Search results for 'Lattices, Distributive' (try it on Scholar)

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  1.  1
    Vincenzo Marra (2008). A Characterization of MV-Algebras Free Over Finite Distributive Lattices. Archive for Mathematical Logic 47 (3):263-276.
    Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.
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  2.  10
    John Bell (1999). Boolean Algebras and Distributive Lattices Treated Constructively. Mathematical Logic Quarterly 45 (1):135-143.
    Some aspects of the theory of Boolean algebras and distributive lattices–in particular, the Stone Representation Theorems and the properties of filters and ideals–are analyzed in a constructive setting.
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  3.  5
    Saburo Tamura (1975). Two Identities for Lattices, Distributive Lattices and Modular Lattices with a Constant. Notre Dame Journal of Formal Logic 16 (1):137-140.
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  4. Yuri Gurevich (1983). Decision Problem for Separated Distributive Lattices. Journal of Symbolic Logic 48 (1):193-196.
    It is well known that for all recursively enumerable sets X 1 , X 2 there are disjoint recursively enumerable sets Y 1 , Y 2 such that $Y_1 \subseteq X_1, Y_2 \subseteq X_2$ and Y 1 ∪ Y 2 = X 1 ∪ X 2 . Alistair Lachlan called distributive lattices satisfying this property separated. He proved that the first-order theory of finite separated distributive lattices is decidable. We prove here that the first-order theory of all separated (...)
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  5.  6
    Viorica Sofronie-Stokkermans (2000). Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I. Studia Logica 64 (1):93-132.
    The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models (...)
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  6.  16
    Viorica Sofronie-Stokkermans (2000). Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics II. Studia Logica 64 (2):151-172.
    The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety (...)
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  7.  21
    Alejandro Petrovich (1996). Distributive Lattices with an Operator. Studia Logica 56 (1-2):205 - 224.
    It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple (...)
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  8.  9
    Jacek Hawranek & Jan Zygmunt (1983). Some Elementary Properties of Conditionally Distributive Lattices. Bulletin of the Section of Logic 12 (3):117-120.
    The notion of a conditionally distributive lattice was introduced by B. Wolniewicz while formally investigating the ontology of situations . In several of this lectures he has appealed for a study of that class of lattices. The present abstract is a response to that request.
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  9.  9
    Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp & Manuel Lerman (1996). Decidability of the Two-Quantifier Theory of the Recursively Enumerable Weak Truth-Table Degrees and Other Distributive Upper Semi-Lattices. Journal of Symbolic Logic 61 (3):880-905.
    We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its (...)
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  10.  12
    Roberto Cignoli (1996). Free Q-Distributive Lattices. Studia Logica 56 (1-2):23 - 29.
    The dual spaces of the free distributive lattices with a quantifier are constructed, generalizing Halmos' construction of the dual spaces of free monadic Boolean algebras.
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  11.  12
    Alasdair Urquhart (1981). Distributive Lattices with a Dual Homomorphic Operation. II. Studia Logica 40 (4):391 - 404.
    An Ockham lattice is defined to be a distributive lattice with 0 and 1 which is equipped with a dual homomorphic operation. In this paper we prove: (1) The lattice of all equational classes of Ockham lattices is isomorphic to a lattice of easily described first-order theories and is uncountable, (2) every such equational class is generated by its finite members. In the proof of (2) a characterization of orderings of with respect to which (...)
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  12. Majid Alizadeh, Antonio Ledda & Hector Freytes (2011). Completion and Amalgamation of Bounded Distributive Quasi Lattices. Logic Journal of the Igpl 19 (1):110-120.
    In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a well-known idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras.
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  13.  14
    Sergio Celani & Ramon Jansana (2005). Bounded Distributive Lattices with Strict Implication. Mathematical Logic Quarterly 51 (3):219-246.
    The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not (...)
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  14.  6
    Sergio Arturo Celani (1999). Distributive Lattices with a Negation Operator. Mathematical Logic Quarterly 45 (2):207-218.
