This book revives the study of conventional implicatures in natural language semantics. H. Paul Grice first defined the concept. Since then his definition has seen much use and many redefinitions, but it has never enjoyed a stable place in linguistic theory. Christopher Potts returns to the original and uses it as a key into two presently under-studied areas of natural language: supplements and expressives. The account of both depends on a theory in which sentence meanings can be multidimensional. The theory (...) is logically and intuitively compositional, and it minimally extends a familiar kind of intensional logic, thereby providing an adaptable, highly useful tool for semantic analysis. The result is a linguistic theory that is accessible not only to linguists of all stripes, but also philosophers of language, logicians, and computer scientists who have linguistic applications in mind. (shrink)

This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will (...) be essential reading for all those working in logic & computer science. (shrink)

The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semanticinterpretations can be formalized in linear logic in a way thatcorrectly explains the observed interactions between quantifier scopeambiguity, bound anaphora and intensionality.Our linear-logic formalization of the compositional properties ofquantifying expressions in natural language obviates the need forspecial mechanisms, such as Cooper storage, in representing thescoping possibilities of quantifying expressions. Instead, thesemantic contribution of a quantifier is recorded as a linear-logicformula whose use in a proof will establish the (...) scope of thequantifier. Different proofs can lead to different scopes. In eachcomplete proof, the properties of linear logic ensure thatquantifiers are properly scoped. (shrink)

We review Potts’ influential book on the semantics of conventional implicature (CI), offering an explication of his technical apparatus and drawing out the proposal’s implications, focusing on the class of CIs he calls supplements. While we applaud many facets of this work, we argue that careful considerations of the pragmatics of CIs will be required in order to yield an empirically and explanatorily adequate account.