語法和語義 畢業(yè)論文外文翻譯

1、<p><b>　　外文文獻譯文</b></p><p>　　Syntax and semantics</p><p>　　A formal language usually requires a set of formation rules—i.e., a complete specification of the kinds of expressions

2、 that shall count as well-formed formulas (sentences or meaningful expressions), applicable mechanically, in the sense that a machine could check whether a candidate satisfies the requirements. This specification usually

3、 contains three parts: (1) a list of primitive symbols (basic units) given mechanically, (2) certain combinations of these symbols, singled out mechanically as fo</p><p>　　An interpretation of a formal langu

4、age 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 an

5、d 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 according to the standard interpretation of

6、logical connectives. For</p><p>　　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

7、are singled out as axioms. These are (the basic) theorems. Each rule of inference is an inductive clause, stating that, if certain sentences are the orems, then another sentence related to them in a suitable way is also

8、atheorem. If p and “either not-p or q” (～p ∨ q) are theorems, for example, then q is a theorem. In general, </p><p>　　In 1931 Gödel made the fundamental discovery that, in most of the interesting (or s

9、ignificant) 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 related to proof theory, must often be distinguished

10、 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 </p><p>　　H

11、istorically, 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

12、 rather than to concentrate exclusively on intuitive meanings. In this way, logic, the axiomatic method (such as that employed in geometry), and semiotic (the general science of signs) converged toward metalogic.</p&

13、gt;<p>　　Truth definition of the given language</p><p>　　The formal system N admits of different interpretations, according to findings of Gödel (from 1931) and of the Norwegian mathematician Th

14、oralf 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,

15、 and the symbols + and · as standing for ordinary addition and multiplication. Relative to this interpretation, itis possible to give a truth </p><p>　　It is necessary first to distinguish between open

16、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, such as 0 = 1 and (?x) (x = 0) or “All x's are zero,” is one that has

17、 a definite truth-value—in this case, false (in the intended interpretation).</p><p>　　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 =

18、 0 is false.</p><p>　　This specification as it 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

19、the intuitive sense.</p><p>　　2. A closed sentence ～A is true if and only if A is not true.</p><p>　　3. A closed sentence A ∨ B is true if and only if either A or B is true.</p><p>

20、　　4. A closed sentence (?ν)A(ν) is true if and only if A(ν) is true for every value of ν—i.e., if A(0), A(1), A(1 + 1), . . . are all true.</p><p>　　The above definition of truth is not an explicit definitio

21、n; it is an inductive one. Using concepts fromset theory, however, it is possible to obtain an explicit definition that yields a set of sentences that consists of all the true ones and only them. If Gödel's meth

22、od of representing symbols and sentences by numbers is employed, it is then possible to obtain in set theory a set of natural numbers that are just the Gödel numbers of the true sentences of N.</p><p>　

23、　There is a definite sense in which it is impossible to define the concept of truth within a language itself. This is proved by the liar paradox: if the sentence “I am lying,” or alternatively</p><p>　　(1)

24、This sentence is not true.</p><p>　　is considered, it is clear—since (1) is “This sentence”—that if (1) is true, then (1) is false; on the other hand, if (1) is false, then (1) is true. In the case of the sy

25、stem N, if the concept of truth were definable in the system itself, then (using a device invented by Gödel) it would be possible to obtain in“ N ”a sentence that amounts to (1) and that thereby yields a contradicti

26、on.</p><p><b>　　外文文獻原文</b></p><p><b>　　語法和語義</b></p><p>　　一份正式的語言通常需要一套形成,齊全的規(guī)格的種類中,作為規(guī)范的表達方式,要計算公式(句子或有意義的表達),適用的機械,在這個意義上說,機器就會檢查是否滿足要求的候選人。本規(guī)格書通常包含三個部分:(1

27、)一個列表的原始的符號(基本單元)給機械,(2)特定的組合,這些符號,特別強調(diào)了機械成形(原子)的簡單句子,以及(3)一組感應(yīng)條款-感應(yīng)鑒于二者規(guī)定自然的組合形成的語態(tài)句這樣的邏輯篇章脫節(jié).因為這些規(guī)格是只關(guān)心與符號及其組合,而不是與意義,他們僅僅包括語法的語言。</p><p>　　語言的一個解釋是由一個正式制定的解釋語言的原子句關(guān)于某個領(lǐng)域的objects.,通過規(guī)定哪些物體的領(lǐng)域得到用這常數(shù)之語言與這關(guān)系和

