《语法和语义毕业论文外文翻译》由会员分享，可在线阅读，更多相关《语法和语义毕业论文外文翻译（9页珍藏版）》请在金锄头文库上搜索。
1、外文文献译文Syntax and semantics A formal language usually requires a set of formation rulesi.e., a complete specification of the kinds of expressions that shall count as well-formed formulas (sentences or meaningful expressions), applicable mechanically, in the sense that a machine could check whether a
2、candidate satisfies the requirements. This specification usually contains three parts: (1) a list of primitive symbols (basic units) given mechanically, (2) certain combinations of these symbols, singled out mechanically as forming the simple (atomic) sentences, and (3) a set of inductive clauses in
3、ductive inasmuch as they stipulate that natural combinations 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 ,” sy
4、mbolized “()”. Since these specifications are concerned only with symbols and their combinations 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 reg
5、ard 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 truth-value (whether “true” or “false”) of every sentence is thus determined accor
6、ding 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 means the conjunction “and,” not the multiplication operation “times.”) Thus, given any interpretation of a formal language, a formal concept of truth is obtained. Tru
7、th, meaning, and denotation are semantic concepts. If, in addition, a formal system in a formal language is introduced, certain syntactic concepts arise namely, axioms, rules of inference, and theorems. Certain sentences are singled out as axioms. These are (the basic) theorems. Each rule of inferen
8、ce is an inductive clause, stating that, if certain sentences are the orems, then another sentence related to them in a suitable way is also atheorem. If p and “either not-p or q” (p q) are theorems, for example, then q is a theorem. In general, a theorem is either an axiom or the conclusion of a ru
9、le of inference whose premises are theorems. In 1931 Gdel 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; thus syntax, which is closely relat
10、ed 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 aggrega
11、tes. 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
12、, logic, the axiomatic method (such as that employed in geometry), and semiotic (the general science of signs) converged toward metalogic.Truth definition of the given languageThe formal system N admits of different interpretations, according to findings of Gdel (from 1931) and of the Norwegian math
13、ematician 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 as standing for ordinary addition and multiplica
14、tion. Relative to this interpretation, itis possible to give a truth definition of the language of N. It is necessary first to distinguish between open and closed sentences. An open sentence, such as x = 1, is one that may be either true or false depending on the value of x, but a closed sentence, s
15、uch as 0 = 1 and (x) (x = 0) or “All xs are zero,” is one that has a definite truth- valuein this case, false (in the intended interpretation). 1. A closed atomic sentence is true if and only if it is true in the intuitive sense; for example, 0 = 0 istrue, 0 + 1 = 0 is false. This specification as i
16、t stands is not syntactic, but, with some care, it is possible to give an explicit and mechanical specification of those closed atomic sentences that are true in the intuitive sense. 2. A closed sentence A is true if and only if A is not true.3. A closed sentence A B is true if and only if either A or B is true. 4. A closed sentence ()A() is true if and only if A() is true for every value of i.e., if A(0), A(
