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邏輯語義篇Ⅱ

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Ⅱ「Semantic Relation between Sentences」

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句子之間也存在某種關(guān)系，即<semantic relation>, 區(qū)別于<sense relation between words>, with some terms of truth conditions.

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(a). <Synonymy>

X is synonymous with Y.

E.g. He was a bachelor all his live＝He never married all his life.

The boy loves the pretty girl that is worthwhile=The pretty girl deserves the boy’s love.

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If X is true, Y is true. And if X is false, Y is false.

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(b). <Inconsistency不一致>

X is inconsistent with Y.

E.g. X: John is a bachelor. Y: John is married.

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If X is true, Y is false. And if X is false, Y is true.

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旗下有概念<Contradiction矛盾>

單句示例——X is a contradiction.

When X is a contradiction, it is invariably false.

E.g. My unmarried sister is married to a bachelor.

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多句示例——A: Mary’s mother-in-law is a doctor.

B: Mary is still single.

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<不一致><矛盾>兩者的區(qū)別，不考。但如果真區(qū)別的話，<Inconsistency>&泛概念；而<Contradiction>&二元對立≈<Complementary Antonyms>.

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看懂直接過！

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(c). <Entailment>

X entails Y. (Y is an entailment of X.)

即，X是Y的充分條件，Y是X的必要條件。

E.g. X: he has been to France. Y: he has been to Europen.

X: John married a black heiress. Y: John married a black girl.

If X is true, Y is necessarily true. And if X is false, Y may be true or false.

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也可以說成X presupposes Y. (Y is a prerequisite of X.)

X: John’s bike needs repairing.

Y: John has a bike.

If X is true, Y must be true. And if X is false, Y is still true.

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與<Entailment>相似，唯一的區(qū)別即Y是否絕對是真！

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兩者的區(qū)別來說，<Entailment>&<Hyponyms>及同義替換, 而<Presuppose>更偏于“有Y才能A”。

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[雜談]——邏輯BUG, 如果John’s bike needs repairing為否，那應(yīng)該是“車不需要修”甚至可以激進理解為"X is a contradiction”, 他就沒有車。

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那就加補丁唄，[星火]默認(rèn)“車不需要修”預(yù)設(shè)了“約翰有車”！

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(d). <Semantic Anomaly>

It means that a sentence is absurd. 即X is semantically anomalous.

E.g. the table has bad intentions.

He is drinking a knife.

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不符合典型的，全部丟進d組就行！

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上述為「Propositional Logic命題邏輯」

【名詞解釋】——<Propositional Logic>, also known as propositional calculus or sentential calculus, is the study of the truth conditions for propositions: how the truth of a composite proposition is determined by the truth value of its constituent propositions and the connections between them.

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屬于「Logical Semantics」

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下面，[胡]大師傾情講解下命題邏輯學(xué)的術(shù)語，

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字母P代表一個簡單命題

符號~或?兩者無差別表示<Negation否定> (插個眼，這里可見符號表達(dá)有不唯一性)

∴If a proposition P is true, then its negation ~P is false. And vice versa.

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符號&或∧為<交集>, 英語語言學(xué)稱其為<Connective Conjunction>.

符號V為<并集>, 英語語言學(xué)稱其為<Connective Disjunction>.

(情況就是這么一個情況，對接高一數(shù)學(xué)∩∧∪V，原理是一樣的！)

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Entailment用符號→表示

the connective implication≈conditional conjunction, ≈corresponds to “if…then…”

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<等值等價>用≡或?表示

單身≡沒結(jié)婚

father?dad

公的?雄性

1+1≡2

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某種角度來說，the connective equivalence also called biconditional conjunction.

p≡q意味著p→q, q→p.

It corresponds to the English expression “if and only if…then…”, 又可寫成“iff…then…”

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表格自己看，

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[補丁]——否定，按理來說可以否任何一個成分，但如果有多個可否定的點，僅限于對錯區(qū)別，本質(zhì)上僅限于二元對立化的處理。這樣才能守住<p與~p必對一個>的邏輯大廈！

p: John isn’t old.

∴~p: John is old. 而不能說John is young.

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由此，結(jié)合<互補反義詞><等級反義詞>再具體問題具體分析！自己推導(dǎo)！

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[胡-第五版]p103倒數(shù)第2段，他表述錯了。因為服從數(shù)學(xué)邏輯來說，如果p是真，則?p一定是假；p是假，?p一定是真。

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然后，一些降智的命題見其弊端，

If snow is black, grass is green.

All men are rational, and Socrates is a man.→Therefore, Socrates is rational.

邏輯性不強，不嚴(yán)謹(jǐn)，推理沒有效，置信度低。

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徒有邏輯符號的外殼作為工具，內(nèi)在的操作空間太大了！

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那如何破局呢？下期見！

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