An unbound variable x differs from a constant in allowing different individual instantiations. Unlike a constant, it does not represent a particular individual element, but any of a set of individual elements. Languages provide a set of constructions which explicitly leave the instantiation of a variable open. Apart from indefinite proforms in general, these include the conditional construction, as in , and the interrogative construction, as in and .

In a conditional construction like and a polar interrogative like , the speaker presupposes a positive and a negative version of the proposition coded by the conditional or interrogative clause: ‘you went to the cinema or you did not go to the cinema’, or generally: p ∨ ¬p. In the case of such a disjunction, a propositional variable may be posited which assumes two values, thus ranging over the alternate instantiations.

The content interrogative clause contains an indefinite proform making explicit the fact that the variable x may be replaced by any of a set of constants. In , the disjunction presupposed might be spelled out as ‘you went to the cinema or you went to the theater or you went to the club or you went to ...’. The set of possible places is potentially infinite. Thus, generally: x ϵ x1 ∨ x ϵ xi ... ∨ x ϵ xn.

The disjunctive basis of interrogative clauses is described in the corresponding article. Likewise, in a conditional construction, the speaker does not commit to either of the alternatives, but only makes an agreement with the interlocutor to hypothetically posit one of the two disjuncts as a proposition in the universe of discourse and to proceed on this basis.

An unbound variable in a construction admits of a set of instantiations. Some linguistic constructions presuppose the disjunction of these instantiations. Now the presupposition of a disjunction that exhausts the logical possibilities is as informative as no presupposition. In the case of conditional and interrogative clauses, the presence of such a disjunction in the presupposition can be proved because the assertion presupposes it. In their assertion, these constructions mark by some grammatical device the fact that no individual instantiation is being chosen – that the disjunction is not resolved. Conjunctions like if and whether mark a binary disjunction; indefinite and interrogative proforms like who, what, where ... mark an infinite disjunction. On this account, constructions with a disjunctive presupposition may be subsumed, as a specific subtype, under the concept of ‘open proposition’.