    In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.
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  15.  13
    Alasdair Urquhart (1979). Distributive Lattices with a Dual Homomorphic Operation. Studia Logica 38 (2):201 - 209.
    The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.
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  16. John Bell, A Representation Theory for Modalized Distributive Lattices.
    By a lattice we shall always mean a distributive lattice which is bounded, i.e. has both a bottom element 0 and a top element 1. Lattice homomorphisms will always be assumed to preserve 0 and 1.
     
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  17.  1
    Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra (2008). Gödel Algebras Free Over Finite Distributive Lattices. Annals of Pure and Applied Logic 155 (3):183-193.
    Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.
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  18. Sergio A. Celani & Ramón Jansana Ferrer (2005). Bounded Distributive Lattices with Strict Implication. Mathematical Logic Quarterly 51 (3):219.
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  19. M. H. Stone (1938). Topological Representations of Distributive Lattices and Brouwerian Logics. Journal of Symbolic Logic 3 (2):90-91.
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  20.  12
    Sebastiaan A. Terwijn (2007). Kripke Models, Distributive Lattices, and Medvedev Degrees. Studia Logica 85 (3):319 - 332.
    We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.
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  21.  5
    M. Sambasiva Rao (2012). Normal Filters of Distributive Lattices. Bulletin of the Section of Logic 41 (3/4):131-143.
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  22.  7
    H. P. Sankappanavar (1985). Distributive Lattices with a Dual Endomorphism. Mathematical Logic Quarterly 31 (25‐28):385-392.
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  23.  8
    D. W. Miller (1979). Metric Postulates for Modular, Distributive, and Boolean Lattices. Bulletin of the Section of Logic 8 (4):191-195.
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  24.  6
    Joanna Grygiel (2004). Some Numerical Characterization of Finite Distributive Lattices. Bulletin of the Section of Logic 33 (3):127-133.
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  25.  6
    Joanna Grygiel (2011). Products of Skeletons of Finite Distributive Lattices. Bulletin of the Section of Logic 40 (1/2):55-61.
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  26.  2
    Jürg Schmid (1979). Algebraically and Existentially Closed Distributive Lattices. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (33):525-530.
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  27.  5
    George Georgescu (1991). F‐Multipliers and the Localization of Distributive Lattices II. Mathematical Logic Quarterly 37 (19‐22):293-300.
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  28.  3
    Alasdair Urquhart (1977). Review: Raymond Balbes, Philip Dwinger, Distributive Lattices. [REVIEW] Journal of Symbolic Logic 42 (4):587-588.
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  29. Mai Gehrke, Matt Insall & Klaus Kaiser (1990). Some Nonstandard Methods Applied to Distributive Lattices. Mathematical Logic Quarterly 36 (2):123-131.
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  30.  2
    Saunders MacLane (1938). Review: M. H. Stone, Topological Representations of Distributive Lattices and Brouwerian Logics. [REVIEW] Journal of Symbolic Logic 3 (2):90-91.
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  31.  1
    Volker Weispfenning (1985). Quantifier Elimination for Distributive Lattices and Measure Algebras. Mathematical Logic Quarterly 31 (14‐18):249-261.
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  32. William Wernick (1965). Review: Boleslaw Sobocinski, Six New Sets of Independent Axioms for Distributive Lattices with O and I. [REVIEW] Journal of Symbolic Logic 30 (3):377-378.
     
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  33.  1
    Bolesław Sobociński (1972). Certain Sets of Postulates for Distributive Lattices with the Constant Elements. Notre Dame Journal of Formal Logic 13 (1):119-123.
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  34. Bolesław Sobociński (1972). An Abbreviation of Croisot's Axiom-System for Distributive Lattices with $I$. Notre Dame Journal of Formal Logic 13 (1):139-141.
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  35. Bolesław Sobociński (1962). Six New Sets of Independent Axioms for Distributive Lattices with $O$ and $I$. Notre Dame Journal of Formal Logic 3 (3):187-192.
