Mental representations: Reference and definiteness

If D denotes a discourse, and p an expression in an utterance u of D, the action, D(p), of D on p, is the set of mental representations of the interpretations of p in D, and corresponds to the discourse ‘meaning’ of p in D. The correspondence p→D(p) is called the reference of the speaker. The domain, dom(p), is defined, and it is shown that the set i(D(p)) of underlying entities of D(p) is contained in or equal to dom(p). A reference is inclusive if i(D(p)) = dom(p); exclusive otherwise. If dom(p) (resp. i(D(p))) consists of a single entity, the reference is said to be unique (resp. unambiguous). It is shown that definite reference is unique in the classical sense, and it is conjectured that a generalization of the notion of ‘familiarity’ holds. A number of putative counterexamples to the classical definition are shown to satisfy the more general definition. Further application is made to specificity, and parameterized nominals.