Subalgebras and generalized tautologies of many - valued logic systems 多值邏輯系統(tǒng)中的子代數(shù)與廣義重言式
Non - classical logic is the theoretical basis of many - valued logic , fuzzy reasoning and fuzzy control . fuzzy logic is the most active branch of non - classical logic 非經(jīng)典邏輯是多值邏輯、模糊推理及模糊控制等的理論基礎(chǔ),模糊邏輯是非經(jīng)典邏輯中極具活力的一個(gè)分支。
It was well known that rq t - norm which rq implication operator residuated to was left - continuous . in fact , any left - continuous t - norm has its own residuum - implication operator . and many - valued system could be obtained from implication operator 事實(shí)上,任一左連續(xù)t -模都可確定一個(gè)與之伴隨的蘊(yùn)涵算子,并且,不同的蘊(yùn)涵算子就可以構(gòu)建不同的多值邏輯系統(tǒng)。
Finte function , the typical representative of many - valued function , is clearly and vividly exposed its complicated alternative character by riemann surface and is thoroughly discussed the key points and the process of monodromic branch ceded from many - valued function 摘要通過討論多值函數(shù)的典型代表根式函數(shù),運(yùn)用黎曼面,清晰、形象地揭示多值函數(shù)復(fù)雜的變換特性,并論述分出多值函數(shù)的各單值分支的關(guān)鍵問題及其方法。
So r0 operator and godel operator are united in the systems ha the negation - a with respect to parameter a is defined in ha , the many - valued system h1 / 2 = ( [ 0 , 1 ] - 1 / 2 , 1 / 2 ) is discussed in detail . the classification theorem of tautologies in f ( s ) is obtained in h1 / 2 . the classfication of tautologies is defined on hq 本文還在h _系統(tǒng)中引入了帶參數(shù)的非運(yùn)算,較細(xì)致地研究了多值系統(tǒng)的子代數(shù)理論,以為賦值域建立了f ( s )中重言式的分類定理,并將廣義重言式分類定理推廣到系統(tǒng)h _ ( 0 1 )中。
many: adj. (more; most) (opp. few; ...valued: adj. 1.貴重的;被尊重的,重要的。 2.估定了價(jià)格 ...infinitely-many-valued logic: 無窮多值邏輯many valued composition law: 多值合成律many valued function: 多值函數(shù)many valued logic: 多值邏輯many valued mapping: 多值映射many-valued function: 多值函數(shù)many-valued logic: 多值邏輯be valued at: 價(jià)值在valued: adj. 1.貴重的;被尊重的,重要的。 2.估定了價(jià)格的;有(一定)價(jià)值的。 valued favour 〔美國(guó)〕 1. 定貨。 2. 【商業(yè)】信;通信。 as many: 一樣多as many as: 多達(dá); 和一樣多; 一樣多many: adj. (more; most) (opp. few; cf. much) 許多的,多數(shù)的,很多的,多。 ★ 1. 在口語(yǔ)中,尤其是在英國(guó)口語(yǔ)中,除用作肯定句的主詞或接用于 too, so, as, how 之后以外,帶有否定、疑問、條件意義:M- people think so. Did you see many people? 2. 在其他肯定句中常作 a lot of, a (large) number of, a great [good] many 等的代用語(yǔ)。 3. 文語(yǔ)中通例是以單數(shù)用作倒裝句法中的表語(yǔ):Many's the time (=often) I've seen him do it。 pron. 許多人[物]。 M- of us were tired. 我們當(dāng)中的許多人都疲倦了。 I have a few, but not many. 我有一點(diǎn)兒,可是不多。 n. 1.多數(shù)人[東西]。 There are a good many of them. 那樣的人很多[那種東西很多]。 A great many stayed away. 很多人沒來。 2.〔the many〕大多數(shù)人,一般人,群眾。 a good [great] many很多的,非常多的。 as many 和…一樣多(的);同數(shù)(的) (He made six mistakes in as many lines. 六行里就錯(cuò)了六處)。 as many again 再同樣多的,加倍的。 as many as ... 1. 多少…多少,…的都… (Take as many as you want. 你要多少就拿多少。 They admit as many as come. 來多少就可以進(jìn)去多少)。 2. 整整的〔一般指數(shù)目而言〕(He has been working at his book as many as five years. 他的書已經(jīng)整整寫了五年了)。 as [like] so many 1.像許多人一樣(He failed like so many before him. 像他前面的許多人一樣,他失敗了)。 2. 同數(shù)的,和…一樣多的(=as many)。 be one too many 多余的東西,礙手礙腳的東西。 be (one) too many for 比某人高明,勝過某人;為某人所不能理解 (He is (one) too many for me. 我弄他不贏,我拿他沒辦法)。 how many 多少,幾何 (How many boys are there? 有多少男孩?)。 many a [an] 〔詩(shī)、古〕許許多多,很多(many a day 多日〔語(yǔ)氣較強(qiáng)于 manydays〕)。 many a [〔古語(yǔ)〕 an] one 許許多多人。 M- a pickle makes a muckle. 積少成多,集腋成裘。 many (and many )a time =many a time and oft 〔詩(shī)、古〕 = on many occasions =many times 多次,不知多少次。 not many 〔俚語(yǔ)〕少許的,些少的。 not so many as 沒那么多,少于。 so many 那么多的,同數(shù)的 (in so many words 露骨地(說)。 So many men, so many minds. 〔諺語(yǔ)〕十人十心。 There are so many mistakes that I can not count them. 錯(cuò)誤多得數(shù)不清)。 many (of): (…中的)許多many a: (天)好多日子, 許多天, 長(zhǎng)時(shí)間里; 許多(謂語(yǔ)用第三人稱單數(shù)); 許多的,一個(gè)又一個(gè)的many as: 和一樣多many-: comb. f. = many. the many: 多數(shù)人, 群眾many-many: 多對(duì)多many-to-many: 多對(duì)多a deal valued at: 一項(xiàng)價(jià)值達(dá)......的生意a valued policy: 定值保單complex-valued: 復(fù)數(shù)的fully valued: 已充分反映實(shí)值股價(jià)能準(zhǔn)確反映公司實(shí)力的股份