@incollection{wille1982restructuring,
  abstract = {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.},
  author = {Wille, Rudolf},
  booktitle = {Ordered Sets},
  doi = {10.1007/978-94-009-7798-3_15},
  editor = {Rival, Ivan},
  interhash = {1e021e8bace9683c92416cd882eb4c4d},
  intrahash = {9f2962c0b9b15ddd770ed8eba3935e72},
  isbn = {978-94-009-7800-3},
  language = {English},
  pages = {445-470},
  publisher = {Springer Netherlands},
  series = {NATO Advanced Study Institutes Series},
  title = {Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts},
  url = {http://dx.doi.org/10.1007/978-94-009-7798-3_15},
  volume = 83,
  year = 1982
}

@article{guigues1986familles,
  author = {Guigues, J.-L. and Duquenne, V.},
  interhash = {3671be91dd80e5c415ede85e94ada3d7},
  intrahash = {fee9525a2e89b5ebced886b3a9f0194d},
  journal = {Mathématiques et Sciences Humaines},
  pages = {5--18},
  title = {Familles minimales d'implications informatives résultant d'un tableau de données binaires},
  volume = 95,
  year = 1986
}

@incollection{wille2009restructuring,
  address = {Berlin / Heidelberg},
  affiliation = {Fachbereich Mathematik, Technische Hochschule Darmstadt, 6100 Darmstadt, Federal Republic of Germany},
  author = {Wille, Rudolf},
  booktitle = {Formal Concept Analysis},
  doi = {10.1007/978-3-642-01815-2_23},
  editor = {Ferré, Sébastien and Rudolph, Sebastian},
  interhash = {d2b646426cb8330a80978721e5047bcd},
  intrahash = {0076ddf2562946e870f89834b6d1cd25},
  isbn = {978-3-642-01814-5},
  keyword = {Computer Science},
  pages = {314-339},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {RESTRUCTURING LATTICE THEORY: AN APPROACH BASED ON HIERARCHIES OF CONCEPTS},
  url = {http://dx.doi.org/10.1007/978-3-642-01815-2_23},
  volume = 5548,
  year = 2009
}

@book{davey1990introduction,
  address = {Cambridge},
  author = {Davey, Brian A. and Priestley, Hilary A.},
  interhash = {7255554003c02eb6ddf14a6fcb9b9f72},
  intrahash = {df19796e33c1e2c861b613e3c8a86f58},
  isbn = {0521365848 9780521365840 0521367662 9780521367660},
  publisher = {Cambridge University Press},
  refid = {471812885},
  title = {Introduction to lattices and order},
  url = {http://www.worldcat.org/search?qt=worldcat_org_all&q=0521367662},
  year = 1990
}

@incollection{ganter1998stepwise,
  abstract = {Lattices are mathematical structures which are frequently used for the representation of data. Several authors have considered the problem of incremental construction of lattices. We show that with a rather general approach, this problem becomes well-structured. We give simple algorithms with satisfactory complexity bounds.},
  address = {Berlin/Heidelberg},
  author = {Ganter, Bernhard and Kuznetsov, Sergei},
  booktitle = {Conceptual Structures: Theory, Tools and Applications},
  doi = {10.1007/BFb0054922},
  editor = {Mugnier, Marie-Laure and Chein, Michel},
  interhash = {6ab4d800575b90bf787ade575b38994b},
  intrahash = {0c986e520647b86c202633cc6945d524},
  isbn = {978-3-540-64791-1},
  pages = {295--302},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Stepwise construction of the Dedekind-MacNeille completion},
  url = {http://dx.doi.org/10.1007/BFb0054922},
  volume = 1453,
  year = 1998
}

@article{yong2001lattices,
  abstract = {The main purposes of this article are to uncover interesting features in real-world citationnetworks, and to highlight important substructures. In particular, it applies lattice theory tocitation analysis. On the applied side, it shows that lattice substructures exist in real-word citationnetworks. It is further shown that, through its relations with co-citations and bibliographiccoupling, the diamond (a four-element lattice) is a basic structural element in citation analysis.Finally, citation compactness is calculated for the four- and five element lattices. },
  author = {Yong, Fang and Rousseau, Ronald},
  doi = {10.1023/A:1010573723540},
  interhash = {e9391bc849fa1c37c94f123a42cce4f3},
  intrahash = {3e02f4c97f1e075cb05e13c235cfd875},
  issn = {0138-9130},
  journal = {Scientometrics},
  month = feb,
  number = 2,
  pages = {273--287},
  title = {Lattices in citation networks: An investigation into the structure of citation graphs},
  url = {http://dx.doi.org/10.1023/A:1010573723540},
  volume = 50,
  year = 2001
}

