caa a22 4500 463187202 CHVBK 20180406164857.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10472-007-9061-6 doi (NATIONALLICENCE)springer-10.1007/s10472-007-9061-6 The structure of the overhanging relations associated with some types of closure systems [Elektronische Daten] [Florent Domenach, Bruno Leclerc] Over many different kinds of cryptomorphisms equivalent with closure systems (and so with closure operators), we focus here on implication relations and the related overhanging relations, as introduced and axiomatized in a previous paper (Domenach and Leclerc, Math Soc Sci 47(3):349-366, 2004). In relation with data analysis motivations, we particularize the axioms on overhanging relations in order to account for some types of closure systems, such as nested or distributive ones. We also examine the lattice structure of overhanging relations, which is isomorphic to the lattice of closure systems, and derived structures for particular sets of overhangings. Springer Science+Business Media B.V., 2007 Closure system nationallicence Distributivity nationallicence Implication nationallicence Tree of subsets nationallicence Domenach Florent Computer Science Department, Intercollege, 46 Makedonitissas Ave, P.O. Box 24005, 1700, Nicosia, Cyprus aut Leclerc Bruno CAMS, EHESS, 54 bd Raspail, 75270, Paris Cedex 06, France aut Annals of Mathematics and Artificial Intelligence Springer Netherlands 49/1-4(2007-04-01), 137-149 1012-2443 49:1-4<137 2007 49 10472 https://doi.org/10.1007/s10472-007-9061-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10472-007-9061-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Domenach Florent Computer Science Department, Intercollege, 46 Makedonitissas Ave, P.O. Box 24005, 1700, Nicosia, Cyprus aut NATIONALLICENCE 700 1- Leclerc Bruno CAMS, EHESS, 54 bd Raspail, 75270, Paris Cedex 06, France aut NATIONALLICENCE 773 0- Annals of Mathematics and Artificial Intelligence Springer Netherlands 49/1-4(2007-04-01), 137-149 1012-2443 49:1-4<137 2007 49 10472 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer