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Review of Type-Logical Semantics(10)

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One of the many roles of linguistics is to address the semantics of natural languages, that is, the meaning of sentences in natural languages. An important part of the meaning of sentences can be characterized by stating the conditions that need to hold fo

of the book,in terms of originality,compositionality,model theory and grammar fragments.Some caveats apply: he studies models of natural language itself,not models of our knowledge or ability to use language;furthermore, these models are not intended to have any metaphysical interpretation,but are only a description and approximation of natural language.

Chapter2,Simply Typed-Calculus,lays out the basic theory of the simply typed-calculus.The simply typed -calculus provides an elegant solution to the problem of giving a denotation for the basic expressions of a language in a compositional manner,as explained in Chapter3.This chapter concentrates on the basic theory,describing the language of the simply typed-calculus,along with a model theory and a proof theory for the logical language,that formalizes whether two-calculus expressions are equal(have the same denotation in all models).The standard-calculus notions of reductions,normal forms,strong normalization,the Church-Rosser theorem,and combinators are discussed.An extension of the simply typed-calculus with sums and products is described.

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