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  1. Provably total functions of Basic Arithemtic.Saeed Salehi - 2003 - Mathematical Logic Quarterly 49 (3):316.
    It is shown that all the provably total functions of Basic Arithmetic BA, a theory introduced by Ruitenburg based on Predicate Basic Calculus, are primitive recursive. Along the proof a new kind of primitive recursive realizability to which BA is sound, is introduced. This realizability is similar to Kleene's recursive realizability, except that recursive functions are restricted to primitive recursives.
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  • A cut-free Gentzen formulation of basic propositional calculus.Kentaro Kikuchi & Katsumi Sasaki - 2003 - Journal of Logic, Language and Information 12 (2):213-225.
    We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...)
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  • New sequent calculi for Visser's Formal Propositional Logic.Katsumasa Ishii - 2003 - Mathematical Logic Quarterly 49 (5):525.
    Two cut-free sequent calculi which are conservative extensions of Visser's Formal Propositional Logic are introduced. These satisfy a kind of subformula property and by this property the interpolation theorem for FPL are proved. These are analogies to Aghaei-Ardeshir's calculi for Visser's Basic Propositional Logic.
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  • 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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  • A Gentzen-style axiomatization for basic predicate calculus.Mojtaba Aghaei & Mohammad Ardeshir - 2003 - Archive for Mathematical Logic 42 (3):245-259.
    We introduce a Gentzen-style sequent calculus axiomatization for Basic Predicate Calculus. Our new axiomatization is an improvement of the previous axiomatizations, in the sense that it has the subformula property. In this system the cut rule is eliminated.
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  • 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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  • Avicenna on Syllogisms Composed of Opposite Premises.Behnam Zolghadr - 2021 - In Mathematics, Logic, and their Philosophies. pp. 433-442.
    This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.
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