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.
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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.