Morozov, A. S.; L’vova, M. A. On computable formal concepts in computable formal contexts. (Russian, English) Zbl 1164.03344 Sib. Mat. Zh. 48, No. 5, 1083-1092 (2007); translation in Sib. Math. J. 48, No. 5, 871-878 (2007). Summary: We introduce and study the notions of computable formal context and computable formal concept. We give some examples of computable formal contexts in which the computable formal concepts fail to form a lattice and study the complexity aspects of formal concepts in computable contexts. In particular, we give some sufficient conditions under which the computability or noncomputability of a formal concept could be recognized from its lattice-theoretic properties. We prove the density theorem showing that in a Cantor-like topology every formal concept can be approximated by computable ones. We also show that not all formal concepts have lattice-theoretic approximations as suprema or infima of families of computable formal concepts. MSC: 03D45 Theory of numerations, effectively presented structures 68T30 Knowledge representation Keywords:formal concept analysis; computable formal context; computable concept; computable model PDFBibTeX XMLCite \textit{A. S. Morozov} and \textit{M. A. L'vova}, Sib. Mat. Zh. 48, No. 5, 1083--1092 (2007; Zbl 1164.03344); translation in Sib. Math. J. 48, No. 5, 871--878 (2007) Full Text: EuDML EMIS