@article{octavio1985nonexistence,
  abstract = {We prove that there is no free object over a countable set in the category of complete distributive lattices with homomorphisms preserving binary meets and arbitrary joins.},
  author = {Garcia, Octavio and Nelson, Evelyn},
  interhash = {c4a8aeddff294dbdd727c05059ab2050},
  intrahash = {d4ce23539ea3bc784068e93dc70387aa},
  journal = {Order},
  month = {December},
  number = 4,
  pages = {399--403},
  title = {On the nonexistence of free complete distributive lattices},
  url = {http://dx.doi.org/10.1007/BF00582745},
  volume = 1,
  year = 1985
}

@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{erne1993distributive,
  abstract = {We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be(1)distributive,(2)a frame (locale, complete Heyting algebra),(3)isomorphic to a topology,(4)completely distributive,(5)superalgebraic (i.e., algebraic and completely distributive).},
  affiliation = {Institut für Mathematik Universität Hannover Hannover Germany},
  author = {Erné, Marcel},
  doi = {10.1007/BF01195382},
  interhash = {f30c769c54f5eb98962742b324651451},
  intrahash = {dd7f97b10532feab21d486ebb6783939},
  issn = {0002-5240},
  issue = {4},
  journal = {Algebra Universalis},
  keyword = {Mathematics and Statistics},
  pages = {538-580},
  publisher = {Birkhäuser Basel},
  title = {Distributive laws for concept lattices},
  url = {http://dx.doi.org/10.1007/BF01195382},
  volume = 30,
  year = 1993
}

@book{JipsenRose,
  author = {Jipsen, Peter and Rose, Henry},
  interhash = {3c059c795ea222bef82aeadbbc53f521},
  intrahash = {9cd44e2dd953968e165fae99cce3f454},
  publisher = {Springer-Verlag},
  title = {Varieties of Lattices},
  year = 1992
}

@article{WilleGer,
  author = {Wille, Rudolf},
  interhash = {46ac7de1dc6e14712068cdbd877528dc},
  intrahash = {36d1027abe1cb91e6849597624d8b3da},
  journal = {J. reine angew. Math.},
  pages = {53--70},
  title = {Subdirekte {P}rodukte voll\-st\"an\-diger {V}erb\"ande},
  volume = {283/284},
  year = 1976
}

@book{GanterWille,
  address = {Berlin/Heidelberg},
  author = {Ganter, Bernhard and Wille, Rudolf},
  interhash = {1b0bf49069eadcdfac42e52addf4eb9d},
  intrahash = {ae14b00b5489de8da6e4578ac3062bfc},
  publisher = {Springer-Verlag},
  title = {Formal Concept Analysis: Mathematical Foundations},
  year = 1999
}

@incollection{Birkhoff,
  author = {Birkhoff, Garrett},
  booktitle = {Colloquium Publications},
  edition = {3.},
  interhash = {155513001f337274bb35db352a6a3a02},
  intrahash = {fefe3c5111aaf07bd2d39c7d6b67f87a},
  publisher = {Amer. Math. Soc.},
  title = {Lattice theory},
  volume = 25,
  year = 1967
}

@article{Duq,
  address = {Amsterdam, The Netherlands, The Netherlands},
  author = {Duquenne, Vincent},
  doi = {http://dx.doi.org/10.1016/0012-365X(91)90043-2},
  interhash = {3fcc87180a838828f74fd82d7b6ac209},
  intrahash = {6c41ab93d9468e2b180b0d1a189c2cb8},
  issn = {0012-365X},
  journal = {Discrete Math.},
  number = {2-3},
  pages = {133--147},
  publisher = {Elsevier Science Publishers B. V.},
  title = {The core of finite lattices},
  volume = 87,
  year = 1991
}

@book{Gratzer,
  author = {Gr\"atzer, George},
  edition = {2.},
  interhash = {a8f3bffb2e67cba1f5e527baf3d52c5c},
  intrahash = {d83a5bf84d8f9a73cfbdf029cf77bd00},
  publisher = {Birkh\"auser Verlag},
  title = {General Lattice Theory},
  year = 1998
}

@article{Day,
  author = {Day, Alan},
  interhash = {92f86651ec58d2172bc37610df3fff80},
  intrahash = {5bb10c218a6f0b7cc434a132264d3f79},
  journal = {Algebra Univ.},
  number = 1,
  pages = {153--162},
  title = {Splitting Algebras and a Weak Notion of Projectivity},
  volume = 5,
  year = 1975
}

@article{GratzerLasker,
  author = {Gr\"atzer, George and Lakser, Henry},
  interhash = {3e9031c3452bda5025b67930098e63da},
  intrahash = {200d680360ef9ab42903d4ea7b947a4b},
  journal = {Trans. Amer. Math. Soc.},
  number = 1,
  pages = {385--405},
  title = {On Complete Congruence Lattices of Complete Lattices},
  volume = 327,
  year = 1991
}

