6 found
Sort by:
  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.
  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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  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, (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  6. Paolo Gentilini & P. Gentilini (1992). Provability Logic in the Gentzen Formulation of Arithmetic. Mathematical Logic Quarterly 38 (1):535-550.
    In this paper are studied the properties of the proofs in PRA of provability logic sentences, i.e. of formulas which are Boolean combinations of formulas of the form PIPRA, where h is the Gödel-number of a sentence in PRA. The main result is a Normal Form Theorem on the proof-trees of provability logic sequents, which states that it is possible to split the proof into an arithmetical part, which contains only atomic formulas and has an essentially intuitionistic character, and into (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation