A logic for conventional implicatures

This chapter presents the technical details of the proposed theory of conventional implicatures, which is based in the lambda calculus. Semantic types play an important role in organizing the logical space into the at-issue and conventional-implicature dimensions. The central rules of semantic composition are presented — those that are particular to this theory and those that are required to achieve a functioning compositional theory. The models for the theory are designed to accommodate basic discourse structures and relations. The chapter ends by discussing some of the major consequences of this general logical apparatus, connecting them to specific features of Grice’s original definition of conventional…