@article{Jonsson,
  author = {J\'{o}nsson, Bjarni},
  interhash = {1e86e1c71951c755a9fc63029c30633e},
  intrahash = {8f84ccdc0213a1c007d63d3473007431},
  journal = {Math. Scand.},
  pages = {110--121},
  title = {Algebras whose Congruence Lattices are Distributive},
  volume = 21,
  year = 1967
}

@phdthesis{Geyer,
  author = {Geyer, Winfried},
  interhash = {318f8784d05f2a85352ace9a528bf766},
  intrahash = {fe7bff84152dbe12bcf502c9092a88c8},
  school = {Technische Hochschule Darmstadt, Fachbereich Mathematik},
  title = {Intervalldopplung und Verwandte Konstruktionen bei Verb\"anden},
  year = 1992
}

@article{Jonsson68,
  author = {J\'{o}nsson, Bjarni},
  interhash = {a4e2c61e772b3fe3876ddee1c372c045},
  intrahash = {7976b282166431d2785cff64b657e8ba},
  journal = {Math. Scand.},
  pages = {187--196},
  title = {Equational Classes of Lattices},
  volume = 22,
  year = 1968
}

@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
}

@article{hales1964nonexistence,
  author = {Hales, A. W.},
  interhash = {2e2b85532b56b6caaac29b23e33f972f},
  intrahash = {4d17473cee1aa8c33d821aacf2fbb95c},
  journal = {Fundamentae Mathematica},
  pages = {45-66},
  title = {On the non-existence of free complete Boolean algebras},
  url = {http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=54},
  volume = 54,
  year = 1964
}

@article{Duquenne1991133,
  abstract = {The meet-core of a finite lattice L is its minimal -- in fact minimum -- partial meet- subsemilattice of which the filter lattice is isomorphic to L. This gives a representation theory for finite lattices, in particular which extends Birkhoff's correspondence between ordered sets and distributive lattices, and is linked with Wille's notion of scaffolding. The meet-cores (and dually the join-cores) of modular, geometric and join-meet-distributive lattices are characterized locally by some obligatory sublattices or by some construction procedures otherwise.},
  author = {Duquenne, Vincent},
  doi = {10.1016/0012-365X(91)90005-M},
  interhash = {3fcc87180a838828f74fd82d7b6ac209},
  intrahash = {3754f36ef7da2a619c34a7c863ba3427},
  issn = {0012-365X},
  journal = {Discrete Mathematics},
  number = {2-3},
  pages = {133 - 147},
  title = {The core of finite lattices},
  url = {http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d},
  volume = 88,
  year = 1991
}

@article{day1979characterizations,
  author = {Day, Alan},
  editor = {unknown},
  interhash = {7615e076b500ccc41926fefe2ae01f15},
  intrahash = {015c99bf1c8d247fbb0db3dc330002f6},
  journal = {Canadian Journal of Mathematics},
  pages = {69-78},
  title = {Characterizations of finite lattices that are bounded-homomorphic images of sublattices of free lattices },
  url = {http://cms.math.ca/cjm/v31/p69#},
  volume = 31,
  year = 1979
}

@article{stumme2002computing,
  abstract = {We introduce the notion of iceberg concept lattices and show their use in knowledge discovery in databases. Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for association rules. Iceberg concept lattices are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery. We present a new algorithm called TITANIC for computing (iceberg) concept lattices. It is based on data mining techniques with a level-wise approach. In fact, TITANIC can be used for a more general problem: Computing arbitrary closure systems when the closure operator comes along with a so-called weight function. The use of weight functions for computing closure systems has not been discussed in the literature up to now. Applications providing such a weight function include association rule mining, functional dependencies in databases, conceptual clustering, and ontology engineering. The algorithm is experimentally evaluated and compared with Ganter's Next-Closure algorithm. The evaluation shows an important gain in efficiency, especially for weakly correlated data.},
  address = {Amsterdam, The Netherlands, The Netherlands},
  author = {Stumme, Gerd and Taouil, Rafik and Bastide, Yves and Pasquier, Nicolas and Lakhal, Lotfi},
  doi = {10.1016/S0169-023X(02)00057-5},
  interhash = {d500ac8a249ca8bf0fb05f382799d48f},
  intrahash = {fc31933f0eec502e305b6aecb9ef6e8a},
  issn = {0169-023X},
  journal = {Data \& Knowledge Engineering},
  month = aug,
  number = 2,
  pages = {189--222},
  publisher = {Elsevier Science Publishers B. V.},
  title = {Computing iceberg concept lattices with TITANIC},
  url = {http://portal.acm.org/citation.cfm?id=606457},
  volume = 42,
  year = 2002
}

