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【正文】 the intuitive sense。del (from 1931) and of the Norwegian mathematician Thoralf Skolem, a pioneer in metalogic (from 1933). The originally intended, or standard, interpretation takes the ordinary nonnegativeintegers {0, 1, 2, . . . } as the domain, the symbols 0 and 1 as denoting zero and one, and the symbols + and del made the fundamental discovery that, in most of the interesting (or significant) formal systems, not all true sentences are theorems. It follows from this finding that semantics cannot be reduced to syntax。 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 1 外文文獻(xiàn)譯文 Syntax and semantics A formal language usually requires a set of formation rules—., a plete specification of the kinds of expressions that shall count as wellformed formulas (sentences or meaningful expressions), applicable mechanically, in the sense that a machine could check whether a candidate satisfies th
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