Inproceedings1143: Unterschied zwischen den Versionen
Aus International Center for Computational Logic
Markus Krötzsch (Diskussion | Beiträge) K (1 Version: Publications of Sebastian Rudlph and Markus Kroetzsch, exported from AIFB) |
Markus Krötzsch (Diskussion | Beiträge) K (Textersetzung - „|Forschungsgruppe=Knowledge Systems“ durch „|Forschungsgruppe=Wissensbasierte Systeme“) |
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{{Publikation Erster Autor | {{Publikation Erster Autor | ||
|ErsterAutorVorname=Markus | |||
|ErsterAutorNachname=Krötzsch | |ErsterAutorNachname=Krötzsch | ||
| | |FurtherAuthors=Grit Malik | ||
}} | }} | ||
{{Inproceedings | {{Inproceedings | ||
|Referiert= | |Referiert=1 | ||
|Title=The Tensor Product as a Lattice of Regular Galois Connections | |Title=The Tensor Product as a Lattice of Regular Galois Connections | ||
|To appear=0 | |||
|Year=2006 | |Year=2006 | ||
|Month=Februar | |Month=Februar | ||
|Booktitle=Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany | |Booktitle=Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany | ||
|Publisher=Springer | |||
|Editor=Rokia Missaoui and Jürg Schmid | |Editor=Rokia Missaoui and Jürg Schmid | ||
|Series=Lecture Notes in Computer Science | |Series=Lecture Notes in Computer Science | ||
|Volume=3874 | |Volume=3874 | ||
|Address=Berlin | |||
}} | }} | ||
{{Publikation Details | {{Publikation Details | ||
|Abstract=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. | |Abstract=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. | ||
|ISBN=3-540-32203-5 | |ISBN=3-540-32203-5 | ||
|Download=KroetzschMalik GaloisConnectionsConceptLattice.pdf | |||
|Link=http://korrekt.org/papers/KroetzschMalik_GaloisConnectionsConceptLattice.pdf, http://korrekt.org/papers/KroetzschMalik_GaloisConnectionsConceptLattice.pdf | |||
|Forschungsgruppe=Wissensbasierte Systeme | |||
|VG Wort-Seiten= | |VG Wort-Seiten= | ||
}} | }} | ||
{{Forschungsgebiet Auswahl | {{Forschungsgebiet Auswahl | ||
|Forschungsgebiet=Formale Begriffsanalyse | |Forschungsgebiet=Formale Begriffsanalyse | ||
}} | }} | ||
Aktuelle Version vom 24. Mai 2016, 18:02 Uhr
The Tensor Product as a Lattice of Regular Galois Connections
Markus KrötzschMarkus Krötzsch, Grit MalikGrit Malik
Markus Krötzsch, Grit Malik
The Tensor Product as a Lattice of Regular Galois Connections
In Rokia Missaoui and Jürg Schmid, eds., Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany, volume 3874 of Lecture Notes in Computer Science, February 2006. Springer
The Tensor Product as a Lattice of Regular Galois Connections
In Rokia Missaoui and Jürg Schmid, eds., Proceedings of the 4th International Conference on Formal Concept Analysis (ICFCA2006), Dresden, Germany, volume 3874 of Lecture Notes in Computer Science, February 2006. Springer
- KurzfassungAbstract
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. - Weitere Informationen unter:Further Information: Link, Link
- Forschungsgruppe:Research Group: Wissensbasierte SystemeKnowledge-Based Systems
@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}
}