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  36. S. T. Fedoryaev (1995). Decidable Algorithmic Problems on Relatively Complemented Distributive Lattices Which Cannot Be Simultaneously Decidable. Bulletin of Symbolic Logic 1:109.
     
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  37. Fred Galvin (1969). Review: U. L. Ersov, Decidability of the Elementary Theory of Relatively Complemented Distributive Lattices and of the Theory of Filters. [REVIEW] Journal of Symbolic Logic 34 (1):126-126.
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  38. Mai Gehrke, Matt Insall & Klaus Kaiser (1990). Some Nonstandard Methods Applied to Distributive Lattices. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (2):123-131.
    No categories
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  39. George Georgescu (1991). F-Multipliers and the Localization of Distributive Lattices II. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (19-22):293-300.
    No categories
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  40. Nicholas Rescher (1952). Review: Yuki Wooyenaka, Remark on a Set of Postulates for Distributive Lattices. [REVIEW] Journal of Symbolic Logic 17 (1):67-68.
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  41. H. P. Sankappanavar (1985). Distributive Lattices with a Dual Endomorphism. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):385-392.
    No categories
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  42. Sebastiaan A. Terwijn (2007). Kripke Models, Distributive Lattices, and Medvedev Degrees. Studia Logica 85 (3):319-332.
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  43. H. E. Vaughan (1948). Review: Garrett Birkhoff, S. A. Kiss, A Ternary Operation in Distributive Lattices. [REVIEW] Journal of Symbolic Logic 13 (1):50-51.
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  44. H. E. Vaughan (1951). Review: Ladislav Rieger, A Note on Topological Representations of Distributive Lattices; Kiyoski Iseki, Une Condition Pour Qu'un Lattice Soit Distributif. [REVIEW] Journal of Symbolic Logic 16 (1):62-62.
  45. Volker Weispfenning (1985). Quantifier Elimination for Distributive Lattices and Measure Algebras. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (14-18):249-261.
    No categories
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  46.  15
    Guram Bezhanishvili & Ramon Jansana (2011). Priestley Style Duality for Distributive Meet-Semilattices. Studia Logica 98 (1-2):83-122.
    We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms. As a result, our duality extends Hansoul’s duality and is an improvement of Celani’s duality.
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  47.  5
    Gabriela Hauser-Bordalo (2011). Prime Filters, Normality and Irreducibility in Lattices. Studia Logica 98 (1-2):5-7.
    We recall some notions introduced and developed by António Aniceto Monteiro, and show how these notions have been used and generalised, thus establishing a direct and indirect influence of Monteiro’s work that extends to this day.
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  48.  24
    Reiner Hähnle (1998). Commodious Axiomatization of Quantifiers in Multiple-Valued Logic. Studia Logica 61 (1):101-121.
    We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation (...)
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  49.  16
    Michał Kozak (2009). Distributive Full Lambek Calculus has the Finite Model Property. Studia Logica 91 (2):201 - 216.
    We prove the Finite Model Property (FMP) for Distributive Full Lambek Calculus ( DFL ) whose algebraic semantics is the class of distributive residuated lattices ( DRL ). The problem was left open in [8, 5]. We use the method of nuclei and quasi–embedding in the style of [10, 1].
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  50.  1
    Matthew Smedberg (2013). A Dense Family of Well-Behaved Finite Monogenerated Left-Distributive Groupoids. Archive for Mathematical Logic 52 (3-4):377-402.
    We construct a family $\fancyscript{F}$ , indexed by five integer parameters, of finite monogenerated left-distributive (LD) groupoids with the property that every finite monogenerated LD groupoid is a quotient of a member of $\fancyscript{F}$ . The combinatorial abundance of finite monogenerated LD groupoids is encoded in the congruence lattices of the groupoids $\fancyscript{F}$ , which we show to be extremely large.
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