 Disjunction and existence properties

A theory has the disjunction property when provability of a closed disjunction implies provability of one disjunct. It has the existence property when a provable existential sentence has a witness whose substitution is provably valid. These are distinct constructive properties; disjunction property of intuitionistic propositional logic is one instance of the former.

Disjunction and existence are concepts that appear in mathematics, logic, and philosophy, often related to the interpretation of statements and claims. ### Disjunction **Definition**: In logic, a disjunction is a compound statement formed using the logical connective "or.