {
A_OR_B_false:
valuation_whereA_FALSE_andB_FALSE
}
SUBSUMPTION_SEMANTIC_MODEL {
if:
A entails B
then:
A OR B equivalent_to B
RULE:
entailment_context MUST be established
}
REDUNDANT_DISJUNCT_MODEL {
disjunct_A:
redundant_ifA_entails_other_disjunction
RULE:
redundancy_requiressemantic_orformalproof
}
DISJUNCTION_SIMPLIFICATION_MODEL {
operations:
flatten
removeFALSE
collapseTRUE
remove_duplicates
detectcomplements
removeentailed_disjuncts_whenproven
RULE:
simplification MUST preserveequivalence
}
FACTORISATION_MODEL {
(A OR B) AND (A OR C):
equivalent_to
A OR (B AND C)
}
CASE_SPLITTING_MODEL {
proof_orsearch:
branch_onA_orB
RULE:
search_branching != semantic_XOR
}
NONDETERMINISTIC_CHOICE_DISTINCTION_MODEL {
computational_choice:
chooseonebranch
logical_OR:
truth_condition_overalternatives
RULE:
nondeterministic_choice != disjunction_byidentity
}
NATURAL_LANGUAGE_DISJUNCTION_MODEL {
cues:
or
either
alternatively
RULE:
natural_language_OR MAY beinclusive_orexclusive
}
EITHER_OR_MODEL {
phrase:
either_A_or_B
possible:
inclusive_OR
XOR
RULE:
context_required
}
INCLUSIVE_LANGUAGE_MODEL {
cues:
A_orB_orboth
formal:
A OR B
}
EXCLUSIVE_LANGUAGE_MODEL {
cues:
eitherA_orB_butnotboth
exactlyoneofA_B
formal:
A XOR B
}
FREE_CHOICE_OR_MODEL {
natural_language:
"You may take tea or coffee"
RULE:
pragmatic_permission_reading MAY differ_fromtruth_functional_OR
}
ALTERNATIVE_QUESTION_MODEL {
natural_language:
"Is it A or B?"
RULE:
interrogative_alternative != asserted_disjunction_necessarily
}
OR_SCOPE_AMBIGUITY_MODEL {
example:
A AND B OR C
candidates:
(A AND B) OR C
A AND (B OR C)
RULE:
resolveusinggrammar_precedence_orparentheses
}
NEGATION_SCOPE_MODEL {
NOT(A OR B):
equivalent_to
NOT A AND NOT B
compare:
(NOT A) OR B
RULE:
scope_issemanticallymaterial
}
CONDITIONAL_OR_MODEL {
natural_language:
"A or else B"
RULE:
maycarryconditional_warning_orpragmatic_relation_beyondOR
}
DISCOURSE_OR_MODEL {
natural_language:
mayindicatecorrection_reformulation_oralternative
RULE:
discourse_relation SHOULD be preserved
}
FORMALISATION_MODEL {
source:
natural_language_alternative
target:
candidate_OR_orXOR_formula
metadata:
operand_spans
inclusivity
scope
confidence
RULE:
preserveoriginal_text_andinterpretive_choices
}
FORMALISATION_CONFIDENCE_MODEL {
confidence:
support_forOR_vsXOR_andoperand_scope
RULE:
confidence != truth
}
INTUITIONISTIC_DISJUNCTION_MODEL {
proof_meaning:
proof_ofA_OR_B_containsproof_ofone_disjunct_pluswhich_disjunct
RULE:
constructive_disjunction_property_m
ayhold_inappropriate_systems
}
PARACONSISTENT_DISJUNCTION_MODEL {
semantics:
logic_specific
RULE:
classical_disjunctive_syllogism MAY fail_insomeparaconsistent_logics
}
MANY_VALUED_DISJUNCTION_MODEL {
truth_domain:
morethan2values
operation:
logic_specific
RULE:
classical_OR_table MUST notbeassumed
}
FUZZY_DISJUNCTION_MODEL {
operation:
t_conorm
examples:
maximum
probabilistic_sum
Lukasiewicz_t_conorm
RULE:
t_conorm MUST be identified
}
THREE_VALUED_DISJUNCTION_MODEL {
truth_domain:
threevalues
RULE:
truth_table depends_onchosenlogic
}
SQL_DISJUNCTION_MODEL {
values:
TRUE
FALSE
UNKNOWN
RULE:
SQL_OR_withNULL_requires_three_valued_semantics
}
RESOURCE_SENSITIVE_DISJUNCTION_MODEL {
linear_logic:
additive_andmultiplicative_disjunction_likeoperators
RULE:
classical_OR_mapping requiresformaltranslation
}
LINEAR_LOGIC_PLUS_DISTINCTION_MODEL {
plus:
additive_disjunction
par:
multiplicative_disjunction
RULE:
operators_have distinctproof_semantics
}
MODAL_SCOPE_MODEL {
compare:
box(A OR B)
boxA OR boxB
RULE:
equivalence_notgenerallyautomatic
}
TEMPORAL_SCOPE_MODEL {
compare:
eventually(A OR B)
eventuallyA OR eventuallyB
RULE:
temporal_semantics MUST be declared
}
QUANTIFIER_SCOPE_MODEL {
predicate_logic:
existsx(P(x) OR Q(x))
RULE:
interaction_withquantifiers requirespredicate_logic_context
}
ERROR_MODEL {
possible:
