%0 Conference Paper %1 doerfel2011contextbased %A Doerfel, Stephan %B Formal Concept Analysis %C Berlin / Heidelberg %D 2011 %E Valtchev, Petko %E Jäschke, Robert %I Springer %K 2011 characterization context da itegpub modular variety myown sdomyown %P 93-106 %R 10.1007/978-3-642-20514-9_9 %T A Context-Based Description of the Doubly Founded Concept Lattices in the Variety Generated by M_3 %U http://dx.doi.org/10.1007/978-3-642-20514-9_9 %V 6628 %X 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.

@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.}, added-at = {2011-05-03T14:10:06.000+0200}, 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}, biburl = {https://www.bibsonomy.org/bibtex/25cee560a10f3cb4ad3cb3726b6a18ff4/sdo}, booktitle = {Formal Concept Analysis}, description = {SpringerLink - Abstract}, doi = {10.1007/978-3-642-20514-9_9}, editor = {Valtchev, Petko and Jäschke, Robert}, interhash = {05f9bbf79efdce60316e0dc25528ea1c}, intrahash = {5cee560a10f3cb4ad3cb3726b6a18ff4}, keywords = {2011 characterization context da itegpub modular variety myown sdomyown}, pages = {93-106}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, timestamp = {2015-08-17T16:14:31.000+0200}, 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 }