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An Implementation of Nonmonotonic Reasoning with System W

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KI 2022: Advances in Artificial Intelligence (KI 2022)

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Abstract

System W is a recently introduced reasoning method for conditional belief bases. While system W exhibits various desirable properties for nonmonotonic reasoning like extending rational closure and fully complying with syntax splitting, an implementation of it has been missing so far. In this paper, we present a first implementation of system W. The implementation is accessible via an extension of an online platform supporting a variety of nonmonotonic reasoning approaches.

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Notes

  1. 1.

    https://jgrapht.org/.

  2. 2.

    https://github.com/jgraph/jgraphx.

  3. 3.

    http://wbs2.fernuni-hagen.de:18081/systemWTest/InfOCF.jsp.

References

  1. Adams, E.: The logic of conditionals. Inquiry 8(1–4), 166–197 (1965)

    Article  Google Scholar 

  2. Beierle, C., Eichhorn, C., Kern-Isberner, G.: Skeptical inference based on c-representations and its characterization as a constraint satisfaction problem. In: Gyssens, M., Simari, G. (eds.) FoIKS 2016. LNCS, vol. 9616, pp. 65–82. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30024-5_4

    Chapter  MATH  Google Scholar 

  3. Beierle, C., Eichhorn, C., Kutsch, S.: A practical comparison of qualitative inferences with preferred ranking models. KI - Künstliche Intelligenz 31(1), 41–52 (2017)

    Article  Google Scholar 

  4. Beierle, C., von Berg, M., Sanin, A.: Realization of skeptical c-inference as a SAT problem. In: Keshtkar, F., Franklin, M. (eds.) Proceedings of the Thirty-Fifth International Florida Artificial Intelligence Research Society Conference (FLAIRS), Hutchinson Island, Florida, USA, 15–18 May 2022 (2022)

    Google Scholar 

  5. Beierle, C., Eichhorn, C., Kern-Isberner, G., Kutsch, S.: Properties of skeptical c-inference for conditional knowledge bases and its realization as a constraint satisfaction problem. Ann. Math. Artif. Intell. 83(3–4), 247–275 (2018)

    Google Scholar 

  6. Beierle, C., Eichhorn, C., Kern-Isberner, G., Kutsch, S.: Properties and interrelationships of skeptical, weakly skeptical, and credulous inference induced by classes of minimal models. Artif. Intell. 297, 103489 (2021)

    Google Scholar 

  7. Beierle, C., Haldimann, J.: Normal forms of conditional belief bases respecting inductive inference. In: Keshtkar, F., Franklin, M. (eds.) Proceedings of the Thirty-Fifth International Florida Artificial Intelligence Research Society Conference (FLAIRS), Hutchinson Island, Florida, USA, 15–18 May 2022 (2022)

    Google Scholar 

  8. Beierle, C., Haldimann, J.: Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings. Ann. Math. Artif. Intell. 90(2), 149–179 (2022)

    Google Scholar 

  9. Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. In: Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (IJCAI 1993), vol. 1, pp. 640–647. Morgan Kaufmann Publishers, San Francisco (1993)

    Google Scholar 

  10. de Finetti, B.: La prévision, ses lois logiques et ses sources subjectives. Ann. Inst. H. Poincaré 7(1), 1–68 (1937). Engl. Transl. Theory Probab. (1974)

    Google Scholar 

  11. Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artif. Intell. 84(1–2), 57–112 (1996)

    Article  MathSciNet  Google Scholar 

  12. Haldimann, J., Beierle, C.: Inference with system W satisfies syntax splitting. In: Kern-Isberner, G., Lakemeyer, G., Meyer, T. (eds.) Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning, KR 2022, Haifa, Israel, 31 July–5 August 2022, pp. 405–409 (2022)

    Google Scholar 

  13. Haldimann, J., Beierle, C.: Properties of system W and its relationships to other inductive inference operators. In: Varzinczak, I. (ed.) Foundations of Information and Knowledge Systems - 12th International Symposium, FoIKS 2022. LNCS, pp. 206–225. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-11321-5_12

  14. Haldimann, J.P., Osiak, A., Beierle, C.: Modelling and reasoning in biomedical applications with qualitative conditional logic. In: Schmid, U., Klügl, F., Wolter, D. (eds.) KI 2020. LNCS (LNAI), vol. 12325, pp. 283–289. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58285-2_24

