The single-conclusion proof logic and inference rules specification

The logic of single-conclusion (functional) proofs (FLP) is introduced. It combines the veri$cation property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that FLP is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicates. The application to arithmetical inference rules speci$cation and PA-admissibility testing is considered. We show that the provability in FLP gives the complete admissibility test for the rules which can be speci$ed 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. c © 2002 Elsevier Science B.V. All rights reserved. MSC: 03F07; 03F45; 03F30; 68T15; 68Q60