Studia Logica 63 (3):301-310 (1999)
This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts  and  the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢PA Sξ and d(S, G) > 0 imply the inconsistency of PA.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
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Citations of this work BETA
Paraconsistent Conjectural Deduction Based on Logical Entropy Measures I: C-Systems as Non-Standard Inference Framework.Paola Forcheri & Paolo Gentilini - 2005 - Journal of Applied Non-Classical Logics 15 (3):285-319.
Proof Theory and Mathematical Meaning of Paraconsistent C-Systems.Paolo Gentilini - 2011 - Journal of Applied Logic 9 (3):171-202.
Paraconsistent Informational Logic.Paola Forcheri & Paolo Gentilini - 2005 - Journal of Applied Logic 3 (1):97-118.
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