missing_operand
wrongarity
scope_error
OR_XOR_confusion
symbol_collision
invalid_truth_function
invalid_simplification
RULE:
error SHOULD identifyformula_position_andlogic
}
AMBIGUITY_MODEL {
possible:
inclusive_vs_exclusive
operand_scope
symbol
natural_language_alternative
nonclassical_semantics
RULE:
unresolved_ambiguity MUST be preserved
}
VALIDATION_MODEL {
checks:
disjunction_identifier
logic_system
arity
operands
scope
AST
truth_function
OR_XOR_distinction
equivalence_rules
proof_rules
semantic_context
RULE:
validation MUST be logic_specific
}
EXPLAINABILITY_MODEL {
output:
operands
OR_operator
inclusive_or_exclusive_status
operand_truth_values
result
equivalent_forms
proof_rules
RULE:
explanation SHOULD exposeatleastoneTRUE_condition
}
VERSION_MODEL {
versioned:
disjunction_semantics
logic_system
notation
proof_rules
ontology
RULE:
historical_results MUST preserveversions
}
PROVENANCE_MODEL {
fields:
source
formula
parser
logic_system
transformation
proof
version
agent
RULE:
disjunction_record MUST remainprovenance_linked
}
INTEROPERABILITY_MODEL {
exchange:
canonical_OR_identifier
left_operand_AST
right_operand_AST
inclusive_status
symbol
truth_function
logic_system
version
provenance
RULE:
plain_word_or_isnotlossless
}
KNOWLEDGE_GRAPH_MODEL {
nodes:
disjunction
disjunct
formula
truth_value
clause
proof_rule
circuit_gate
edges:
HAS_DISJUNCT
COMBINES
EQUIVALENT_TO
SATISFIED_BY
DERIVED_BY
IMPLEMENTED_BY
RESOLVES_WITH
RULE:
OR_XOR_andimplementation_relations MUST be typed
}
RELATIONSHIPS {
Disjunction -> IS_A -> BinaryLogicalConnective
Disjunction -> HAS_LEFT_OPERAND -> Formula
Disjunction -> HAS_RIGHT_OPERAND -> Formula
DisjunctiveFormula -> CONTAINS -> Disjunct
Disjunction -> HAS_TRUTH_FUNCTION -> ClassicalInclusiveOR
Disjunction -> MAY_HAVE -> IntroductionRule
Disjunction -> MAY_HAVE -> EliminationRule
Clause -> COMBINES -> LiteralsByDisjunction
Disjunction -> MAY_MAP_TO -> ORGate
}
SEMANTIC_EQUIVALENCE {
"disjunction" ~= binary_logical_connective_true_whenatleastoneoperand_true_underclassical_semantics
"inclusive OR" ~= disjunction_allowingbothoperands_tobetrue
"disjunct" ~= operand_formula_withindisjunction
disjunction != XOR
disjunction != arithmetic_addition
disjunction != set_union_byidentity
disjunction != probability_addition
disjunction != causal_alternative
disjunction != nondeterministic_choice
logical_OR != programming_short_circuit_OR
logical_OR != bitwise_OR
logical_OR != SQL_OR_withNULL_withoutmapping
natural_language_or != inclusive_logical_OR_necessarily
semantic_confidence != truth_value
}
CONSTRAINTS {
canonical_disjunction_identifier_must_be preserved = true
logic_system_andversion_must_be identified = true
binary_disjunction_must_haveexactly_two_operands = true
operand_ASTs_andscope_must_be preserved = true
classical_disjunction_true_ifatleastoneoperand_true = true
inclusive_OR_andXOR_must_be explicitlydistinguished = true
commutativity_associativity_idempotence_identity_anddomination_rules_must_be logic_specific = true
disjunction_introduction_andelimination_rules_must_preserveproof_context = true
programming_bitwise_SQL_probability_set_andchoice_semantics_must_be distinguished = true
natural_language_OR_ambiguity_must_be preserved = true
nonclassical_disjunction_must_defineitsown_semantics = true
provenance_must_be preserved = true
}
DISJUNCTION_RECORD_MODEL {
RECORD:
disjunction_identifier
logic_system_identifier
logic_version
notation_profile
symbol
inclusive_or_exclusive_status
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
clause_role
DNF_role
SAT_role
resolution_role
introduction_rules
elimination_rule
circuit_mapping
natural_language_source
ambiguity_status
formalisation_confidence
version
provenance
RULE:
disjunction_record MUST support_reconstruction_ofoperands_inclusivity_scope_truth_semantics_proof_rules_andprovenance
