Abstract
In a number of papers M.Ginsberg introduced algebras called bilattices having two separate lattice structure and one additional basic unary operation. They originated as an algebraization of some nonclassical logics that arise in artificial intelligence and knowledge-based logic programming. In this paper we introduce some new class of bilattices which originate from interval lattices and show that each of them is simple. A known simple lattices are used to give other examples of simple bilattices. We also describe simple bilattices satisfying some additional identities so called P-bilattices (or interlaced bilattices).
The paper was written within the framework of COST Action 274.
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References
Avron, A.: The structure of interlaced bilattices. Math. Structures Comput. Sci. 6 (1996) 287–299
Duthie, W.: Segments of order sets. Trans. Amer. Math. Soc. 51(1942) 1–14
Fitting, M.: Bilattices and the theory of truth. Journal of Philosophical Logic 18(1989) 225–256
Fitting, M.: Bilattices in logic programming. The Twentieth International Symposium on Multiple-Valued Logic (ed. Epstein, G.) IEEE (1990) 238–246
Fitting, M.: Kleene's logic, generalized. J. Logic Computat. 1 (1991) 797–810
Ginsberg, M.: Multi-valued logics. Proc. AAAI-86, Fifth National Conference on Artificial Intelligence, Morgan Kaufmann Publishers (1986) 243–247
Ginsberg, M.: Multivalued logics: A uniform approach to inference in artificial intelligence. Computational Intelligence 4(1988) 265–316
Igoshin, V.: Algebraic characteristic of interval lattices/Russian/. Uspekhi Mat. Nauk 40(1985) 205–206
McKenzie, R., McNulty, G., Taylor, W.: Algebras, Lattices, Varieties. The Wadsworth and Brooks, Monterey (1987)
Mobasher, B., Pigozzi, D., Slutzki, G., Voutsadakis, G.: A Duality theory for bilattices. Algebra Universalis 43(2000) 109–125
Odintsov, V.: Congruences on lattices of intervals /Russian/. Mat. Zap. 14(1988) 102–111
Pynko, A.: Regular bilattices. Journal of Applied Non-Classical Logics 10(2000) 93–111
Romanowska, A., Trakul, A.( Pilitowska A.): On the structure of some bilattices. In: Hakowska, K., Stawski, B.(eds.) Universal and Applied Algebra, World Scientific (1989) 235–253
Wille, R.: A note on simple lattices. Col. Math. Soc. Janos Bolyai, 14. Lattice Theory, Szeged (1974) 455–462
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© 2002 Springer-Verlag Berlin Heidelberg
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Pilitowska, A. (2002). Interval Bilattices and Some Other Simple Bilattices. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_13
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DOI: https://doi.org/10.1007/3-540-36280-0_13
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