28、功能是通過引入,謂詞的字母和功能的符號。(是否的應(yīng)著重于“對”或“否”)的每一個句子是按照這樣的標(biāo)準解釋邏輯篇章。例如,p?問是真的,當(dāng)且僅當(dāng)p和q是真實的。(在這里,點手段的結(jié)合”,“不是一個令人討厭的乘法運算”的時代。)因此,給出任何解釋一套正式的語言,一種是真理的形式概念設(shè)計提供了依據(jù)。真理、意義以及外延是語義的概念。</p><p>　　此外,如果一個正式的制度形式語言的概念,介紹了某種特定的句法規(guī)則,公

29、理,即產(chǎn)生的推論,和定理。某些句子都是選作公理系統(tǒng)。這些都是(基本)定理。每一個規(guī)則的推理是一種感應(yīng)條款,說明,如果某些句子相似定理,然后另一個句子與他們相關(guān)的是在一種合適的方式也atheorem。如果p和q”或“要么not-p～p∨(q)是定理,舉個例子,然后問是一個定理。一般來說,一個定理要么是一個公理或結(jié)論法治的推理的前提定理。</p><p>　　1931年哥德爾做出了基本的發(fā)現(xiàn),在大部分的有趣(或重要)

30、正規(guī)制度,并不是所有真正的句子都是定理。有發(fā)現(xiàn),不可能被簡化到句法語義語法,這是,因此密切相關(guān)理論,常常需要證明,這是區(qū)別于語義模型理論密切相關(guān)。大致來說,語法,作為孕育于哲學(xué)的一個分支,是數(shù)學(xué)數(shù)論、和語義集合論的一個分支,這涉及到自然及兩者的關(guān)系蘊。</p><p>　　從歷史上看,邏輯和公理系統(tǒng)變得越來越精確,出現(xiàn)了,這是為了回應(yīng)明朗了,想要更多地傾向于更加關(guān)注人的句法特點的語言雇傭而不是專注于直觀的意義。通

31、過這種方式,邏輯,在公理化方法(如,雇用了幾何),和符號(一般科學(xué)向元邏輯)聚合的跡象。</p><p><b>　　給定語言的真理定義</b></p><p>　　正式制度N承認的不同的解釋,根據(jù)調(diào)查結(jié)果,從1931年拍攝)和哥德爾(挪威數(shù)學(xué)家Thoralf先驅(qū)、斯柯林元邏輯(從1933年)。原本打算的,或者標(biāo)準的,普通的解釋體制{ 0、1、2、。。。}是本領(lǐng)域,0

32、和1作為符號表示零的一個,和標(biāo)志+和?成站立為普通的加法和乘法。相對于這個解釋的話,那么可以比較真實的語言定義的N。</p><p>　　有必要先區(qū)分開啟和關(guān)閉的句子。一個開放的句子,如x = 1,是一種,可能為真或假根據(jù)x的價值,而是一種封閉的句子,如?0 = 1和(x)(x = 0),或“所有的x是零”,是假(預(yù)期解釋)，在這種情況下指一個明確的真值。</p><p>　　1。一個封閉

33、的原子的句子是真的當(dāng)且僅當(dāng)它是真的在直覺上的觀念;例如,0 = 0為真,0 + 1 = 0是假的。</p><p>　　本規(guī)格書正如眼下的不是句法,但是,跟一些照顧,就有可能給出一個明確的和機械規(guī)格的原子的句子是真的關(guān)閉在直覺上說得過去。</p><p>　　2。一個封閉的句子一句是真的～當(dāng)且僅當(dāng)一個是不正確的</p><p>　　3。一個封閉的判∨B是真的,當(dāng)且僅

34、當(dāng)要么A或B是真實的。</p><p>　　4.一個封閉的句子(?ν)A(ν) 當(dāng)且僅當(dāng)對于每一個ν—i的值都是真的：A(0), A(1), A(1 + 1), . . .全真</p><p>　　上述定義的真相并不是一個顯式定義;它是一種感應(yīng)。利用概念fromset理論,然而,它有可能獲得一個顯式定義能夠產(chǎn)生一個的句子,由所有的真實的故事,只有他們。如果哥德爾的符號和句子的表達方式由編號

35、被錄用,然后你就可以獲得在集合論一套自然的數(shù)字,只是哥德爾的編號的真正的句子N。</p><p>　　有明確的意義上,它是不可能在界定概念真理的一種語言本身。這是證明的說謊者悖論:如果這句話我說謊,”或干脆：“(1)這句話是不正確的?！北徽J為是,很明顯的,因為(1),是“這句話里的" -如果(1)是真實的,那么(1)是虛假的;另一方面,如果(1)是假的,然后是(1)是真實的。在這個例子中,如果系統(tǒng)N的概