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  1. Paola Forcheri & Paolo Gentilini (2005). Paraconsistent Conjectural Deduction Based on Logical Entropy Measures I: C-Systems as Non-Standard Inference Framework. Journal of Applied Non-Classical Logics 15 (3):285-319.
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  2. Paolo Gentilini (1999). Proof-Theoretic Modal Pa-Completeness I: A System-Sequent Metric. Studia Logica 63 (1):27-48.
    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(S, G): we (...)
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  3. Paolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness II: The Syntactic Countermodel. Studia Logica 63 (2):245-268.
    This paper is the second part of the syntactic demonstration of the Arithmetical Completeness of the modal system G, the first part of which is presented in [9]. Given a sequent S so that ⊢GL-LIN S, ⊬G S, and given its characteristic formula H = char(S), which expresses the non G-provability of S, we construct a canonical proof-tree T of ~ H in GL-LIN, the height of which is the distance d(S, G) of S from G. T is the syntactic (...)
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  4. Paolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof. Studia Logica 63 (3):301-310.
    This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] 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, (...)
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  5. Paolo Gentilini (1993). Syntactical Results on the Arithmetical Completeness of Modal Logic. Studia Logica 52 (4):549 - 564.
    In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the (...)
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  6. Paolo Gentilini & P. Gentilini (1992). Provability Logic in the Gentzen Formulation of Arithmetic. Mathematical Logic Quarterly 38 (1):535-550.
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