Taking Scope ─ The Natural Semantics of Quantifiers

In Taking Scope, Mark Steedman considers the syntax and semanticsof quantifier scope in interaction with negation, polarity, coordination, and pronominal binding,among other constructions. The semantics is "surface compositional," in that there is adirect correspondence between syntactic types and operations of composition and types andcompositions at the level of logical form. In that sense, the semantics is in the "naturallogic" tradition of Aristotle, Leibniz, Frege, Russell, and others who sought to define apsychologically real logic directly reflecting natural language grammar.

The bookreunites the generative-transformational tradition initiated by Chomsky--which views the formalsyntactic component as entirely autonomous---with the older, strongly lexicalist, construction-basedtradition, which has sought to define a more lingistically transparent theory of meaningrepresentation. Steedman offers a logical formalism that relates directly to the surface form oflanguage and to the process of inference and proof that it must support. Such a natural logic,although formal by definition, should be allowed to grow organically from attested languagephenomena rather than be axiomatized a priori in terms of any standard logic. Steedman alsoconsiders the application of natural semantic interpretations to practical natural languageprocessing tasks, emphasizing throughout the elimination of traditional quantifiers from semanticformalism in favor of devices such as Skolem terms and structure-sharing among representations inprocessing.

Mark Steedman is Professor of Cognitive Science in the Division of Informatics at the University of Edinburgh. He is the author of Surface Structure and Interpretation (1996) and The Syntactic Process (2000), both published by the MIT Press.