Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets

International Journal of Approximate Reasoning

Volumn 55, Issue 1 PART 4, 2014, Pages 427-435

  Dzik, Wojciech ^a   Järvinen, Jouni ^b   Kondo, Michiro ^c  

^a UNIVERSITY OF SILESIA   (Poland)

^b not available   (Finland)

^c TOKYO DENKI UNIVERSITY   (Japan)

Author keywords

Heyting algebras; Heyting Brouwer algebras; Intuitionistic logic; Representation theorems; Rough sets

Indexed keywords

ALGEBRA; APPROXIMATION ALGORITHMS;

BOUNDED DISTRIBUTIVE LATTICE; COMPLEX ALGEBRA; GALOIS CONNECTION; HEYTING ALGEBRAS; INTUITIONISTIC LOGIC; REPRESENTATION THEOREM; ROUGH SET APPROXIMATION; UPPER AND LOWER APPROXIMATION;

ROUGH SET THEORY;

EID: 84889880993     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2013.07.005     Document Type: Article

References (19)

1. P. Alexandroff Diskrete Räume Matematičeskij Sbornik 2 1937 501 518
2. R. Balbes, and Ph. Dwinger Distributive Lattices 1974 University of Missouri Press Columbia, MO
3. R. Belohlavek Optimal triangular decompositions of matrices with entries from residuated lattices International Journal of Approximate Reasoning 50 2009 1250 1258
4. G. Birkhoff Rings of sets Duke Mathematical Journal 3 1937 443 454
5. B.A. Davey, and H.A. Priestley Introduction to Lattices and Order 2nd edition 2002 Cambridge University Press
6. W. Dzik, J. Järvinen, and M. Kondo Intuitionistic propositional logic with Galois connections Logic Journal of the IGPL 18 2010 837 858
7. W. Dzik, J. Järvinen, and M. Kondo Intuitionistic logic with a Galois connection has the finite model property Logic Journal of the IGPL 21 2013 199 204
8. G. Fischer Servi Axiomatizations for some intuitionistic modal logics Rendiconti del Seminario Matematico dell'Università Politecnica di Torino 42 1984 179 194
9. G. Grätzer General Lattice Theory 2nd edition 1998 Birkhäuser Basel
10. M. Hooshmandasl, A. Karimi, M. Almbardar, and B. Davvaz Axiomatic systems for rough set-valued homomorphisms of associative rings International Journal of Approximate Reasoning 54 2013 297 306
11. J. Järvinen Lattice theory for rough sets Transactions on Rough Sets VI 2007 400 498
12. J. Järvinen, M. Kondo, and J. Kortelainen Logics from Galois connections International Journal of Approximate Reasoning 49 2008 595 606
13. B. Jónsson, and A. Tarski Boolean algebras with operators. Part I American Journal of Mathematics 73 4 1951 891 939
14. J.-M. Ma, and W.-X. Zhang Axiomatic characterizations of dual concept lattices International Journal of Approximate Reasoning 54 2013 690 697
15. E. Orłowska, and Z. Pawlak Representation of nondeterministic information Theoretical Computer Science 29 1984 27 39
16. E. Orłowska, and I. Rewitzky Discrete dualities for Heyting algebras with operators Fundamenta Informaticae 81 2007 275 295
17. Z. Pawlak Rough sets International Journal of Computer and Information Sciences 11 1982 341 356
18. C. Rauszer Semi-Boolean algebras and their applications to intuitionistic logic with dual operations Fundamenta Mathematicae 83 1974 219 249
19. L. Shen, and D. Zhang The concept lattice functors International Journal of Approximate Reasoning 54 2013 166 183