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  1. Mohammad Ardeshir & S. Mojtaba Mojtahedi (2014). Completeness of Intermediate Logics with Doubly Negated Axioms. Mathematical Logic Quarterly 60 (1-2):6-11.
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  2. Mohammad Ardeshir & Rasoul Ramezanian (2012). A Solution to the Surprise Exam Paradox in Constructive Mathematics. Review of Symbolic Logic 5 (4):679-686.
    We represent the well-known surprise exam paradox in constructive and computable mathematics and offer solutions. One solution is based on Brouwer’s continuity principle in constructive mathematics, and the other involves type 2 Turing computability in classical mathematics. We also discuss the backward induction paradox for extensive form games in constructive logic.
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  3. Mohammad Ardeshir & Rasoul Ramezanian (2012). On the Constructive Notion of Closure Maps. Mathematical Logic Quarterly 58 (4‐5):348-355.
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  4. Mohammad Ardeshir & Rasoul Ramezanian (2010). The Double Negation of the Intermediate Value Theorem. Annals of Pure and Applied Logic 161 (6):737-744.
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  5. Mohammad Ardeshir & Rasoul Ramezanian (2009). Decidability and Specker Sequences in Intuitionistic Mathematics. Mathematical Logic Quarterly 55 (6):637-648.
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  6. Majid Alizadeh & Mohammad Ardeshir (2006). Amalgamation Property for the Class of Basic Algebras and Some of its Natural Subclasses. 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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  7. Majid Alizadeh & Mohammad Ardeshir (2006). On Löb Algebras. Mathematical Logic Quarterly 52 (1):95-105.
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  8. Mojtaba Aghaei & Mohammad Ardeshir (2003). A Gentzen-Style Axiomatization for Basic Predicate Calculus. 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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  9. Mohammad Ardeshir, Wim Ruitenburg & Saeed Salehi (2003). Intuitionistic Axiomatizations for Bounded Extension Kripke Models. Annals of Pure and Applied Logic 124 (1-3):267-285.
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  10. Mohammad Ardeshir & Bardyaa Hesaam (2002). Every Rooted Narrow Tree Kripke Model of HA is Locally PA. Mathematical Logic Quarterly 48 (3):391-395.
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  11. Mojtaba Aghaei & Mohammad Ardeshir (2001). Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic. Studia Logica 68 (2):263-285.
    We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.
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  12. Mohammad Ardeshir & Wim Ruitenburg (2001). Basic Propositional Calculus II. Interpolation. Archive for Mathematical Logic 40 (5):349-364.
    Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such that A∧C 1⊢C (...)
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  13. Mohammad Ardeshir (1999). A Translation of Intuitionistic Predicate Logic Into Basic Predicate Logic. Studia Logica 62 (3):341-352.
    Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.
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  14. Mohammad Ardeshir & Mojtaba Moniri (1998). Intuitionistic Open Induction and Least Number Principle and the Buss Operator. Notre Dame Journal of Formal Logic 39 (2):212-220.
    In "Intuitionistic validity in -normal Kripke structures," Buss asked whether every intuitionistic theory is, for some classical theory , that of all -normal Kripke structures for which he gave an r.e. axiomatization. In the language of arithmetic and denote PA plus Open Induction or Open LNP, and are their intuitionistic deductive closures. We show is recursively axiomatizable and , while . If proves PEM but not totality of a classically provably total Diophantine function of , then and so . A (...)
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  15. Mohammad Ardeshir & Wim Ruitenburg (1998). Basic Propositional Calculus I. Mathematical Logic Quarterly 44 (3):317-343.
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