Results for 'Priestley duality'

998 found
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  1.  14
    The Syntax and Semantics of Entailment in Duality Theory.B. A. Davey, M. Haviar & H. A. Priestley - 1995 - Journal of Symbolic Logic 60 (4):1087-1114.
    Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the (...)
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  2.  20
    Duality for Double Quasioperator Algebras Via Their Canonical Extensions.M. Gehrke & H. A. Priestley - 2007 - Studia Logica 86 (1):31-68.
    This paper is a study of duality in the absence of canonicity. Specifically it concerns double quasioperator algebras, a class of distributive lattice expansions in which, coordinatewise, each operation either preserves both join and meet or reverses them. A variety of DQAs need not be canonical, but as has been shown in a companion paper, it is canonical in a generalized sense and an algebraic correspondence theorem is available. For very many varieties, canonicity (as traditionally defined) and correspondence lead (...)
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  3.  73
    Optimal Natural Dualities for Varieties of Heyting Algebras.B. A. Davey & H. A. Priestley - 1996 - Studia Logica 56 (1-2):67 - 96.
    The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.
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  4.  32
    Natural Dualities for Varieties Ofn-Valued Łukasiewicz Algebras.H. A. Priestley - 1995 - Studia Logica 54 (3):333 - 370.
    Natural dualities are developed for varieties ofn-valued ukasiewicz algebras with and without negation. These dualities are based on hom-functors, and parallel Stone duality for Boolean algebras. A translation is described which relates the natural dualities to the corresponding restricted Priestley dualities. This enables a unified approach to free algebras to be presented, whence R. Cignoli's characterisations of the finitely generated free algebras are elucidated and new descriptions of arbitrary free algebras obtained. Finally it is shown how dualities for (...)
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  5.  13
    Natural Dualities Through Product Representations: Bilattices and Beyond.L. M. Cabrer & H. A. Priestley - 2016 - Studia Logica 104 (3):567-592.
    This paper focuses on natural dualities for varieties of bilattice-based algebras. Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying bilattices-based algebras is product representation. The authors recently set up a widely applicable algebraic framework which enabled product representations over a base variety to be derived in a uniform and categorical manner. By combining this methodology with that of natural duality theory, we demonstrate how to (...)
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  6.  21
    Canonical Extensions and Discrete Dualities for Finitely Generated Varieties of Lattice-Based Algebras.B. A. Davey & H. A. Priestley - 2012 - Studia Logica 100 (1-2):137-161.
    The paper investigates completions in the context of finitely generated lattice-based varieties of algebras. In particular the structure of canonical extensions in such a variety $${\mathcal {A}}$$ is explored, and the role of the natural extension in providing a realisation of the canonical extension is discussed. The completions considered are Boolean topological algebras with respect to the interval topology, and consequences of this feature for their structure are revealed. In addition, we call on recent results from duality theory to (...)
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  7.  39
    Priestley Duality for Bilattices.A. Jung & U. Rivieccio - 2012 - Studia Logica 100 (1-2):223-252.
    We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.
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  8.  11
    Priestley Duality for Paraconsistent Nelson’s Logic.Sergei P. Odintsov - 2010 - Studia Logica 96 (1):65-93.
    The variety of N4? -lattices provides an algebraic semantics for the logic N4?, a version of Nelson 's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of N4?-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
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  9.  40
    The Priestley Duality for Wajsberg Algebras.N. G. Martínez - 1990 - Studia Logica 49 (1):31 - 46.
    The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way.As a first application of this duality, a theorem about unicity of the structure is given.
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  10.  45
    Applications of Priestley Duality in Transferring Optimal Dualities.Brian A. Davey & Miroslav Haviar - 2004 - Studia Logica 78 (1-2):213 - 236.
    This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety of Kleene algebras and the quasi-varieties n of pseudocomplemented distributive lattices (n 1).
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  11.  18
    Priestley Duality for Some Subalgebra Lattices.Georges Hansoul - 1996 - Studia Logica 56 (1-2):133 - 149.
    Priestley duality can be used to study subalgebras of Heyting algebras and related structures. The dual concept is that of congruence on the dual space and the congruence lattice of a Heyting space is dually isomorphic to the subalgebra lattice of the dual algebra. In this paper we continue our investigation of the congruence lattice of a Heyting space that was undertaken in [10], [8] and [12]. Our main result is a characterization of the modularity of this lattice (...)
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  12. Priestley's Writings on Philosophy, Science, and Politics.J. Priestley - 1965
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  13.  12
    Free Modal Lattices Via Priestley Duality.Claudia B. Wegener - 2002 - Studia Logica 70 (3):339 - 352.
    A Priestley duality is developed for the variety j of all modal lattices. This is achieved by restricting to j a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety j was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos'' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with (...)
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  14. A Free Discussion of the Doctrines of Materialism, and Philosophical Necessity in a Correspondence Between Dr. Price, and Dr. Priestley. To Which Are Added, by Dr. Priestley, an Introduction, Explaining the Nature of the Controversy, and Letters to Several Writers Who Have Animadverted on His Disquisitions Relating to Matter and Spirit, or His Treatise on Necessity. [REVIEW]Joseph Priestley & Richard Price - 1778 - Printed for J. Johnson ... And T. Cadell.
  15.  45
    Priestley Style Duality for Distributive Meet-Semilattices.Guram Bezhanishvili & Ramon Jansana - 2011 - 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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  16.  28
    Priestley Duality for Quasi-Stone Algebras.Hernando Gaitán - 2000 - Studia Logica 64 (1):83-92.
    In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite set.
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  17.  9
    Priestley Duality for Paraconsistent Nelson’s Logic.Sergei P. Odintsov - 2010 - Studia Logica 96 (1):65-93.
  18.  33
    Fine Hierarchies Via Priestley Duality.Victor Selivanov - 2012 - Annals of Pure and Applied Logic 163 (8):1075-1107.
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  19. List of Published Papers Studia Logica 56 (1996), 277-290 Special Issue: Priestley Duality.M. E. Adams & W. Dziobiak - 1996 - Studia Logica 56:277-290.
     
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  20. Special Issue on Priestley Duality.M. Adams & W. Dziobiak - 1996 - Studia Logica 56:1-2.
  21. Priestley Duality for Quasi-Stone Algebras.(English Summary).Lutz Heindorf - 2000 - Studia Logica 64 (1):83-92.
     
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  22.  12
    Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hern?N. J. San Mart?N. - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator r preserving finite meets which also satisfies the equation?? b V, for all a,b? A. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak (...)
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  23. Miscellaneous Observations Relating to Education: More Especially as It Respects the Conduct of the Mind.Joseph Priestley - 2013 - Cambridge University Press.
    The English polymath Joseph Priestley wrote on a wide range of scientific, theological and pedagogical subjects. After the appearance of his influential Rudiments of English Grammar and A Course of Lectures on the Theory of Language and Universal Grammar, both of which are reissued in this series, Priestley produced in 1765 his Essay on a Course of Liberal Education, which is included and expanded on in this 1778 publication. Here he explains the reasons behind his decision to guide (...)
     
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  24.  21
    Duality for Algebras of Relevant Logics.Alasdair Urquhart - 1996 - Studia Logica 56 (1-2):263 - 276.
    This paper defines a category of bounded distributive lattice-ordered grupoids with a left-residual operation that corresponds to a weak system in the family of relevant logics. Algebras corresponding to stronger systems are obtained by adding further postulates. A duality theoey piggy-backed on the Priestley duality theory for distributive lattices is developed for these algebras. The duality theory is then applied in providing characterizations of the dual spaces corresponding to stronger relevant logics.
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  25. Political Writings.Joseph Priestley - 1993 - Cambridge University Press.
    Joseph Priestley (1733-1804) was arguably the most important English theorist to focus on the issue of political liberty during the English Enlightenment. His concept of freedom is of crucial importance to two of the major issues of his day: the right of dissenters to religious toleration, and the right of the American colonists to self-government. Priestley's writings lack a modern edition and this new collection will be the first to render accessible his Essay on First Principles, The Present (...)
     
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  26.  21
    A Coalgebraic View of Heyting Duality.Brian A. Davey & John C. Galati - 2003 - Studia Logica 75 (3):259 - 270.
    We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.
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  27.  6
    Restricted Priestley Dualities and Discriminator Varieties.B. A. Davey & A. Gair - 2017 - Studia Logica 105 (4):843-872.
    Anyone who has ever worked with a variety \ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one—but until now there has been no abstract definition. Here we provide one. After deriving some basic properties of a restricted Priestley dual category \ of such a variety, we give a characterisation, in terms of \, of finitely generated discriminator subvarieties of \. As an application of (...)
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  28.  54
    Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I.Viorica Sofronie-Stokkermans - 2000 - 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 for logics (...)
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  29.  29
    Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics II.Viorica Sofronie-Stokkermans - 2000 - 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 (...)
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  30.  24
    A Simplified Duality for Implicative Lattices and L-Groups.Nestor G. Martinez - 1996 - Studia Logica 56 (1-2):185 - 204.
    A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given (...)
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  31.  24
    De Morgan Heyting Algebras Satisfying the Identity Xn ≈ X.Valeria Castaño & Marcela Muñoz Santis - 2011 - Mathematical Logic Quarterly 57 (3):236-245.
    In this paper we investigate the sequence of subvarieties equation imageof De Morgan Heyting algebras characterized by the identity xn ≈ x. We obtain necessary and sufficient conditions for a De Morgan Heyting algebra to be in equation image by means of its space of prime filters, and we characterize subdirectly irreducible and simple algebras in equation image. We extend these results for finite algebras in the general case equation image. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  32.  24
    Distributive Lattices with a Negation Operator.Sergio Arturo Celani - 1999 - 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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  33.  8
    The Strong Endomorphism Kernel Property in Double MS-Algebras.Jie Fang - 2017 - Studia Logica 105 (5):995-1013.
    An endomorphism on an algebra \ is said to be strong if it is compatible with every congruence on \; and \ is said to have the strong endomorphism kernel property if every congruence on \, other than the universal congruence, is the kernel of a strong endomorphism on \. Here we characterise the structure of those double MS-algebras that have this property by the way of Priestley duality.
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  34. Collected Works of John Stuart Mill, Volume X, Essays on Ethics, Religion and Society.John Stuart Mill, J. M. Robson, F. E. L. Priestley & D. P. Dryer - 1970 - Philosophy 45 (173):252-254.
     
