4 found
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  1.  74
    On the Infinite-Valued Łukasiewicz Logic That Preserves Degrees of Truth.Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (7):839-868.
    Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...)
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  2.  46
    Protoalgebraic Gentzen Systems and the Cut Rule.Àngel J. Gil & Jordi Rebagliato - 2000 - Studia Logica 65 (1):53-89.
    In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in (...)
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  3.  19
    A Strong Completeness Theorem for the Gentzen Systems Associated with Finite Algebras.Àngel J. Gil, Jordi Rebagliato & Ventura Verdú - 1999 - Journal of Applied Non-Classical Logics 9 (1):9-36.
    ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case (...)
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  4.  38
    On Gentzen Relations Associated with Finite-Valued Logics Preserving Degrees of Truth.Angel J. Gil - 2013 - Studia Logica 101 (4):749-781.
    When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a (...)
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