disjunction property
disjunction property
1. For a deductive system , the property that for every disjunctive
-theorem
, either
is theorem of
or
is theorem of
. Most notably, intuitionistic logic enjoys the disjunction property.
2. For a theory and deductive system
, the property holding of
when
only if
or
. The disjunction property is most commonly discussed in the context of intuitionistic logic, e.g., the intuitionistic Heyting Arithmetic
enjoys the disjunction property.