形式逻辑电子教案下载-样章doc--浏览

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第十讲复合命题及其推理(二)

一、假言命题

例:

, 如果某行为是犯罪行为，那么该行为是违法行为。

, 如果某对夫妇计划外生育，那么该行为是违法行为。

, 如果明天下雨，运动会就延期举行。

, 如果一个人得了阑尾炎，他就会肚子痛。

, 只有是受精卵，鸡蛋才能孵出小鸡。

, 只有具备适宜温度，鸡蛋才能孵出小鸡。

, 只有某人年满18周岁，他才有选举权。

, 亚里士多德学院的门口竖着一块牌子，上面写着“不懂逻辑者不得入内”。这天，

来了一群人，他们都是懂逻辑的人。

, 柏拉图学院的门口:“只有懂几何者方可入内。”

, 如果对角线垂直平分且相等，四边形就是正方形。

, 只有对角线垂直平分且相等，四边形才是正方形。

, 当且仅当对角线垂直平分且相等，则四边形是正方形。

, 只要地球由东向西自转，太阳就会从西边出来。

1、定义:断定事物之间条件关系的命题。

A conditional statement is an “if…then…”statement. The component statement i mmediately following the “if” is called the antecedent, and

the one following the “then” is called the consequent. A is said to be a sufficient condition for B whenever the occurrence of A is all that is needed for the occurrence of B. On the other hand, B is said to a necessary condition for A whenever A cannot occur without the occurrence of B.

The horseshoe symbol is also used to translate “implies”. Although “implies” is used most probably to describe the relationship between the premises and conclusion.

(The statement that follows “if” is always the antecedent, and the statement that follows “only if” is always the consequent. Event A is said to be a sufficient condition for event B whenever the occurrence of A is all that is

required for the occurrence of B. On the other hand, event A is said to be a necessary condition for event B whenever B cannot occur without the occurrence of A.)

2、结构:前件、后件，联结词。对应假设、条件复句。

注:联言肢、选言肢从逻辑意义上不分前后，前后件不然。

3、分类、逻辑形式:

, 充分条件:有前件就有后件。

, 必要条件:没有前件就没有后件。

, 充分必要条件(充要条件):有前件就有后件，没有前件就没有后件。

, 充分条件假言命题

, 必要条件假言命题

, 充要条件假言命题

注:这种分类实际是充分不必要、必要不充分、充分且必要。否则充要条件包含在充分和

必要条件里面，充分和必要也是交叉的，则犯了子项相容的逻辑错误。 4、联结词:

, 充分:如果……那么;如果……就;只要……就;若……则。

, 必要:只有……才;不……不;没有……没有。

, 充要:当且仅当……则;只要而且只有……才; 若……则，且若不……则不。

5、联系:

, 充分和必要条件假言命题可以相互转化:前后件换位;同时否定前后件。

(p?q)?(q?p)?(，p?，q)

(p?q)?(q?p)?(，p?，q)

, 充分加必要等于充分必要。(p?q)(p?q)?(p?q) 6、真值表:

q p?q ?

p

T T T

T F F

F T T

F F T

p q p?q ?

T T T

T F T

F T F

F F T

p q p?q ?

T T T

T F F

F T F

F F T

, 逻辑性质:

o 充分假言:前件真而且后件假，命题才假。其余真。

The truth table shows that a conditional statement is false when the antecedent is true and the consequent false and is true in all other cases.

o 必要假言:前件假而且后件真，命题才假。其余真。

o 充要假言:前真后假或前假后真，命题才假。

前后件同真或同假，命题才真。

The truth table shows that the biconditional is true when its two components have the same truth value and that otherwise it is false.

8、联言、选言命题真假取决于肢命题的真假的数目，而假言命题真假则取决于前后件之

间的真假组合关系。联言命题肢命题必须同真，选言命题至少有一个真，而假言命题可同

假，且同真同假时，假言命题必真。

The meaning of statements symbolized in terms of the logical operators conforms fairly closely to that of English statements, but it occasionally breaks down, especially with conditional and biconditional statements.

二、假言推理