Studia Logica 63 (1):27-48 (1999)

Abstract
This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d: we calculate a canonical characteristic fomula H of S ) so that ⊢G ∼ H → and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d of S from G. Then, in order to produce the whole completeness proof as an induction on this d, we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char and σ = d.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
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DOI 10.1023/A:1005203020301
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Paraconsistent Informational Logic.Paola Forcheri & Paolo Gentilini - 2005 - Journal of Applied Logic 3 (1):97-118.

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