A reduction rule for Peirce formula

✍ Scribed by Sachio Hirokawa; Yuichi Komori; Izumi Takeuti

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 365 KB
• Volume: 56
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00372774

✦ Synopsis

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a A-calculus with a new constant P((~-a)-'~)-~. It is shown that all terms with the same type are equivalent with respect to/?-reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for tiP-reduction. Weak normalization is shown for tiP-reduction with another reduction rule which simplifies c~ of ((o~ --*/~) --* a) --* a into an atomic type.