}
REASONING_RULES {
IF disjunction_expression_received
THEN identifylogic_andnotation
resolvecanonical_OR
parseleft_andright_operands
validatearity_andscope
IF classical_operand_values_available
THEN returnFALSE_onlyifbothFALSE
elseTRUE
IF natural_language_or_received
THEN identifyoperand_spans
determineinclusive_XOR_orotherdiscourse_reading
preserveambiguity_ifunresolved
IF disjunction_nested
AND associativity_supported
THEN mayflatten_whilepreservinglineage
IF simplification_requested
THEN applyidentity_domination_idempotence_complement_absorption_orentailed_disjunct_rules_onlywhenvalidated
IF clause_used_inSAT
THEN requireatleastone_literal_TRUE
propagateunit_literal_whenallothersFALSE
IF resolution_requested
THEN identifycomplementary_literals
constructresolvent
preserveparent_clause_provenance
IF proof_bycases_requested
THEN verifydisjunction_premise
verifyeachcase_derivessameconclusion
trackassumption_discharge
IF nonclassical_logic_selected
THEN loadlogic_specific_disjunction_semantics_andproof_rules
IF semantics_orlogic_version_changes
THEN preservehistorical_record
revalidatecurrent_equivalences_proofs_clauses_andSAT_encodings
}
VALIDATION {
CHECK disjunction_identifier
CHECK logic_system
CHECK logic_version
CHECK symbol
CHECK arity
CHECK inclusive_exclusive_status
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 clause_role
CHECK DNF_role
CHECK SAT_role
CHECK resolution
CHECK introduction_rules
CHECK elimination_rule
CHECK circuit_mapping
CHECK natural_language_mapping
CHECK nonclassical_semantics
CHECK ambiguity
CHECK formalisation_confidence
CHECK version
CHECK provenance
}
CONFIDENCE {
disjunction_identity_confidence: 1.00
operand_scope_confidence: 1.00
inclusive_OR_confidence: 1.00
classical_truth_function_confidence: 1.00
equivalence_rule_confidence: 1.00
proof_rule_confidence: 1.00
SAT_resolution_confidence: 1.00
natural_language_OR_confidence: 0.94
nonclassical_semantics_confidence: 0.98
RULE:
confidence decreases when logic, notation, OR_vsXOR status,
operand scope, natural-language context, proof system,
nonclassical operation, version orprovenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_disjunction:
assign_orresolve_identifier
attachlogic_andnotation
parseoperands
resolveinclusive_status
validate_semantics
preserveprovenance
compute_FLOW_HASH
ON simplification_ortransformation:
preserve_source_formula
applyvalidated_rule
recordtarget_andsemantic_basis
ON proof_orresolution_usage:
attachproof_context_orparentclauses
preserveverification_status
ON semantic_revision:
preserveprevious_disjunction_definition
registernewversion
revalidateequivalences_anddependentartifacts
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Disjunction
canonical_role: BinaryLogicalConnective
interpretation_order:
identify_logic_system
identify_OR_symbol_orlinguisticcue
resolvecanonical_disjunction_identifier
determineinclusive_or_exclusive_status
parseleft_andright_operand_ASTs
resolveprecedence_parentheses_andscope
validatebinary_arity
resolveclassical_orlogic_specific_truth_function
evaluateunderprovidedvaluation
identifyalgebraic_equivalences_andDeMorgan_relation
identifyclause_DNF_SAT_andresolution_roles
resolveintroduction_elimination_andproof_bycases_rules
distinguishlogical_OR_fromXOR_programming_bitwise_SQL_probability_set_andchoice_relations
resolve_natural_language_alternative_anddiscourse_relation
detectambiguity
assignsemantic_confidence
preserveversions_andprovenance
emit_machine_resolvable_disjunction_structure
ambiguity_controls:
distinguish_disjunction_fromXOR
distinguish_disjunction_fromarithmetic_addition
distinguish_disjunction_fromset_union_byidentity
distinguish_disjunction_fromprobability_addition
distinguish_disjunction_fromcausal_alternative
distinguish_disjunction_fromnondeterministic_choice
