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  1. The Lattice of Modal Logics: An Algebraic Investigation.W. J. Blok - 1984 - Journal of Symbolic Logic 49 (4):1419-1420.
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  • Topoi: The Categorial Analysis of Logic.R. I. Goldblatt - 1982 - British Journal for the Philosophy of Science 33 (1):95-97.
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  • Categories for the Working Mathematician.Saunders Maclane - 1971 - Springer.
    Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...)
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  • The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
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  • Splitting lattices of logics.Wolfgang Rautenberg - 1980 - Archive for Mathematical Logic 20 (3-4):155-159.
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  • Algebraic Logic.Paul Richard Halmos - 2014 - New York, NY, USA: Chelsea.
    2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In "Algebraic Logic" Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient (...)
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  • On some intuitionistic modal logics.Hiroakira Ono - 1977 - Bulletin of the Section of Logic 6 (4):182-184.
    Some modal logics based on logics weaker than the classical logic have been studied by Fitch [4], Prior [7], Bull [1], [2], [3], Prawitz [6] etc. Here we treat modal logics based on the intuitionistic propositional logic, which call intuitionistic modal logics.
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  • Superintuitionistic companions of classical modal logics.Frank Wolter - 1997 - Studia Logica 58 (2):229-259.
    This paper investigates partitions of lattices of modal logics based on superintuitionistic logics which are defined by forming, for each superintuitionistic logic L and classical modal logic , the set L[] of L-companions of . Here L[] consists of those modal logics whose non-modal fragments coincide with L and which axiomatize if the law of excluded middle p V p is added. Questions addressed are, for instance, whether there exist logics with the disjunction property in L[], whether L[] contains a (...)
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  • On maximal intermediate logics with the disjunction property.Larisa L. Maksimova - 1986 - Studia Logica 45 (1):69 - 75.
    For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.
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  • Varieties of monadic Heyting algebras part II: Duality theory.Guram Bezhanishvili - 1999 - Studia Logica 62 (1):21-48.
    In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.
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  • Varieties of monadic Heyting algebras. Part III.Guram Bezhanishvili - 2000 - Studia Logica 64 (2):215-256.
    This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in (...)
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  • Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
    This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that (...)
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  • Universal Algebra.P. M. Cohn - 1969 - Journal of Symbolic Logic 34 (1):113-114.
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  • MIPC as the formalisation of an intuitionist concept of modality.R. A. Bull - 1966 - Journal of Symbolic Logic 31 (4):609-616.
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