9 found
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  1. Counting the Maximal Intermediate Constructive Logics.Mauro Ferrari & Pierangelo Miglioli - 1993 - Journal of Symbolic Logic 58 (4):1365-1401.
    A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and the explicit definability property have the power of continuum. To prove our results, we introduce various notions which might be interesting by themselves. In particular, we illustrate a method to generate wide sets of pairwise "constructively incompatible constructive logics". We use a notion of "semiconstructive" logic and define wide sets of "constructive" (...)
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  2.  8
    Some Results on Intermediate Constructive Logics.Pierangelo Miglioli, Ugo Moscato, Mario Ornaghi, Silvia Quazza & Gabriele Usberti - 1989 - Notre Dame Journal of Formal Logic 30 (4):543-562.
  3.  86
    On Maximal Intermediate Predicate Constructive Logics.Alessandro Avellone, Camillo Fiorentini, Paolo Mantovani & Pierangelo Miglioli - 1996 - Studia Logica 57 (2-3):373 - 408.
    We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.
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    An Infinite Class of Maximal Intermediate Propositional Logics with the Disjunction Property.Pierangelo Miglioli - 1992 - Archive for Mathematical Logic 31 (6):415-432.
    Infinitely many intermediate propositional logics with the disjunction property are defined, each logic being characterized both in terms of a finite axiomatization and in terms of a Kripke semantics with the finite model property. The completeness theorems are used to prove that any two logics are constructively incompatible. As a consequence, one deduces that there are infinitely many maximal intermediate propositional logics with the disjunction property.
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  5.  1
    A Method to Single Out Maximal Propositional Logics with the Disjunction Property I.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (1):1-46.
    This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximal. To deal with these logics, we use a method based on the search of suitable nonstandard logics, which has an heuristic content and has allowed us to discover a wide family of logics, as well as to get their maximality proofs in a uniform way. The present part illustrates (...)
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  6. A Method to Single Out Maximal Propositional Logics with the Disjunction Property II.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (2):117-168.
    This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property , whose first part has appeared in this journal with the title “A method to single out maximal propositional logics with the disjunction property I”. In the first part we have explained the general results upon which a method to single out maximal constructive logics is based and have illustrated such a method by exhibiting the Kripke semantics of (...)
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  7.  6
    A Constructivism Based on Classical Truth.Pierangelo Miglioli, Ugo Moscato, Mario Ornaghi & Gabriele Usberti - 1988 - Notre Dame Journal of Formal Logic 30 (1):67-90.
  8.  12
    On Canonicity and Strong Completeness Conditions in Intermediate Propositional Logics.Silvio Ghilardi & Pierangelo Miglioli - 1999 - Studia Logica 63 (3):353-385.
    By using algebraic-categorical tools, we establish four criteria in order to disprove canonicity, strong completeness, w-canonicity and strong w-completeness, respectively, of an intermediate propositional logic. We then apply the second criterion in order to get the following result: all the logics defined by extra-intuitionistic one-variable schemata, except four of them, are not strongly complete. We also apply the fourth criterion in order to prove that the Gabbay-de Jongh logic D1 is not strongly w-complete.
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  9.  1
    Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property.Guido Bertolotti, Pierangelo Miglioli & Daniela Silvestrini - 1996 - Mathematical Logic Quarterly 42 (1):501-536.
    We provide results allowing to state, by the simple inspection of suitable classes of posets , that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of (...)
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