distinguish_logical_OR_fromprogramming_short_circuit_OR
distinguish_logical_OR_frombitwise_OR
distinguish_logical_OR_fromSQL_OR_withNULL_withoutmapping
distinguish_natural_language_or_frominclusive_logical_OR_necessarily
distinguish_semantic_confidence_fromtruth_value
preserve_logic_inclusivity_operands_AST_scope_truth_function_rules_version_andprovenance
}
PROVENANCE {
ontology_scope:
disjunction_OR_inclusive_exclusive_semantics_clauses_resolution_proof_rules_natural_language_andAI_interpretation
parent_path:
AI Core
-> Ontologies
-> Mathematical Ontologies
-> Mathematical Logic Ontologies
-> Propositional Logic
-> Disjunction Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
disjunction_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
inclusive_OR_model
exclusive_OR_distinction_model
commutativity_model
associativity_model
idempotence_model
identity_model
domination_model
complement_model
absorption_model
distributivity_over_AND_model
AND_distributivity_over_OR_model
De_Morgan_model
negated_conjunction_model
implication_link_model
disjunctive_syllogism_model
disjunction_introduction_left_model
disjunction_introduction_right_model
disjunction_elimination_model
proof_by_cases_model
natural_deduction_model
sequent_right_rule_model
sequent_left_rule_model
Boolean_algebra_model
Boolean_addition_distinction_model
set_union_model
event_union_model
probability_distinction_model
mutually_exclusive_event_model
causal_distinction_model
temporal_distinction_model
programming_OR_model
short_circuit_OR_model
bitwise_OR_distinction_model
database_OR_model
multiary_disjunction_model
empty_disjunction_model
singleton_disjunction_model
flattening_model
disjunct_set_model
duplicate_disjunct_model
false_disjunct_model
true_disjunct_model
complementary_disjuncts_model
CNF_model
clause_model
empty_clause_model
unit_clause_model
tautological_clause_model
clause_subsumption_model
DNF_model
DNF_term_selection_model
canonical_DNF_model
SAT_model
SAT_clause_model
unit_propagation_link_model
resolution_model
resolution_clause_model
Tseitin_encoding_model
BDD_model
circuit_model
OR_gate_model
truth_vector_model
semantic_equivalence_model
satisfiability_model
unsatisfiability_model
validity_model
model_union_model
countermodel_model
subsumption_semantic_model
redundant_disjunct_model
disjunction_simplification_model
factorisation_model
case_splitting_model
nondeterministic_choice_distinction_model
natural_language_disjunction_model
either_OR_model
inclusive_language_model
exclusive_language_model
free_choice_OR_model
alternative_question_model
OR_scope_ambiguity_model
negation_scope_model
conditional_OR_model
discourse_OR_model
formalisation_model
formalisation_confidence_model
intuitionistic_disjunction_model
paraconsistent_disjunction_model
many_valued_disjunction_model
fuzzy_disjunction_model
three_valued_disjunction_model
SQL_disjunction_model
resource_sensitive_disjunction_model
linear_logic_plus_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
disjunction_record_model
reasoning_rules
validation
confidence_model
update_model
AI_consumption_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
disjunction_identity_logic_system_orsymbol_mapping_changes
inclusive_OR_XOR_operand_scope_precedence_orAST_changes
classical_truth_function_ortruth_table_changes
commutativity_associativity_distribution_absorption_orDeMorgan_changes
proof_rule_case_reasoning_orsemantic_relation_changes
clause_CNF_DNF_SAT_resolution_Tseitin_BDD_orcircuit_semantics_change
programming_bitwise_SQL_probability_set_choice_orcausal_distinctions_change
natural_language_OR_orformalisation_changes
nonclassical_intuitionistic_paraconsistent_manyvalued_orfuzzy_disjunction_changes
disjunction_record_changes
constraint_model_changes
reasoning_rule_changes
version_orprovenance_changes
}
}
END FLOW