Ellipsis in a Labelled Deduction System
Ruth Kempson · Logic Journal of IGPL · 1995
Using the LDSNL model of utterance interpretation being developed by Gabbay and Kempson (cf. [17, 29, 30]), this paper demonstrates how the dynamics of the proof process adopted explains configurational restrictions imposed on the interpretation of elliptical fragments. The blurring of traditional semantic and syntactic dichotomies in the LDSNL proof-theoretic reconstruction of interpretation successfully provides a basis for predicting the array of variation displayed by different elliptical forms. The logic adopted is a composite system of a type logic nested within a database logic. Two resource-sensitive sub-types of Conditional Introduction form the basis for explaining the ellipsis data. The result is a demonstration of how the simple device of adding labels to an inference system can provide a useful tool not only at the meta-logic level of comparing alternative logic and grammar formalisms, but also at the level of explaining natural language data.