Contrast and Implication in Natural Language

In this paper we introduce a theoretical framework and a logical application for analyzing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of both contrastive conjunctions and indicative conditionals. Following previous proposals, conditions on contrast in a conjunction are analyzed as presuppositions of the conjunction. Further linguistic evidence leads to a distinction between restrictive and non-restrictive connectives of contrast, and consequently between direct and indirect contrast, which are given a precise definition. A general interface for a theory of contrast using possible world semantics for implication is then presented. As a test case, we show how this interface is applicable to the semantics for conditionals that was introduced by Veltman in his article "Data Semantics and the Pragmatics of Indicative Conditionals" (1986). This application yields an extension of Veltman’s Data Logic, called Contrastive Data Logic. Once appropriate modifications are added to Veltman’s pragmatic considerations, we show that contrastive data logic provides an adequate tool for the analysis of substantial linguistic data concerning contrast and implication in natural language.