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Inproceedings1143
Abstract Galois connections between concept lattice
Galois connections between concept lattices can be represented as binary relations on the context level, known as dual bonds. The latter also appear as the elements of the tensor product of concept lattices, but it is known that not all dual bonds between two lattices can be represented in this way. In this work, we define <i>regular</i> Galois connections as those that are represented by a dual bond in a tensor product, and characterize them in terms of lattice theory. Regular Galois connections turn out to be much more common than irregular ones, and we identify many cases in which no irregular ones can be found at all. To this end, we demonstrate that irregularity of Galois connections on sublattices can be lifted to superlattices, and observe close relationships to various notions of distributivity. This is achieved by combining methods from algebraic order theory and FCA with recent results on dual bonds. Disjunctions in formal contexts play a prominent role in the proofs and add a logical flavor to our considerations. Hence it is not surprising that our studies allow us to derive corollaries on the contextual representation of deductive systems.
xtual representation of deductive systems.  +
Author Markus Krötzsch + , Grit Malik +
BibTex
@inproceedings{KM2006,
  author    = {Markus Kr{\"{o}}tzsch and Grit Malik},
  title     = {The Tensor Product as a Lattice of Regular Galois Connections},
  editor    = {Rokia Missaoui and J{\"{u}}rg Schmid},
  booktitle = {Proceedings of the 4th International Conference on Formal Concept
               Analysis (ICFCA2006), Dresden, Germany},
  series    = {Lecture Notes in Computer Science},
  volume    = {3874},
  publisher = {Springer},
  year      = {2006},
  month     = {February}
}
Bibtype Inproceedings  +
Booktitle Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany  +
Download KroetzschMalik GaloisConnectionsConceptLattice.pdf  +
Editor Rokia Missaoui and Jürg Schmid  +
ErsterAutorNachname Krötzsch  +
ErsterAutorVorname Markus  +
Forschungsgebiet Formale Begriffsanalyse +
Forschungsgruppe Wissensbasierte Systeme +
ISBN 3-540-32203-5  +
Link http://korrekt.org/papers/KroetzschMalik_GaloisConnectionsConceptLattice.pdf  + , http://korrekt.org/papers/KroetzschMalik_GaloisConnectionsConceptLattice.pdf, http://korrekt.org/papers/KroetzschMalik_GaloisConnectionsConceptLattice.pdf  +
Month Februar  +
Publication text Markus Krötzsch, Grit Malik<br/> '''
Markus Krötzsch, Grit Malik<br/> '''[[Inproceedings1143|<b>The Tensor Product as a Lattice of Regular Galois Connections</b>]]''' <br/>__NOTOC__In Rokia Missaoui and Jürg Schmid, eds., <i>Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany</i>, volume 3874 of Lecture Notes in Computer Science, February 2006. Springer<br/><span class="glyphicon glyphicon-chevron-right" style="font-size: 85%;" ></span> [[Inproceedings1143|Details]] <span class="glyphicon glyphicon-chevron-right" style="font-size: 85%; margin-left: 2ex; "></span> [[Media:KroetzschMalik GaloisConnectionsConceptLattice.pdf|Download]]
isConnectionsConceptLattice.pdf|Download]]  +
Publication text en Markus Krötzsch, Grit Malik<br/> '''
Markus Krötzsch, Grit Malik<br/> '''[[Inproceedings1143/en|<b>The Tensor Product as a Lattice of Regular Galois Connections</b>]]''' <br/>__NOTOC__In Rokia Missaoui and Jürg Schmid, eds., <i>Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany</i>, volume 3874 of Lecture Notes in Computer Science, February 2006. Springer<br/><span class="glyphicon glyphicon-chevron-right" style="font-size: 85%;" ></span> [[Inproceedings1143|Details]] <span class="glyphicon glyphicon-chevron-right" style="font-size: 85%; margin-left: 2ex;" ></span> [[Media:KroetzschMalik GaloisConnectionsConceptLattice.pdf|Download]]
isConnectionsConceptLattice.pdf|Download]]  +
Publisher Springer  +
Referiert 1  +
Series Lecture Notes in Computer Science  +
Title The Tensor Product as a Lattice of Regular Galois Connections  +
To appear 0  +
Type inproceedings  +
Volume 3874  +
Year 2006  +
Hat Abfrage
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Kategorien Publikation , Inproceedings
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