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Textural dependency and concept lattices. (English) Zbl 1522.68534

Summary: In this paper, the dependence spaces are discussed for textural formal concepts considering the method given by Ma et al. A complete congruence on a complete lattice is an equivalence relation if it satisfies the infinite substitution property. More generally, a join-dependence and a meet-dependence space with respect to infinite domain of discourse are presented. Using the duality in textures, the closure and interior operators are defined to obtain the intensions and co-intensions of concept lattices, respectively. The main theorem for dual formal concept lattices given by Chen and Yao is stated. Further, it is shown that the co-intensions of a dual formal concept lattice can be obtained using an interior operator. Finally, the independency notion of Novotný for t-formal concepts is discussed.

MSC:

68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence
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