◆ わからない問題はここに書いてね ２１８ ◆
256 ：１３２人目の素数さん：
数理論理学という分野なんだが英語で問題出されてさっぱりわからん
日本語の解答でもいいらしいので誰かおしえてくれまいか。
（１）Let "r" be thr rank function
(a)Show that r(φ)≦number of occurrences of connectives of φ.
(b)Give examples of φ such that < or = holds in (a).
(c)Show that r(φ) < r(ψ) if φ is a proper subformula of ψ.
Hint : For (a) and (c) , use induction
(2) Using natural deduction show that
(a)├（φ→ψ)→｛（φ→（ψ→σ））→（φ→σ）｝
(b)├（φ∧¬（φ∧¬ψ））→ψ
Note. You are asked to give a purely syntactical proof. This means that you are Not allowed to give
a semantival argument ( using for examle a truth table) and then appeal to the completeness theorem.
日本語の解答でもいいらしいので誰かおしえてくれまいか。
（１）Let "r" be thr rank function
(a)Show that r(φ)≦number of occurrences of connectives of φ.
(b)Give examples of φ such that < or = holds in (a).
(c)Show that r(φ) < r(ψ) if φ is a proper subformula of ψ.
Hint : For (a) and (c) , use induction
(2) Using natural deduction show that
(a)├（φ→ψ)→｛（φ→（ψ→σ））→（φ→σ）｝
(b)├（φ∧¬（φ∧¬ψ））→ψ
Note. You are asked to give a purely syntactical proof. This means that you are Not allowed to give
a semantival argument ( using for examle a truth table) and then appeal to the completeness theorem.
|
|
|