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The Logic of AGM Learning from Partial Observations

  • Alexandru Baltag
  • Aybüke Özgün
  • Ana Lucia Vargas-SandovalEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12005)

Abstract

We present a dynamic logic for inductive learning from partial observations by a “rational” learner, that obeys AGM postulates for belief revision. We apply our logic to an example, showing how various concrete properties can be learnt with certainty or inductively by such an AGM learner. We present a sound and complete axiomatization, based on a combination of relational and neighbourhood version of the canonical model method.

References

  1. 1.
    Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50, 510–530 (1985)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., de Lima, T.: ‘Knowable’ as ‘known after an announcement’. Rev. Symb. Log. 1, 305–334 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Baltag, A., Gierasimczuk, N., Özgün, A., Vargas Sandoval, A.L., Smets, S.: A dynamic logic for learning theory. In: Madeira, A., Benevides, M. (eds.) DALI 2017. LNCS, vol. 10669, pp. 35–54. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-73579-5_3CrossRefzbMATHGoogle Scholar
  4. 4.
    Baltag, A., Gierasimczuk, N., Smets, S.: Belief revision as a truth-tracking process. In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 187–190. ACM (2011)Google Scholar
  5. 5.
    Baltag, A., Gierasimczuk, N., Smets, S.: On the solvability of inductive problems: a study in epistemic topology. In: Ramanujam, R. (ed.) Proceedings of the 15th Conference TARK, also Available as a Technical Report in ILLC Prepublication Series PP-2015-13 (2015)Google Scholar
  6. 6.
    Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Proceedings of the 7th Conference TARK, pp. 43–56. Morgan Kaufmann Publishers Inc. (1998)Google Scholar
  7. 7.
    Baltag, A., Özgün, A., Vargas Sandoval, A.L.: Topo-logic as a dynamic-epistemic logic. In: Baltag, A., Seligman, J., Yamada, T. (eds.) LORI 2017. LNCS, vol. 10455, pp. 330–346. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-662-55665-8_23CrossRefzbMATHGoogle Scholar
  8. 8.
    Baltag, A., Renne, B.: Dynamic epistemic logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Winter 2016 edn. (2016)Google Scholar
  9. 9.
    Baltag, A., Smets, S.: A qualitative theory of dynamic interactive belief revision. Texts Log. Games 3, 9–58 (2008)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Board, O.: Dynamic interactive epistemology. Games Econ. Behav. 49, 49–80 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Chellas, B.F.: Basic conditional logic. J. Philos. Log. 4, 133–153 (1975)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Dabrowski, A., Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. Ann. Pure Appl. Log. 78, 73–110 (1996)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Gold, E.M.: Language identification in the limit. Inf. Control 10, 447–474 (1967)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Grahne, G.: Updates and counterfactuals. J. Log. Comput. 8, 87–117 (1998)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lewis, D.K.: Counterfactuals. Blackwell, Oxford (1973)zbMATHGoogle Scholar
  16. 16.
    Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. In: Proceedings of the 4th TARK, pp. 95–105. Morgan Kaufmann (1992)Google Scholar
  17. 17.
    van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Log. 14, 2004 (2004)Google Scholar
  18. 18.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, 1st edn. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-1-4020-5839-4CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alexandru Baltag
    • 1
  • Aybüke Özgün
    • 1
    • 2
  • Ana Lucia Vargas-Sandoval
    • 1
    Email author
  1. 1.ILLCUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.ArchéUniversity of St. AndrewsSt AndrewsUK

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