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  1. Algebraic Semantics for the (↔,¬¬)‐Fragment of IPC.Katarzyna Słomczyńska - 2012 - Mathematical Logic Quarterly 58 (1-2):29-37.
    We show that the variety of equivalential algebras with regularization gives the algebraic semantics for the -fragment of intuitionistic propositional logic. We also prove that this fragment is hereditarily structurally complete.
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  • Algebraic Semantics for the -Fragment of IPC and its Properties.Katarzyna Słomczyńska - 2017 - Mathematical Logic Quarterly 63 (3-4):202-210.
    We study the variety of equivalential algebras with zero and its subquasivariety that gives the equivalent algebraic semantics for the math formula-fragment of intuitionistic propositional logic. We prove that this fragment is hereditarily structurally complete. Moreover, we effectively construct the finitely generated free equivalential algebras with zero.
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  • Singly Generated Quasivarieties and Residuated Structures.Tommaso Moraschini, James G. Raftery & Johann J. Wannenburg - 2020 - Mathematical Logic Quarterly 66 (2):150-172.
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  • On Rules.Rosalie Iemhoff - 2015 - Journal of Philosophical Logic 44 (6):697-711.
    This paper contains a brief overview of the area of admissible rules with an emphasis on results about intermediate and modal propositional logics. No proofs are given but many references to the literature are provided.
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  • Hereditarily Structurally Complete Positive Logics.Alex Citkin - 2020 - Review of Symbolic Logic 13 (3):483-502.
    Positive logics are $\{ \wedge, \vee, \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.
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  • Admissibility in Positive Logics.Alex Citkin - 2017 - Logica Universalis 11 (4):421-437.
    The paper studies admissibility of multiple-conclusion rules in positive logics. Using modification of a method employed by M. Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility of multiple-conclusion rules in the positive logics is equivalent to the problem of admissibility in intermediate logics defined by positive additional axioms. Moreover, a multiple-conclusion rule \ follows from a set of multiple-conclusion rules \ over a positive logic \ if and only if \ follows from (...)
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  • Unification with Parameters in the Implication Fragment of Classical Propositional Logic.Philippe Balbiani & Mojtaba Mojtahedi - forthcoming - Logic Journal of the IGPL.
    In this paper, we show that the implication fragment of classical propositional logic is finitary for unification with parameters.
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  • The Admissible Rules of ${{Mathsf{BD}_{2}}}$ and ${Mathsf{GSc}}$.Jeroen P. Goudsmit - 2018 - Notre Dame Journal of Formal Logic 59 (3):325-353.
    The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and GSc.
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  • Algebraic Logic Perspective on Prucnal’s Substitution.Alex Citkin - 2016 - Notre Dame Journal of Formal Logic 57 (4):503-521.
    A term td is called a ternary deductive term for a variety of algebras V if the identity td≈r holds in V and ∈θ yields td≈td for any A∈V and any principal congruence θ on A. A connective f is called td-distributive if td)≈ f,…,td). If L is a propositional logic and V is a corresponding variety that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and the (...)
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  • Admissible Rules and the Leibniz Hierarchy.James G. Raftery - 2016 - Notre Dame Journal of Formal Logic 57 (4):569-606.
    This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.
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  • A Syntactic Approach to Unification in Transitive Reflexive Modal Logics.Rosalie Iemhoff - 2016 - Notre Dame Journal of Formal Logic 57 (2):233-247.
    This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are presented and these results are extended to negationless fragments. In particular, a syntactic proof of Ghilardi’s result that $\mathsf {S4}$ has finitary unification is provided. In this approach the relation between classical valuations, projective unifiers, and admissible rules is clarified.
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  • Unification on Subvarieties of Pseudocomplemented Distributive Lattices.Leonardo Cabrer - 2016 - Notre Dame Journal of Formal Logic 57 (4):477-502.
    In this paper subvarieties of pseudocomplemented distributive lattices are classified by their unification type. We determine the unification type of every particular unification problem in each subvariety of pseudocomplemented distributive lattices.
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  • Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras.Wojciech Dzik & Sándor Radeleczki - 2016 - Bulletin of the Section of Logic 45 (3/4).
    We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering unification. We consider (...)
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  • Proof Complexity of Intuitionistic Implicational Formulas.Emil Jeřábek - 2017 - Annals of Pure and Applied Logic 168 (1):150-190.
  • KD is Nullary.Philippe Balbiani & Çiğdem Gencer - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):196-205.
    In the ordinary modal language, KD is the modal logic determined by the class of all serial frames. In this paper, we demonstrate that KD is nullary.
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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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  • Admissible Bases Via Stable Canonical Rules.Nick Bezhanishvili, David Gabelaia, Silvio Ghilardi & Mamuka Jibladze - 2016 - Studia Logica 104 (2):317-341.
    We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.
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  • Preservation of Admissible Rules When Combining Logics.João Rasga, Cristina Sernadas & Amílcar Sernadas - 2016 - Review of Symbolic Logic 9 (4):641-663.
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  • Structural Completeness in Relevance Logics.J. G. Raftery & K. Świrydowicz - 2016 - Studia Logica 104 (3):381-387.
    It is proved that the relevance logic \ has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.
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  • Unification in Intermediate Logics.Rosalie Iemhoff & Paul Rozière - 2015 - Journal of Symbolic Logic 80 (3):713-729.
  • On Unification and Admissible Rules in Gabbay–de Jongh Logics.Jeroen P. Goudsmit & Rosalie Iemhoff - 2014 - Annals of Pure and Applied Logic 165 (2):652-672.
    In this paper we study the admissible rules of intermediate logics. We establish some general results on extensions of models and sets of formulas. These general results are then employed to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.
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