【正文】
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 the requirements. This specification usually contains three parts: (1) a list of primitive symbols (basic units) given mechanically, (2) certain binations of these symbols, singled out mechanically as forming the simple (atomic) sentences, and (3) a set of inductive clauses— inductive inasmuch as they stipulate that natural binations of given sentences formed by such logical connectives as the disjunction “or,” which is symbolized “∨” 。 “not,” symbolized “~” 。 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 q is true if and only if p and q are true. (Here, the dot mean