Dealing with Ambiguities by Underspecification: Construction, Representation and Deduction

In this paper we develop a theory of language meaning that represents scope ambiguities by underspecified structures. The set of possible meanings of a sentence, or text is determined by a set of meta-level constraints that restricts the class of semantic representations appropriately. Thus the way ambiguities are represented does not correspond to any of the usual concepts of formalizing ambiguities by means of disjunctions. A sound and complete proof theory is provided that relates these structures directly, without considering cases.