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The application of logic to grammar is a fundamental issue in philosophy and has been investigated by such renowned philosophers as Leibniz, Bolzano, Frege, and Husserl. Language and Grammar examines categorial grammars and type-logical grammars, two linguistic theories that play a significant role in this area of study yet have been overshadowed until recently. The prominent scholars contributing to this volume also explore the impact of the Lambek program on linguistics and logical grammar, producing, ultimately, an exciting and important resource that demonstrates how type-logical grammars are promising future models of reasoning and computation.

Mixed category constructions like the English verbal gerund involve words that seem to be central members of more that one part of speech. This poses a problem for the standard view of syntactic categories.

This book presents a novel analysis of this and similar mixed category constructions in languages including Quechua, Tibetan, Arabic, Fijian, Dagaare, and Jacaltec. Under this analysis, Robert P. Malouf shows that verbal gerunds share the selectional properties of verbs and the distributional properties of nouns. He further shows that since different dimensions of grammatical information can vary independently, the behavior of mixed categories creates no paradox. These dimensions are in principle independent. However, certain types of mixed categories are quite common in the world's languages, while others are rare or nonexistent. The book discusses how cross-linguistic variation can be accounted for by a lexical categorial prototype. By stating these prototypes as default constraints in a hierarchy of lexical information, Malouf argues that one can bring insights from cognitive and functional approaches to linguistics into a formal analysis, thus building on the strengths of both approaches.