逻辑语义篇Ⅱ

Ⅱ「Semantic Relation between Sentences」

句子之间也存在某种关系，即<semantic relation>, 区别于<sense relation between words>, with some terms of truth conditions.

【资料图】

(a). <Synonymy>

X is synonymous with Y.

. 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.

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

(b). <Inconsistency不一致>

X is inconsistent with Y.

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

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

旗下有概念<Contradiction矛盾>

单句示例——X is a contradiction.

When X is a contradiction, it is invariably false.

. My unmarried sister is married to a bachelor.

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

B: Mary is still single.

<不一致><矛盾>两者的区别，不考。但如果真区别的话，<Inconsistency>&泛概念；而<Contradiction>&二元对立≈<Complementary Antonyms>.

看懂直接过！

(c). <Entailment>

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

即，X是Y的充分条件，Y是X的必要条件。

. 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.

也可以说成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.

与<Entailment>相似，唯一的区别即Y是否绝对是真！

两者的区别来说，<Entailment>&<Hyponyms>及同义替换, 而<Presuppose>更偏于“有Y才能A”。

[杂谈]——逻辑BUG, 如果John’s bike needs repairing为否，那应该是“车不需要修”甚至可以激进理解为"X is a contradiction”, 他就没有车。

那就加补丁呗，[星火]默认“车不需要修”预设了“约翰有车”！

(d). <Semantic Anomaly>

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

. the table has bad intentions.

He is drinking a knife.

不符合典型的，全部丢进d组就行！

上述为「Propositional Logic命题逻辑」

【名词解释】——<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.

属于「Logical Semantics」

下面，[胡]大师倾情讲解下命题逻辑学的术语，

字母P代表一个简单命题

符号~或¬两者无差别表示<Negation否定> (插个眼，这里可见符号表达有不唯一性)

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

符号&或∧为<交集>, 英语语言学称其为<Connective Conjunction>.

符号V为<并集>, 英语语言学称其为<Connective Disjunction>.

(情况就是这么一个情况，对接高一数学∩∧∪V，原理是一样的！)

Entailment用符号→表示

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

<等值等价>用≡或↔表示

单身≡没结婚

father↔dad

公的↔雄性

1+1≡2

某种角度来说，the connective equivalence also called biconditional conjunction.

p≡q意味着p→q, q→p.

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

表格自己看，

[补丁]——否定，按理来说可以否任何一个成分，但如果有多个可否定的点，仅限于对错区别，本质上仅限于二元对立化的处理。这样才能守住<p与~p必对一个>的逻辑大厦！

p: John isn’t old.

∴~p: John is old. 而不能说John is young.

由此，结合<互补反义词><等级反义词>再具体问题具体分析！自己推导！

[胡-第五版]p103倒数第2段，他表述错了。因为服从数学逻辑来说，如果p是真，则¬p一定是假；p是假，¬p一定是真。

然后，一些降智的命题见其弊端，

If snow is black, grass is green.

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

逻辑性不强，不严谨，推理没有效，置信度低。

徒有逻辑符号的外壳作为工具，内在的操作空间太大了！

那如何破局呢？下期见！