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Attribute Exploration with Multiple Contradicting Partial Experts

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Graph-Based Representation and Reasoning (ICCS 2022)

Abstract

Attribute exploration is a method from Formal Concept Analysis (FCA) that helps a domain expert discover structural dependencies in knowledge domains which can be represented as formal contexts (cross tables of objects and attributes). In this paper we present an extension of attribute exploration that allows for a group of domain experts and explores their shared views. Each expert has their own view of the domain and the views of multiple experts may contain contradicting information.

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Notes

  1. 1.

    https://doi.org/10.48550/arXiv.2205.15714.

  2. 2.

    For modeling incomplete information, we later extend \(\{\times ,o\}\) by “?”, cf. Definition 2.1.

  3. 3.

    Note that we consider \(\mathcal {L}\) an implication theory because it is easier to work with. In practice we can use any set of implications where the closure is satisfiable in \(\mathbb {K}\).

References

  1. Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logic. Episteme, vol. 2, pp. 5–37. Springer, Dordrecht (1977). https://doi.org/10.1007/978-94-010-1161-7_2

  2. Burmeister, P.: Merkmalimplikationen bei unvollständigem wissen. In: Lex, W. (ed.) Arbeitstagung Begriffsanalyse und Künstliche Intelligenz, pp. 15–46. No. 89/3 in Informatik-Bericht, Clausthal-Zellerfeld (1991)

    Google Scholar 

  3. Burmeister, P., Holzer, R.: On the treatment of incomplete knowledge in formal concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS-ConceptStruct 2000. LNCS (LNAI), vol. 1867, pp. 385–398. Springer, Heidelberg (2000). https://doi.org/10.1007/10722280_27

    Chapter  Google Scholar 

  4. Felde, M., Stumme, G.: Interactive collaborative exploration using incomplete contexts. CoRR abs/1908.08740 (2019)

    Google Scholar 

  5. Felde, M., Stumme, G.: Triadic exploration and exploration with multiple experts. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds.) ICFCA 2021. LNCS (LNAI), vol. 12733, pp. 175–191. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77867-5_11

    Chapter  Google Scholar 

  6. Fitting, M.: Kleene’s logic, generalized. Logic Comput. 1(6), 797–810 (1991)

    Article  MathSciNet  Google Scholar 

  7. Ganter, B.: Two basic algorithms in concept analysis. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS (LNAI), vol. 5986, pp. 312–340. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11928-6_22

    Chapter  MATH  Google Scholar 

  8. Ganter, B.: Attribute exploration with background knowledge. Theoret. Comput. Sci. 217(2), 215–233 (1999)

    Article  MathSciNet  Google Scholar 

  9. Ganter, B., Obiedkov, S.: Implications in triadic formal contexts. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS-ConceptStruct 2004. LNCS (LNAI), vol. 3127, pp. 186–195. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27769-9_12

    Chapter  Google Scholar 

  10. Ganter, B., Obiedkov, S.: More expressive variants of exploration. In: Conceptual Exploration, pp. 237–292. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49291-8_6

    Chapter  MATH  Google Scholar 

  11. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  12. Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Comput. Intell. 4(3), 265–316 (1988)

    Article  Google Scholar 

  13. Guigues, J.L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 95, 5–18 (1986)

    Google Scholar 

  14. Hanika, T., Zumbrägel, J.: Towards collaborative conceptual exploration. In: Chapman, P., Endres, D., Pernelle, N. (eds.) ICCS 2018. LNCS (LNAI), vol. 10872, pp. 120–134. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91379-7_10

    Chapter  Google Scholar 

  15. Holzer, R.: Methoden der formalen Begriffsanalyse bei der Behandlung unvollständigen Wissens. Dissertation, TU Darmstadt, Shaker (2001)

    Google Scholar 

  16. Holzer, R.: Knowledge acquisition under incomplete knowledge using methods from formal concept analysis: Part I. Fund. Inform. 63(1), 17–39 (2004)

    MathSciNet  MATH  Google Scholar 

  17. Holzer, R.: Knowledge acquisition under incomplete knowledge using methods from formal concept analysis: Part II. Fund. Inform. 63(1), 41–63 (2004)

    MathSciNet  MATH  Google Scholar 

  18. Kriegel, F.: Parallel attribute exploration. In: Haemmerlé, O., Stapleton, G., Faron Zucker, C. (eds.) ICCS 2016. LNCS (LNAI), vol. 9717, pp. 91–106. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40985-6_8

    Chapter  Google Scholar 

  19. Stumme, G.: Attribute exploration with background implications and exceptions. In: Bock, H.H., Polasek, W. (eds.) Data Analysis and Information Systems. Statistical and Conceptual Approaches. Proceedings GfKl 1995. Studies in Classification, Data Analysis, and Knowledge Organization, vol. 7. pp. 457–469. Springer, Heidelberg (1996). https://doi.org/10.1007/978-3-642-80098-6_39

  20. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Springer, Dordrecht (1982). https://doi.org/10.1007/978-94-009-7798-3_15

    Chapter  Google Scholar 

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Correspondence to Maximilian Felde .

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Felde, M., Stumme, G. (2022). Attribute Exploration with Multiple Contradicting Partial Experts. 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_5

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  • DOI: https://doi.org/10.1007/978-3-031-16663-1_5

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