@article{stumme98free,
  author = {Stumme, Gerd},
  comment = {alpha},
  interhash = {c5fb9e79ebca290916dac9d193033a19},
  intrahash = {de157d21efb3d9723fb937be024f84cd},
  journal = {{In:} {O}rder},
  pages = {179-189},
  title = {Free Distributive Completions of Partial Complete Lattices},
  url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2000/SIGKDD_Explorations00.ps},
  volume = 14,
  year = 1998
}

@inproceedings{daniel2009concept,
  abstract = {Concept lattices with symmetries may be simplified by “folding” them along the orbits of their automorphism group. The resulting
diagram is often more intuitive than the full lattice diagram, but well defined annotations are required to make the foldeddiagram as informative as the original one. The folding procedure can be extended to formal contexts.},
  author = {Borchmann, Daniel and Ganter, Bernhard},
  interhash = {d526f70f97c8f2628cef9c6286fd7464},
  intrahash = {143fb790f3f81b72cb39556d8e822248},
  journal = {Formal Concept Analysis},
  pages = {22--37},
  title = {Concept Lattice Orbifolds – First Steps},
  url = {http://dx.doi.org/10.1007/978-3-642-01815-2_2},
  year = 2009
}

@article{freeman1993galois,
  abstract = {Galois lattices are introduced as a device to provide a general representation for two mode social network data. It is shown that Galois lattices yield a single visual image of such data in cases where most alternative models produce dual images. The inzage provided by the Galois lattice produces, moreover, an inzage that can suggest useful insights about the structural properties of the data. An example, based on data from Davis, Gardner, and Gardner (1941), is used to spell out in detail the kinds of structural insights that can be gained from this approach. In addition, other potential applications are suggested.},
  author = {Freeman, L.C. and White, D.R.},
  interhash = {8231848d3051b517f6dc33e54e6e76d2},
  intrahash = {50103469c4e839b6f05a522eaacaa3a8},
  journal = {Sociological Methodology},
  pages = {127--146},
  title = {Using Galois Lattices to Represent Network Data},
  url = {http://www.polisci.berkeley.edu/courses/coursepages/Fall2004/ps289/Galois.pdf},
  volume = 23,
  year = 1993
}

@inproceedings{kuznetsov07reducing,
  address = {Berlin, Heidelberg},
  author = {Kuznetsov, Sergei and Obiedkov, Sergei and Roth, Camille},
  booktitle = {Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007)},
  crossref = {conf/iccs/2006},
  editor = {Priss, Uta and Polovina, Simon and Hill, Richard},
  interhash = {29e6d97fed3a32d028548c3f069936f1},
  intrahash = {ea581cd4026047bdf4dd0ab80ace7f28},
  isbn = {3-540-73680-8},
  month = {July},
  pages = {241-254},
  publisher = {Springer-Verlag},
  series = {Lecture Notes in Artificial Intelligence},
  title = {Reducing the Representation Complexity of Lattice-Based Taxonomies},
  volume = 4604,
  year = 2007
}

@inproceedings{DBLP:conf/iccs/GanterR01,
  author = {Ganter, Bernhard and Rudolph, Sebastian},
  bibsource = {DBLP, http://dblp.uni-trier.de},
  booktitle = {Proceedings of the 9th International Conference on Conceptual Structures (ICCS 2001)},
  crossref = {DBLP:conf/iccs/2001},
  editor = {Delugach, Harry S. and Stumme, Gerd},
  ee = {http://link.springer.de/link/service/series/0558/bibs/2120/21200143.htm},
  interhash = {7e65d75d108c42ac5449e9a0f094cfca},
  intrahash = {a25ab4987c25f31c9c7a69b9925ec8f9},
  isbn = {3-540-42344-3},
  pages = {143-156},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Formal Concept Analysis Methods for Dynamic Conceptual Graphs.},
  volume = 2120,
  year = 2001
}

@inproceedings{wille1982restructuring,
  abstract = {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.},
  address = {Dordrecht--Boston},
  author = {Wille, Rudolf},
  booktitle = {Ordered sets},
  editor = {Rival, Ivan},
  interhash = {1e021e8bace9683c92416cd882eb4c4d},
  intrahash = {e43626656aa7d98700fb4572b75bcbb1},
  pages = {445--470},
  publisher = {Reidel},
  title = {Restructuring lattice theory: an approach based on hierarchies of concepts},
  year = { 1982 }
}

@book{birkhoff40,
  address = {Providence, Rhode Island},
  author = {Birkhoff, Garrett},
  edition = {3.},
  interhash = {155513001f337274bb35db352a6a3a02},
  intrahash = {693d3857c685d6eb6c2edfdeb51180f8},
  publisher = {American Mathematical Society},
  series = {American Mathematical Society Colloqium Publi},
  title = {Lattice Theory},
  volume = {XXV},
  year = 1967
}