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Orbital Concept Lattices

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Graph-Based Representation and Reasoning (ICCS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13403))

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Abstract

The paper introduces orbital concept lattices, which enhance concept lattices of relational structures with a semigroup action that encodes projection, renaming and duplication operations on concept extents, and fuses them with their counterparts on concept intents (formalized by tableau queries). This strengthens the existing connections between this branch of FCA and database theory, and it opens up a new possibility of characterizing such concept lattices by a set of axioms. The orbital semilattices, also introduced in this paper, are a first step in this direction, as they characterize the subsemilattices generated by finite queries, and thereby also enable a connection with algebraic logic.

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Notes

  1. 1.

    Thanks to one of the anonymous reviewers for the insightful remark.

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Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, Dresden, Germany

    Jens Kötters & Stefan E. Schmidt

Authors
  1. Jens Kötters
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  2. Stefan E. Schmidt
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Correspondence to Jens Kötters .

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Editors and Affiliations

  1. University of Münster, Münster, Germany

    Tanya Braun

  2. Babes-Bolyai University, Cluj-Napoca, Romania

    Diana Cristea

  3. Humboldt-Universität zu Berlin, Berlin, Germany

    Robert Jäschke

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Kötters, J., Schmidt, S.E. (2022). Orbital Concept Lattices. In: Braun, T., Cristea, D., Jäschke, R. (eds) Graph-Based Representation and Reasoning. ICCS 2022. Lecture Notes in Computer Science(), vol 13403. Springer, Cham. https://doi.org/10.1007/978-3-031-16663-1_6

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  • DOI: https://doi.org/10.1007/978-3-031-16663-1_6

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