Gerhard Jäger. Partial Variables and Specificity, manuscript, University of Potsdam

In this paper I propose a novel analysis of the semantics of specific indefinites. Following standard DRT, I assume that indefinites introduce a free variable into the logical representation, but I assume the the descriptive content of an indefinite DP is interpreted as a precondition of the corresponding variable to denote. Formally this is implemented by an extension of classical predicate logic with partial variables. If a restricted variable is quantified over, the restriction the variable is interpreted as a restriction on the binding quantifier in a syntactically unrestricted way. After an overview over the major existing theories of the scope of indefinites, the central part of the paper is devoted to develop a model-theoretic semantics for this extension of predicate logic. Finally the paper argues that partial variables lends themselves to the analysis of other linguistic phenomena as well. Especially presuppositions can be analyzed as restrictions on variables in a natural way.