A Discrete Representation for Dicomplemented Lattices

• Autorzy: Düntsch I. , Kwuida L. , Orłowska E.

Identyfikatory

DOI

10.3233/FI-2017-1609

• 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.

Słowa kluczowe

EN

distributive lattice; Dedekind cut; Heyting algebra; discrete geometry

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 156, nr 3/4
• Strony: 281--295
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Düntsch I.

• Dept of Computer Science, Brock University, St Catharines, ON, L2S 3A1, Canada

autor

Kwuida L.

• Fachbereich Wirtschaft, Berner Fachhochschule, CH-3005, Bern, Switzerland

autor

Orłowska E.

• National Institute of Telecommunications, Szachowa 1, 04–894, Warszawa, Poland

Bibliografia

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• [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.
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• [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).