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  1. Larisa Maksimova on Implication, Interpolation, and Definability.Sergei Odintsov (ed.) - 2018 - Cham, Switzerland: Springer Verlag.
    This edited volume focuses on the work of Professor Larisa Maksimova, providing a comprehensive account of her outstanding contributions to different branches of non-classical logic. The book covers themes ranging from rigorous implication, relevance and algebraic logic, to interpolation, definability and recognizability in superintuitionistic and modal logics. It features both her scientific autobiography and original contributions from experts in the field of non-classical logics. Professor Larisa Maksimova's influential work involved combining methods of algebraic and relational semantics. Readers will be able (...)
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  • Why Does Halldén-Completeness Matter?George F. Schumm - 1993 - Theoria 59 (1-3):192-206.
  • Nikolaos Galatos.Hiroakira Ono - 2006 - Studia Logica 83 (1-3):1-32.
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  • Proof Analysis in Intermediate Logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1-2):71-92.
    Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...)
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  • Interconnection of the Lattices of Extensions of Four Logics.Alexei Y. Muravitsky - 2017 - Logica Universalis 11 (2):253-281.
    We show that the lattices of the normal extensions of four well-known logics—propositional intuitionistic logic \, Grzegorczyk logic \, modalized Heyting calculus \ and \—can be joined in a commutative diagram. One connection of this diagram is an isomorphism between the lattices of the normal extensions of \ and \; we show some preservation properties of this isomorphism. Two other connections are join semilattice epimorphims of the lattice of the normal extensions of \ onto that of \ and of the (...)
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  • Algebraization of Quantifier Logics, an Introductory Overview.István Németi - 1991 - Studia Logica 50 (3-4):485 - 569.
    This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...)
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  • A Syntactic Approach to Maksimova's Principle of Variable Separation for Some Substructural Logics.H. Naruse, Bayu Surarso & H. Ono - 1998 - Notre Dame Journal of Formal Logic 39 (1):94-113.
  • 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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  • Craig's Interpolation Theorem for the Intuitionistic Logic and its Extensions—A Semantical Approach.Hiroakira Ono - 1986 - Studia Logica 45 (1):19-33.
    A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.
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  • Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Studia Logica 83 (1-3):279-308.
    Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
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  • A Cut-Free Gentzen-Type System for the Logic of the Weak Law of Excluded Middle.Branislav R. Boričić - 1986 - Studia Logica 45 (1):39-53.
    The logic of the weak law of excluded middleKC p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented (...)
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  • On Variable Separation in Modal and Superintuitionistic Logics.Larisa Maksimova - 1995 - Studia Logica 55 (1):99 - 112.
    In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any normal modal logic is equivalent to the so-called super-embedding property of a suitable class of modal algebras. The joint embedding property of a class of algebras is equivalent to the Pseudo-Relevance Property. We consider connections of the above-mentioned properties with interpolation and amalgamation. Also an algebraic equivalent of of the principle of variable separation in superintuitionistic logics will (...)
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  • Definability and Interpolation in Non-Classical Logics.Larisa Maksimova - 2006 - Studia Logica 82 (2):271-291.
    Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal and positive logics,and (...)
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  • The Disjunction Property of Intermediate Propositional Logics.Alexander Chagrov & Michael Zakharyashchev - 1991 - Studia Logica 50 (2):189 - 216.
    This paper is a survey of results concerning the disjunction property, Halldén-completeness, and other related properties of intermediate prepositional logics and normal modal logics containing S4.
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  • The Undecidability of the Disjunction Property of Propositional Logics and Other Related Problems.Alexander Chagrov & Michael Zakharyaschev - 1993 - Journal of Symbolic Logic 58 (3):967-1002.
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  • Interpolation Theorems for Intuitionistic Predicate Logic.G. Mints - 2001 - Annals of Pure and Applied Logic 113 (1-3):225-242.
    Craig interpolation theorem implies that the derivability of X,X′ Y′ implies existence of an interpolant I in the common language of X and X′ Y′ such that both X I and I,X′ Y′ are derivable. For classical logic this extends to X,X′ Y,Y′, but for intuitionistic logic there are counterexamples. We present a version true for intuitionistic propositional logic, and more complicated version for the predicate case.
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  • Intuitionistic Logic and Implicit Definability.Larisa Maksimova - 2000 - Annals of Pure and Applied Logic 105 (1-3):83-102.
    It is proved that there are exactly 16 superintuitionistic propositional logics with the projective Beth property. These logics are finitely axiomatizable and have the finite model property. Simultaneously, all varieties of Heyting algebras with strong epimorphisms surjectivity are found.
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  • Interpolation and Beth’s Property in Propositional Many-Valued Logics: A Semantic Investigation.Franco Montagna - 2006 - Annals of Pure and Applied Logic 141 (1):148-179.
    In this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional many-valued logics extending Hájek’s Basic Logic [P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most interesting extensions of in the language of have deductive interpolation, very few of them have Beth’s property or Craig interpolation. Thus in the last part of the (...)
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