A Discrete Representation for Dicomplemented Lattices

Issue title: Helena Rasiowa’s Heritage in Mathematical Logic. Centenary Special Issue

Guest editors: Damian Niwiński and Ewa Orłowska

Article type: Research Article

Authors: Düntsch, Ivo^{a; *} | Kwuida, Léonard^b | Orłowska, Ewa^{c; †}

Affiliations: [a] Dept of Computer Science, Brock University, St Catharines, ON, L2S 3A1, Canada. duentsch@brocku.ca | [b] Fachbereich Wirtschaft, Berner Fachhochschule, CH-3005, Bern, Switzerland. leonard.kwuida@bfh.ch | [c] National Institute of Telecommunications, Szachowa 1, 04–894, Warszawa, Poland. orlowska@itl.waw.pl

Correspondence: [†] Ewa Orłowska gratefully acknowledges support from the National Science Centre project DEC-2011/02/A/HS1/00395. Address for correspondence: National Institute of Telecommunications, Szachowa 1, 04–894, Warszawa, Poland

Note: [*] Ivo Düntsch gratefully acknowledges support by the Natural Sciences and Engineering Research Council of Canada Discovery Grant 250153 and by the Bulgarian National Fund of Science, contract DN02/15/19.12.2016.

Abstract: 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.

DOI: 10.3233/FI-2017-1609

Journal: Fundamenta Informaticae, vol. 156, no. 3-4, pp. 281-295, 2017