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Abstrakty
Rough relation algebras are a generalization of relation algebras such that the underlying lattice structure is a regular double Stone algebra. Standard models are algebras of rough relations. A discrete duality is a relationship between classes of algebras and classes of relational systems (frames). In this paper we prove a discrete duality for a class of rough relation algebras and a class of frames.
Wydawca
Czasopismo
Rocznik
Tom
Strony
35--47
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Brock University, St. Catharines, Ontario, Canada, L2S 3A1
autor
- National Institute of Telecommunications, Szachowa 1, 04–894 Warsaw, Poland.
Bibliografia
- [1] Banerjee, M. and Chakraborty, M. (2004). Algebras from rough sets. In S.K. Pal, L. Polkowski, and A.Skowron, editors, Rough-Neuro Computing: Techniques for Computing with Words, pages 157-184. Springer, Heidelberg.
- [2] Chin, L. and Tarski, A. (1951). Distributive and modular laws in the arithmetic of relation algebras. University of California Publications in Mathematics, 1:341-384.
- [3] Comer, S. (1993). On connections between information systems, rough sets, and algebraic logic. In Rauszer, C., editor, Algebraic Methods in Logic and Computer Science, volume 28 of Banach Center Publications, pages 117-124. Polish Academy of Science, Warszawa.
- [4] Demri, S. and Orłowska, E. (2002). Incomplete Information: Stucture, Inference, Complexity. EATCS Monographs in Theoretical Computer Science. Springer Verlag, Heidelberg.
- [5] Duntsch, I. (1994). Rough relation algebras. Fundamenta Informaticae, 21:321-331.
- [6] Duntsch, I. (1997). A logic for rough sets. Theoretical Computer Science, 179(1-2):427-436.
- [7] Duntsch, I. and Orłowska, E. (2011). Discrete dualities for double Stone algebras. Studia Logica, 99:127-142.
- [8] Duntsch, I. and Winter, M. (2006). Rough relation algebras revisited. Fundamenta Informaticae, 74:283-300.
- [9] Gratzer, G. (2000). General Lattice Theory. Birkhauser, Basel, 2nd edition.
- [10] Iturrioz, L. (1998). Rough sets and three valued structures. In Orłowska, E., editor, Logic at Work, pages 596-603. Physica - Verlag, Heidelberg.
- [11] Orłowska, E. and Golinska-Pilarek, J. (2011). Dual Tableaux: Foundation, Methodology, Case Studies, volume 33 of Trends in Logic. Springer Verlag, Heidelberg.
- [12] Orłowska, E. and Rewitzky, I. (2005). Duality via Truth: Semantic frameworks for lattice-based logics. Logic Journal of the IGPL, 13(4):467-490.
- [13] Orłowska, E. and Rewitzky, I. (2007). Discrete duality and its applications to reasoning with incomplete information. In Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms, volume 4585 of Lecture Notes in Artificial Intelligence, pages 51-56. Springer.
- [14] Orłowska, E. and Rewitzky, I. (2009). Discrete duality for relation algebras and cylindric algebras. In Berghammer, R., Jaoua, A., and Moller, B., editors, RelMiCS, volume 5827 of Lecture Notes in Computer Science, pages 291-305. Springer.
- [15] Pagliani, P. (1998). Rough Sets Theory and Logic-Algebraic Structures. In Orłowska, E., editor, Incomplete Information -Rough Set Analysis, pages 109-190. Physica - Verlag, Heidelberg.
- [16] Pawlak, Z. (1982). Rough Sets. Internat. J. Comput. Inform. Sci., 11:341-356.
- [17] Pawlak, Z. (1981). Rough Relations. ICS PAS Reports 435, Warsaw.
- [18] Pomykała, J. and Pomykała, J. A. (1988). The Stone algebra of rough sets. Bull. Polish Acad. Sci. Math., 36:495-508.
- [19] Tarski, A. (1941). On the calculus of relations. Journal of Symbolic Logic, 6:73-89.
- [20] Urquhart, A. (1996). Duality for algebras of relevant logics. Studia Logica, 56:263-276.
- [21] Varlet, J. C. (1968). Algebres des Lukasiewicz Trivalentes. Bull. Soc. Roy. Sci. Liege, 36:399-408.
- [22] Varlet, J. C. (1972). A regular variety of type (2,2,1,1,0,0). Algebra Universalis, 2:218-223.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f54eab9c-3bdb-456f-8329-63a80fd50988