The Role of Deduction Rules in Semantics

The distinction between 'partial ' and 'total ' interpretations (models) is discussed and related to the distinction between proof-theoretical and model-theoretical treatments of logic. It is claimed that there is a parallel between the construction of a proof based on a set of premises and e.g. the production of a natural-language text which is based on information in some kind of data-base. The main part of the paper is devoted to a discussion of the relations between the deduction rules traditionally associated with the existential quantifier and notions pertaining to the theory of reference such as specificity and referentiality / attributivity. Two types of spe-cificity are distinguished, which can be connected with 'Existential Elimination * and 'Existen-tial Introduction', respectively. A distinction is further made between trivial and non-trivial 'Existential Introduction', where only the latter kind involves erasure of 'coreference links.' It is argued that an analogous treatment of the referential-attributive distinction is a way of making sense of Donnellan's suggestion that the latter may depend on the description's role in an argument. Finally, the notions of 'external anchoring ' and 'stability of individual con