語(yǔ)法和語(yǔ)義畢業(yè)論文外文翻譯-其他專業(yè)-全文預(yù)覽
【正文】 s the ordinary nonnegativeintegers {0, 1, 2, . . . } as the domain, the symbols 0 and 1 as denoting zero and one, and the symbols + and and “for all ,” symbolized “(?),” are again sentences. [“(?)” is called a quantifier, as is also “there is some ,” symbolized “(?)”.] Since these specifications are concerned only with symbols and their binations and not with meanings, they involve only the syntax of the language. An interpretation of a formal language is determined by formulating an interpretation of the atomic sentences of the language with regard to a domain of objects., by stipulating which objects of the domain are denoted by which constants of the language and which relations and functions are denoted by which predicate letters and function symbols. The truthvalue (whether “true” or “false”) of every sentence is thus determined according to the standard interpretation of logical connectives. For example, p “not,” symbolized “～” 。 thus syntax, which is closely related to proof theory, must often be distinguished from semantics, which is closely related to model theory. Roughly speaking, syntax， as conceived in the philosophy of mathematics， is a branch of number theory, and semantics is a branch of set theory, which deals with the nature and relations of aggregates. Historically, as logic and axiomatic systems became more and more exact, there emerged, in response to a desire for greater lucidity, a tendency to pay greater attention to the syntactic features of the languages employed rather than to concentrate exclusively on intuitive meanings. In this way, logic, the axiomatic method (such as that employ
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