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Probabilistic Epistemic Updates on Algebras

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Logic, Rationality, and Interaction (LORI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9394))

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Abstract

The present paper contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL.

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References

  1. Artemov, S., Protopopescu, T.: Intuitionistic epistemic logic. preprint arXiv:1406.1582 (2014)

    Google Scholar 

  2. Baltag, A., Christo, Z., Hansen, J.U., Smets, S.: Logical models of informational cascades. Studies in Logic. College Publications (2013)

    Google Scholar 

  3. Bakhtiari, Z., Rivieccio, U.: Epistemic updates on bilattices (submitted) (2015)

    Google Scholar 

  4. Conradie, W., Craig, A.: Canonicity results for mu-calculi: An algorithmic approach. Journal of Logic and Computation (forthcoming) (2015)

    Google Scholar 

  5. Conradie, W., Frittella, S., Palmigiano, A., Tzimoulis, A., Wijnberg, N.: Probabilistic epistemic updates on algebras (in preparation)

    Google Scholar 

  6. Conradie, W., Fomatati, Y., Palmigiano, A., Sourabh, S.: Algorithmic correspondence for intuitionistic modal mu-calculus. Theoretical Computer Science 564, 30–62 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Conradie, W., Ghilardi, S., Palmigiano, A.: Unified correspondence. In: Baltag, A., Smets, S. (eds.) Johan F.A.K. van Benthem on Logical and Informational Dynamics. Outstanding Contributions to Logic. Springer (2014) (in print)

    Google Scholar 

  8. Conradie, W., Palmigiano, A.: Algorithmic correspondence and canonicity for non-distributive logics. Journal of Logic and Computation (forthcoming) (2015)

    Google Scholar 

  9. Conradie, W., Palmigiano, A., Sourabh, S.: Algebraic modal correspondence: Sahlqvist and beyond (submitted) (2015)

    Google Scholar 

  10. Davey, B.A., Priestley, H.A.: Lattices and Order. Cambridge Univerity Press (2002)

    Google Scholar 

  11. Frittella, S., Greco, G., Kurz, A., Palmigiano, A., Sikimić, V.: A multi-type display calculus for dynamic epistemic logic. Journal of Logic and Computation, Special Issue on Substructural Logic and Information Dynamics (2014)

    Google Scholar 

  12. Frittella, S., Greco, G., Kurz, A., Palmigiano, A., Sikimić, V.: Multi-type sequent calculi. In: Zawidzki, M., Indrzejczak, A., Kaczmarek, J. (eds.) Trends in Logic XIII, pp. 81–93. Lodź University Press (2014)

    Google Scholar 

  13. Frittella, S., Greco, G., Kurz, A., Palmigiano, A., Sikimić, V.: A proof-theoretic semantic analysis of dynamic epistemic logic. Journal of Logic and Computation (2014)

    Google Scholar 

  14. Frittella, S., Greco, G., Kurz, A., Palmigiano, A.: Multi-type display calculus for propositional dynamic logic. Journal of Logic and Computation, Special Issue on Substructural Logic and Information Dynamics (2014)

    Google Scholar 

  15. Greco, G., Kurz, A., Palmigiano, A.: Dynamic epistemic logic displayed. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2014. LNCS, vol. 8196, pp. 135–148. Springer, Heidelberg (2013)

    Google Scholar 

  16. Greco, G., Ma, M., Palmigiano, A., Tzimoulis, A., Zhao, Z.: Unified correspondence as a proof-theoretic tool (sumbitted) (2015)

    Google Scholar 

  17. Kooi, B.P.: Probabilistic dynamic epistemic logic. Journal of Logic, Language and Information 12(4), 381–408 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kurz, A., Palmigiano, A.: Epistemic updates on algebras. Logical Methods in Computer Science, abs/1307.0417 (2013)

    Google Scholar 

  19. Ma, M., Palmigiano, A., Sadrzadeh, M.: Algebraic semantics and model completeness for intuitionistic public announcement logic. Annals of Pure and Applied Logic 165(4), 963–995 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Palmigiano, A., Sourabh, S., Zhao, Z.: Jónsson-style canonicity for ALBA-inequalities. Journal of Logic and Computation (forthcoming) (2015)

    Google Scholar 

  21. Palmigiano, A., Sourabh, S., Zhao, Z.: Sahlvist theory for impossible worlds. Journal of Logic and Computation (forthcoming) (2015)

    Google Scholar 

  22. Rivieccio, U.: Algebraic semantics for bilattice public announcement logic. In: Studia Logica, Proc. Trends in Logic XIII. Springer (2014)

    Google Scholar 

  23. van Benthem, J., Gerbrandy, J., Kooi, B.P.: Dynamic update with probabilities. Studia Logica 93(1), 67–96 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Weatherson, B.: From classical to intuitionistic probability. Notre Dame Journal of Formal Logic 44(2), 111–123 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa

    Willem Conradie & Alessandra Palmigiano

  2. LIF, Aix-Marseille Université, CNRS UMR 7279, Marseille, France

    Sabine Frittella

  3. Faculty of Technology, Policy and Management, Delft University of Technology, Delft, The Netherlands

    Alessandra Palmigiano & Apostolos Tzimoulis

Authors
  1. Willem Conradie
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  2. Sabine Frittella
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  3. Alessandra Palmigiano
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  4. Apostolos Tzimoulis
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Corresponding author

Correspondence to Willem Conradie .

Editor information

Editors and Affiliations

  1. Dept of Comp Sci, Univ of Liverpool, Liverpool, United Kingdom

    Wiebe van der Hoek

  2. Department of Philosophy, Group in Logic & the Methodology of Sci. University of California, Berkeley, California, USA

    Wesley H. Holliday

  3. Institute of Philosophy of Mind and Cognition, National Yang-Ming University, Taipei, Taiwan

    Wen-fang Wang

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Conradie, W., Frittella, S., Palmigiano, A., Tzimoulis, A. (2015). Probabilistic Epistemic Updates on Algebras. In: van der Hoek, W., Holliday, W., Wang, Wf. (eds) Logic, Rationality, and Interaction. LORI 2015. Lecture Notes in Computer Science(), vol 9394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48561-3_6

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  • DOI: https://doi.org/10.1007/978-3-662-48561-3_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48560-6

  • Online ISBN: 978-3-662-48561-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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