 Adopting an algebraic perspective Keenan and Faltz (1985) showed that we can capture all these uses identifying disjunction with the join operator in a Boolean algebra (or, simplifying a bit, set union). In the special case of disjunction at the sentence level, the Boolean operator boils down to the classical propositional operator on truth values (see  section 7.1  for a recent account which identifies disjunction with the join operator in a Heyting algebra, which at the sentence level yields a non-classical (inquisitive) propositional operator). As an illustration consider the following interpretation of generalized, cross-categorial or in terms of generalized union, adapted from Gazdar (1980) (see also Winter 2001). The crucial assumption behind this definition is that noun phrases like John or every man denote sets or functions rather than individuals (as in Montague 1973).