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Restructuring lattice theory: an approach based on hierarchies of concepts. (English) Zbl 1247.06004
Ferré, Sébastien (ed.) et al., Formal concept analysis. 7th international conference, ICFCA 2009, Darmstadt, Germany, May 21–24, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-01814-5/pbk). Lecture Notes in Computer Science 5548. Lecture Notes in Artificial Intelligence, 314-339 (2009).
Summary: Lattice theory today reflects the general status of current mathematics: there is a rich production of theoretical concepts, results, and developments, many of which are reached by elaborate mental gymnastics; on the other hand, the connections of the theory to its surroundings are getting weaker and weaker, with the result that the theory and even many of its parts become more isolated. Restructuring lattice theory is an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory.
This is a facsimile reprint of the author’s paper originally published in [Ordered sets, Proc. NATO Adv. Study Inst., Banff/Can. 1981, 445–470 (1982; Zbl 0491.06008)].
For the entire collection see [Zbl 1163.68003].

MSC:
06B05 Structure theory of lattices
06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B15 Representation theory of lattices
06B23 Complete lattices, completions
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