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Formal \(\mathcal{F}\)-contexts and Their Induced Implication Rule Systems

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Book cover Formal Concept Analysis (ICFCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7880))

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Abstract

Formal concept analysis (FCA) provides an approach to restructuring important lattice structures such as complete lattices, distributive lattices and algebraic lattices. In this paper, we focus on the theoretical aspect of FCA and study the representation of algebraic domains by a special type of formal contexts. We first propose the notion of consistent \(\mathcal{F}\)-context and investigate the detailed properties. Then we study the induced implication rule systems of the consistent \(\mathcal{F}\)-contexts and propose the notion of formal implication rule systems as the axiomatization. The results show that \(\mathcal{F}\)-concepts inherent in consistent \(\mathcal{F}\)-contexts can be characterized equivalently by closed subsets derived from the formal implication rule systems. Furthermore, we study the order-theoretical properties of \(\mathcal{F}\)-concepts hierarchy (respectively, closed subsets family) of consistent \(\mathcal{F}\)-contexts (respectively, formal implication rule system). It is shown that both \(\mathcal{F}\)-contexts and formal implication rule systems can serve as appropriate tools to concretely represent algebraic domains.

This work is partly supported by the NSERC Discovery research grants of the third and fourth authors, and China Postdoctoral Science Foundation (No. 2012M521515) of the first author.

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Authors and Affiliations

  1. Département d’Informatique, Université du Québec à Montréal Centre-Ville, Montréal, Québec, H3C 3J7, Canada

    Lankun Guo, Petko Valtchev & Robert Godin

  2. College of Information Science and Engineering, Hunan University, Changsha, Hunan, 410012, P.R. China

    Lankun Guo

  3. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, P.R. China

    Qingguo Li

Authors
  1. Lankun Guo
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  2. Qingguo Li
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  3. Petko Valtchev
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  4. Robert Godin
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Editor information

Editors and Affiliations

  1. IRISA, 263 avenue du Général Leclerc, 35042, Rennes, France

    Peggy Cellier

  2. Computer Science Department, TU Dresden, Nöthnitzer Str. 46, 01062, Dresden, Germany

    Felix Distel

  3. Department of Mathematics, TU Dresden, Zellescher Weg 12-14, 01062, Dresden, Germany

    Bernhard Ganter

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Guo, L., Li, Q., Valtchev, P., Godin, R. (2013). Formal \(\mathcal{F}\)-contexts and Their Induced Implication Rule Systems. In: Cellier, P., Distel, F., Ganter, B. (eds) Formal Concept Analysis. ICFCA 2013. Lecture Notes in Computer Science(), vol 7880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38317-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-38317-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38316-8

  • Online ISBN: 978-3-642-38317-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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