    Chapter  Google Scholar 

  15. Kern-Isberner, G.: A thorough axiomatization of a principle of conditional preservation in belief revision. Ann. Math. Artif. Intell. 40(1–2), 127–164 (2004)

    Article  MathSciNet  Google Scholar 

  16. Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44600-1

  17. Kern-Isberner, G., Beierle, C., Brewka, G.: Syntax splitting = relevance + independence: new postulates for nonmonotonic reasoning from conditional belief bases. In: Calvanese, D., Erdem, E., Thielscher, M. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the 17th International Conference, KR 2020, pp. 560–571. IJCAI Organization (2020)

    Google Scholar 

  18. Komo, C., Beierle, C.: Nonmonotonic inferences with qualitative conditionals based on preferred structures on worlds. In: Schmid, U., Klügl, F., Wolter, D. (eds.) KI 2020. LNCS (LNAI), vol. 12325, pp. 102–115. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58285-2_8

    Chapter  Google Scholar 

  19. Komo, C., Beierle, C.: Nonmonotonic reasoning from conditional knowledge bases with system W. Ann. Math. Artif. Intell. 90(1), 107–144 (2021). https://doi.org/10.1007/s10472-021-09777-9

    Article  MathSciNet  MATH  Google Scholar 

  20. Kraus, S., Lehmann, D.J., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)

    Article  MathSciNet  Google Scholar 

  21. Kutsch, S.: InfOCF-Lib: a Java library for OCF-based conditional inference. In: Proceedings DKB/KIK-2019. CEUR Workshop Proceedings, vol. 2445, pp. 47–58. CEUR-WS.org (2019)

    Google Scholar 

  22. Kutsch, S., Beierle, C.: InfOCF-web: an online tool for nonmonotonic reasoning with conditionals and ranking functions. In: Zhou, Z. (ed.) Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event/Montreal, Canada, 19–27 August 2021, pp. 4996–4999 (2021). ijcai.org

  23. Kutsch, S., Beierle, C.: Semantic classification of qualitative conditionals and calculating closures of nonmonotonic inference relations. Int. J. Approx. Reason. 130, 297–313 (2021). https://doi.org/10.1016/j.ijar.2020.12.020

  24. Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55, 1–60 (1992)

    Article  MathSciNet  Google Scholar 

  25. Parikh, R.: Beliefs, belief revision, and splitting languages. Logic Lang. Comput. 2, 266–278 (1999)

    MathSciNet  MATH  Google Scholar 

  26. Pearl, J.: System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning About Knowledge (TARK 1990), pp. 121–135. Morgan Kaufmann Publishers Inc., San Francisco (1990)

    Google Scholar 

  27. Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, II, pp. 105–134. Kluwer Academic Publishers (1988)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Knowledge-Based Systems, FernUniversität in Hagen, 58084, Hagen, Germany

    Christoph Beierle, Jonas Haldimann, Daniel Kollar, Kai Sauerwald & Leon Schwarzer

Authors
  1. Christoph Beierle
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  2. Jonas Haldimann
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  3. Daniel Kollar
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  4. Kai Sauerwald
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  5. Leon Schwarzer
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Corresponding author

Correspondence to Christoph Beierle .

Editor information

Editors and Affiliations

  1. University of Trier, Trier, Rheinland-Pfalz, Germany

    Ralph Bergmann

  2. University of Trier, Trier, Germany

    Lukas Malburg

  3. University of Trier, Trier, Germany

    Stephanie C. Rodermund

  4. University of Trier, Trier, Germany

    Ingo J. Timm

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Beierle, C., Haldimann, J., Kollar, D., Sauerwald, K., Schwarzer, L. (2022). An Implementation of Nonmonotonic Reasoning with System W. In: Bergmann, R., Malburg, L., Rodermund, S.C., Timm, I.J. (eds) KI 2022: Advances in Artificial Intelligence. KI 2022. Lecture Notes in Computer Science(), vol 13404. Springer, Cham. https://doi.org/10.1007/978-3-031-15791-2_1

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  • DOI: https://doi.org/10.1007/978-3-031-15791-2_1

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