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  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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  • Some Obstacles Facing a Semantic Foundation for Constructive Mathematics.Michael R. Koss - 2015 - Erkenntnis 80 (5):1055-1068.
    This paper discusses Michael Dummett’s attempt to base the use of intuitionistic logic in mathematics on a proof-conditional semantics. This project is shown to face significant obstacles resulting from the existence of variants of standard intuitionistic logic. In order to overcome these obstacles, Dummett and his followers must give an intuitionistically acceptable completeness proof for intuitionistic logic relative to the BHK interpretation of the logical constants, but there are reasons to doubt that such a proof is possible. The paper concludes (...)
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  • Should Anti-Realists Be Anti-Realists About Anti-Realism?Roy T. Cook - 2014 - Erkenntnis 79 (S2):233-258.
    On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourse and a corresponding refusal to assert at least some instances of excluded middle (which can be understood as expressing this determinacy of subject matter). In short: one is an anti-realist about a discourse if and only if one accepts intuitionistic logic as correct for that discourse. On careful examination, the strongest (...)
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  • All Intermediate Logics with Extra Axioms in One Variable, Except Eight, Are Not Strongly Ω-Complete.Camillo Fiorentini - 2000 - Journal of Symbolic Logic 65 (4):1576-1604.
    In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly ω-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, ω-canonicity and strong ω-completeness is given.
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  • Maximality and Refutability.Tom Skura - 2004 - Notre Dame Journal of Formal Logic 45 (2):65-72.
    In this paper we study symmetric inference systems (that is, pairs of inference systems) as refutation systems characterizing maximal logics with certain properties. In particular, the method is applied to paraconsistent logics, which are natural examples of such logics.
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  • A New Solution to a Problem of Hosoi and Ono.Michael Zakharyaschev - 1994 - Notre Dame Journal of Formal Logic 35 (3):450-457.
    This paper gives a new, purely semantic proof of the following theorem: if an intermediate propositional logic L has the disjunction property then a disjunction free formula is provable in L iff it is provable in intuitionistic logic. The main idea of the proof is to use the well-known semantic criterion of the disjunction property for "simulating" finite binary trees (which characterize the disjunction free fragment of intuitionistic logic) by general frames.
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  • Admissibility and Refutation: Some Characterisations of Intermediate Logics.Jeroen P. Goudsmit - 2014 - Archive for Mathematical Logic 53 (7-8):779-808.
    Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...)
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  • 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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  • The Disjunction Property of Intermediate Propositional Logics.Alexander Chagrov & Michael Zakharyashchev - 1991 - Studia Logica 50 (2):189 - 216.
    This paper is a survey of results concerning the disjunction property, Halldén-completeness, and other related properties of intermediate prepositional logics and normal modal logics containing S4.
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  • The Undecidability of the Disjunction Property of Propositional Logics and Other Related Problems.Alexander Chagrov & Michael Zakharyaschev - 1993 - Journal of Symbolic Logic 58 (3):967-1002.
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  • 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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  • 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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