語(yǔ)法和語(yǔ)義畢業(yè)論文外文翻譯-其他專(zhuān)業(yè)-展示頁(yè)
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【正文】 e 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 “～” 。 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. Truth, 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 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 atheorem. If p and “either notp 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 rule of inference whose premises are theorems. In 1931 G246。 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
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