@inproceedings{doerfel2011contextbased, abstract = {In universal algebra and in lattice theory the notion of varieties is very prominent, since varieties describe the classes of all algebras (or of all lattices) modeling a given set of equations. While a comprehensive translation of that notion to a similar notion of varieties of complete lattices – and thus to Formal Concept Analysis – has not yet been accomplished, some characterizations of the doubly founded complete lattices of some special varieties (e.g. the variety of modular or that of distributive lattices) have been discovered. In this paper we use the well-known arrow relations to give a characterization of the formal contexts of doubly founded concept lattices in the variety that is generated by M 3 – the smallest modular, non-distributive lattice variety.}, address = {Berlin / Heidelberg}, affiliation = {Knowledge & Data Engineering Group, Department of Mathematics and Computer Science, University of Kassel, Wilhelmshöher Allee 73, 34121 Kassel, Germany}, author = {Doerfel, Stephan}, booktitle = {Formal Concept Analysis}, doi = {10.1007/978-3-642-20514-9_9}, editor = {Valtchev, Petko and Jäschke, Robert}, interhash = {05f9bbf79efdce60316e0dc25528ea1c}, intrahash = {5cee560a10f3cb4ad3cb3726b6a18ff4}, pages = {93-106}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {A Context-Based Description of the Doubly Founded Concept Lattices in the Variety Generated by M_3}, url = {http://dx.doi.org/10.1007/978-3-642-20514-9_9}, vgwort = {23}, volume = 6628, year = 2011 } @article{ganter1981finite, author = {Ganter, Bernhard and Poguntke, Werner and Wille, Rudolf}, interhash = {0ca78ea0263b8ed16512692b01d9f48a}, intrahash = {52fc3b6964fc9df1069a4b8e3c010ca4}, journal = {Algebra Universalis}, month = {December}, number = 1, pages = {160--171}, title = {Finite sublattices of four-generated modular lattices}, url = {http://dx.doi.org/10.1007/BF02483876}, volume = 12, year = 1981 } @article{faigle1981projective, abstract = {A set of axioms is presented for a projective geometry as an incidence structure on partially ordered sets of "points" and "lines". The axioms reduce to the axioms of classical projective geometry in the case where the points and lines are unordered. It is shown that the lattice of linear subsets of a projective geometry is modular and that every modular lattice of finite length is isomorphic to the lattice of linear subsets of some finite-dimensional projective geometry. Primary geometries are introduced as the incidence-geometric counterpart of primary lattices. Thus the theory of finite-dimensional projective geometries includes the theory of finite- 3-dimensional projective Hjelmslev-spaces of level $n$ as a special case. Finally, projective geometries are characterized by incidence properties of points and hyperplanes.}, author = {Faigle, Ulrich and Herrmann, Christian}, copyright = {Copyright © 1981 American Mathematical Society}, interhash = {c46eccd07dd31a7ca082f971f7dee7cd}, intrahash = {86caaca1e2111b3675308a1a30498c66}, issn = {00029947}, journal = {Transactions of the American Mathematical Society}, jstor_articletype = {research-article}, jstor_formatteddate = {Jul., 1981}, language = {English}, number = 1, pages = {pp. 319-332}, publisher = {American Mathematical Society}, title = {Projective Geometry on Partially Ordered Sets}, url = {http://www.jstor.org/stable/1998401}, volume = 266, year = 1981 } @article{GPW, author = {Ganter, Bernhard and Poguntke, Werner and Wille, Rudolf}, interhash = {0ca78ea0263b8ed16512692b01d9f48a}, intrahash = {bd16dcc0461cbe4b19296828e312a106}, journal = {Algebra Univ.}, pages = {160--171}, title = {Finite sublattices of four-generated modular lattices}, volume = 12, year = 1981 }