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Tytuł artykułu

A Discrete Representation for Dicomplemented Lattices

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Dicomplemented lattices were introduced as an abstraction of Wille’s concept algebras which provided negations to a concept lattice. We prove a discrete representation theorem for the class of dicomplemented lattices. The theorem is based on a topology free version of Urquhart’s representation of general lattices.
Wydawca
Rocznik
Strony
281--295
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
  • Dept of Computer Science, Brock University, St Catharines, ON, L2S 3A1, Canada
autor
  • Fachbereich Wirtschaft, Berner Fachhochschule, CH-3005, Bern, Switzerland
autor
  • National Institute of Telecommunications, Szachowa 1, 04–894, Warszawa, Poland
Bibliografia
  • [1] Wille R. Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival I (ed.), Ordered sets, NATO Advanced Studies Institute, vol. 83 pp. 445–470. Reidel, Dordrecht, 1982. URL https://doi.org/10.1007/978-94-009-7798-3_15.
  • [2] Kwuida L. Dicomplemented Lattices. A Contextual Generalization of Boolean Algebras. Ph. D. Thesis, Technische Universität Dresden, 2004.
  • [3] Rauszer C. Semi-Boolean algebras and their applications to intuitionistic logic with dual operations. Fundamenta Mathematicae, 1974;83(3):219–249. URL http://eudml.org/doc/214696.
  • [4] Rasiowa H. An Algebraic Approach to non-Classical Logics, volume 78 of Studies in Logic and Foundations of Mathematics. North Holland and PWN, 1974. doi:10.2307/2272879.
  • [5] Urquhart A. A topological representation theorem for lattices. Algebra Universalis, 1978;8(1):45–58. URL https://doi.org/10.1007/BF02485369.
  • [6] Birkhoff G. Lattice Theory, volume 25 of Am. Math. Soc. Colloquium Publications. AMS, Providence, 2nd edition 1948. URL https://books.google.pl/books?id=eBFHAQAAIAAJ.
  • [7] Orłowska E, Rewitzky I, Radzikowska A. Dualities for Structures of Applied Logics, volume 56 of Studies in Logic. College Publications, 2015. ISBN-10: 184890181X, 13: 978-1848901810.
  • [8] Moore EH. Introduction to a form of general analysis. Yale University Press, New Haven, 1910. URL http://trove.nla.gov.au/version/47765419.
  • [9] Everett C. Closure Operators and Galois Theory in Lattices. Transactions of the American Mathematical Society, 1944;55(3):514–525. URL https://doi.org/10.1090/S0002-9947-1944-0010556-9.
  • [10] Ore O. Galois connexions. Transactions of the American Mathematical Society, 1944;55:493–513. URL https://doi.org/10.1090/S0002-9947-1944-0010555-7.
  • [11] Gargov G, Passy S, Tinchev T. Modal Environment for Boolean Speculations. In: Skordev D (ed.), Mathematical Logic and Applications. Plenum Press, New York, 1987 pp. 253–263. URL https://doi.org/10.1007/978-1-4613-0897-3_17.
  • [12] Düntsch I, Orłowska E. A representation of lattice frames, 2017. Manuscript.
  • [13] Wille R. Boolean Concept Logic. In: Ganter B, Mineau G (eds.), Proc. 8th Int. Conf. on Conceptual Structures ICCS 2000, volume 1867 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, 2000 pp. 317–331. URL https://doi.org/10.1007/10722280_22.
  • [14] Dzik W, Orlowska E, van Alten C. Relational Representation Theorems for General Lattices with Negations. In: Schmidt R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006, volume 4136 of Lecture Notes in Computer Science. Springer, Berlin, Heidelberg, 2006 pp. 162–176. ISBN 978-3-540-37873-0, 978-3-540-37874-7, 2006. URL https://doi.org/10.1007/11828563_11.
  • [15] Craig A, Haviar M. Reconciliation of approaches to the construction of canonical extensions of bounded lattices. Mathematica Slovaka, 2014;64(6):1335–1356. URL https://doi.org/10.2478/s12175-014-0278-7.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6df0f47f-bd02-4f7c-b57c-eabbfc72f0ff
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