[定理] 論理的帰結と充足不能性 節集
合 {F1, F2, ・・・, Fn}が充足可能なら
ば,式 G が {F1, F2, ・・・, Fn} の論
理的帰結であるとき,およびその時に限り {F1, F2,
・・・, Fn, ¬G} は充足不能である.
(例2)
以下の自然言語による文章を一階述語論理に変換し,融合法により "John
is happy"が以下の文章の論理的帰結になっていることを証明する.
Anyone passing their history exams and winning the lottery is
happy. But anyone who studies or is lucky can pass all their exams.
John did not study but he is lucky. Anyone who is lucky wins the
lottery.
(例3)
以下の自然言語による文章を一階述語論理に変換し,融合法により "Can
anyone be found with an exciting life?の真偽を証明する.("Someone
can be found with an exciting life"が以下の文章の論理的帰結になってい
ることを証明する.)
All people that are not poor and are smart are happy. Those
people that read are not stupid. John can read and is wealthy. Happy
people have exciting lives. "