10 found
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  1.  19
    Boolean Algebras in Visser Algebras.Majid Alizadeh, Mohammad Ardeshir & Wim Ruitenburg - 2016 - Notre Dame Journal of Formal Logic 57 (1):141-150.
    We generalize the double negation construction of Boolean algebras in Heyting algebras to a double negation construction of the same in Visser algebras. This result allows us to generalize Glivenko’s theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras.
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  2.  43
    Uniform Interpolation in Substructural Logics.Majid Alizadeh, Farzaneh Derakhshan & Hiroakira Ono - 2014 - Review of Symbolic Logic 7 (3):455-483.
  3.  24
    On the Linear Lindenbaum Algebra of Basic Propositional Logic.Majid Alizadeh & Mohammad Ardeshir - 2004 - Mathematical Logic Quarterly 50 (1):65.
    We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra.
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  4.  14
    On Löb Algebras.Majid Alizadeh & Mohammad Ardeshir - 2006 - Mathematical Logic Quarterly 52 (1):95-105.
    We study the variety of Löb algebras , the algebraic structures associated with formal propositional calculus. Among other things, we prove a completeness theorem for formal propositional logic with respect to the variety of Löb algebras. We show that the variety of Löb algebras has the weak amalgamation property. Some interesting subclasses of the variety of Löb algebras, e.g. linear, faithful and strongly linear Löb algebras are introduced.
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  5.  21
    Basic Propositional Logic and the Weak Excluded Middle.Majid Alizadeh & Mohammad Ardeshir - 2019 - Logic Journal of the IGPL 27 (3):371-383.
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  6. Unification Types in Euclidean Modal Logics.Majid Alizadeh, Mohammad Ardeshir, Philippe Balbiani & Mojtaba Mojtahedi - forthcoming - Logic Journal of the IGPL.
    We prove that $\textbf {K}5$ and some of its extensions that do not contain $\textbf {K}4$ are of unification type $1$.
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  7.  14
    Completion and Amalgamation of Bounded Distributive Quasi Lattices.Majid Alizadeh, Antonio Ledda & Hector Freytes - 2011 - Logic Journal of the IGPL 19 (1):110-120.
    In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a well-known idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras.
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  8.  7
    Remarks on Stable Formulas in Intuitionistic Logic.Majid Alizadeh & Ali Bibak - forthcoming - Logic and Logical Philosophy:1.
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  9.  3
    Lyndon’s Interpolation Property for the Logic of Strict Implication.Narbe Aboolian & Majid Alizadeh - 2022 - Logic Journal of the IGPL 30 (1):34-70.
    The main result proves Lyndon’s and Craig’s interpolation properties for the logic of strict implication ${\textsf{F}}$, with a purely syntactical method. A cut-free G3-style sequent calculus $ {\textsf{GF}} $ and its single-succedent variant $ \textsf{GF}_{\textsf{s}} $ are introduced. $ {\textsf{GF}} $ can be extended to a G3-variant of the sequent calculus GBPC3 for Visser’s basic logic. Also a simple syntactic proof of known embedding result of $ {\textsf{F}} $ into $ {\textsf{K}} $ is provided. An extension of $ {\textsf{F}} $, (...)
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  10.  12
    Amalgamation Property for the Class of Basic Algebras and Some of its Natural Subclasses.Majid Alizadeh & Mohammad Ardeshir - 2006 - Archive for Mathematical Logic 45 (8):913-930.
    We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property.
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