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  35.  33
    Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...)
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  36.  63
    Ockham Algebras with Balanced Double Pseudocomplementation.Jie Fang - 2008 - Studia Logica 90 (2):189-209.
    In this paper, we introduce a variety bdO of Ockham algebras with balanced double pseudocomplementation, consisting of those algebras of type where is an Ockham algebra, is a double p -algebra, and the operations and are linked by the identities [ f ( x )]* = [ f ( x )] + = f 2 ( x ), f ( x *) = x ** and f ( x + ) = x ++ . We give a description of the (...)
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  37.  32
    On Some Compatible Operations on Heyting Algebras.Rodolfo Cristian Ertola Biraben & Hernán Javier San Martín - 2011 - Studia Logica 98 (3):331-345.
    We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding (...)
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  38. Pudgalavāda Buddhist Philosophy.Leonard Priestley - 2005 - Internet Encyclopedia of Philosophy.
     
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  39. Disquisitions Relating to Matter and Spirit.Joseph Priestley - 1777 - Arno Press.
  40.  31
    Semi-Demorgan Algebras.David Hobby - 1996 - Studia Logica 56 (1-2):151 - 183.
    Semi-DeMorgan algebras are a common generalization of DeMorgan algebras and pseudocomplemented distributive lattices. A duality for them is developed that builds on the Priestley duality for distributive lattices. This duality is then used in several applications. The subdirectly irreducible semi-DeMorgan algebras are characterized. A theory of partial diagrams is developed, where properties of algebras are tied to the omission of certain partial diagrams from their duals. This theory is then used to find and give axioms for (...)
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  41.  11
    Linear Heyting Algebras with a Quantifier.Laura Rueda - 2001 - Annals of Pure and Applied Logic 108 (1-3):327-343.
    A Q -Heyting algebra is an algebra of type such that is a Heyting algebra and the unary operation ∇ satisfies the conditions ∇0=0, a ∧∇ a = a , ∇=∇ a ∧∇ b and ∇=∇ a ∨∇ b , for any a , b ∈ H . This paper is devoted to the study of the subvariety QH L of linear Q -Heyting algebras. Using Priestley duality we investigate the subdirectly irreducible linear Q -Heyting algebras and, as (...)
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  42.  5
    The Balanced Pseudocomplemented Ockham Algebras with the Strong Endomorphism Kernel Property.Jie Fang - 2019 - Studia Logica 107 (6):1261-1277.
    An endomorphism on an algebra \ is said to be strong if it is compatible with every congruence on \; and \ is said to have the strong endomorphism kernel property if every congruence on \, other than the universal congruence, is the kernel of a strong endomorphism on \. Here we characterise the structure of Ockham algebras with balanced pseudocomplementation those that have this property via Priestley duality.
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  43. A Free Discussion of the Doctrines of Materialism, and Philosophical Necessity in a Correspondence Between Dr. Price, and Dr. Priestly.Richard Price & Joseph Priestley - 1778 - Printed for J. Johnson and T. Cadell.
  44.  16
    Weak-Quasi-Stone Algebras.Sergio A. Celani & Leonardo M. Cabrer - 2009 - Mathematical Logic Quarterly 55 (3):288-298.
    In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the (...)
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  45.  16
    Emptiness in Thesatyasiddhi.C. D. C. Priestley - 1970 - Journal of Indian Philosophy 1 (1):30-39.
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  46. Letters to a Philosophical Unbeliever (1787).Joseph Priestley - 1974 - New York: Garland.
     
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  47.  13
    Mead, George Herbert, 133,135,171 Mill, John Stuart, 55,188, 242.Phillip E. Johnson, Thomas Kuhn, Abraham Lefkowitz, Henry Linville, John Locke, Helen Longino, Hermann Lotze, Arthur O. Lovejoy & Joseph Priestley - 2002 - In F. Thomas Burke, D. Micah Hester & Robert B. Talisse (eds.), Dewey's Logical Theory: New Studies and Interpretations. Vanderbilt University Press.
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  48.  12
    Koromu Temporal Expressions.Carol Priestley - 2012 - In L. Filipovic & K. M. Jaszczolt (eds.), Space and Time in Languages and Cultures: Language, Culture, and Cognition. John Benjamins. pp. 143.
  49.  10
    Weak‐Quasi‐Stone Algebras.Sergio A. Celani & Leonardo M. Cabrer - 2009 - Mathematical Logic Quarterly 55 (3):288-298.
    In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the (...)
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  50.  8
    Physical Science and Objective Reality.H. J. Priestley - 1923 - Australasian Journal of Philosophy 1 (3):208 – 212.
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