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Reasoning Web. Explainable Artificial Intelligence pp 153–195Cite as

Explaining Data with Formal Concept Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11810))

Abstract

We give a brief introduction into Formal Concept Analysis, an approach to explaining data by means of lattice theory.

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Notes

  1. 1.

    Note that the underlying data is somewhat outdated, if not to say antiquated.

  2. 2.

    I. e., for each subset of concepts, there is always a unique greatest common subconcept and a unique least common superconcept.

  3. 3.

    It is not easy to say which is the most efficient data type for formal contexts. This depends, of course, on the operations we want to perform with formal contexts. The most important ones are the derivation operators, to be defined in the next subsection.

  4. 4.

    This reconstruction is assured by the Basic Theorem given below.

  5. 5.

    Unfortunately, the word “lattice” is used with different meanings in mathematics. It also refers to generalized grids.

  6. 6.

    An introduction to lattices and order by B. Davey and H. Priestley is particularly popular among CS students.

  7. 7.

    For our algorithm it is not important how the closure is computed.

  8. 8.

    If M is infinite, this may require infinitely many iterations.

  9. 9.

    ‘Recursive’ is meant here with respect to set inclusion. Compare with the following recursive definition: A natural number is prime iff it is greater than 1 and not divisible by any smaller prime number.

  10. 10.

    The reader might wonder why we use the stem base to construct the stem base. As we shall see soon, this works, due to the recursive definition of the stem base.

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Acknowledgments

We are grateful for the valuable feedback from the anonymous reviewers, which helped greatly to improve this work. Special thanks to Thomas Feller for his very careful proof-reading. This work has been funded by the European Research Council via the ERC Consolidator Grant No. 771779 (DeciGUT).

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Authors and Affiliations

  1. TU Dresden, Dresden, Germany

    Bernhard Ganter & Sebastian Rudolph

  2. Uni Kassel, Kassel, Germany

    Gerd Stumme

Authors
  1. Bernhard Ganter
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  2. Sebastian Rudolph
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  3. Gerd Stumme
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Corresponding author

Correspondence to Sebastian Rudolph .

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Editors and Affiliations

  1. Technische Universität Dresden, Dresden, Sachsen, Germany

    Markus Krötzsch

  2. Bosch Center for Artificial Intelligence, Renningen, Germany

    Daria Stepanova

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Ganter, B., Rudolph, S., Stumme, G. (2019). Explaining Data with Formal Concept Analysis. In: Krötzsch, M., Stepanova, D. (eds) Reasoning Web. Explainable Artificial Intelligence. Lecture Notes in Computer Science(), vol 11810. Springer, Cham. https://doi.org/10.1007/978-3-030-31423-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-31423-1_5

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-31423-1

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