The single-conclusion proof logic and inference rules specification

✍ Scribed by Vladimir N. Krupski

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 187 KB
• Volume: 113
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(01)00058-6

✦ Synopsis

The logic of single-conclusion (functional) proofs (FLP) is introduced. It combines the veriÿcation property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that FLP is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicates. The application to arithmetical inference rules speciÿcation and PA-admissibility testing is considered. We show that the provability in FLP gives the complete admissibility test for the rules which can be speciÿed by schemes in FLP-language. The test is supplied with the ground proof extraction algorithm which eliminates the admissible rules from a PA-proof by utilizing the information from the corresponding FLP-proofs.