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An Epistemic Separation Logic

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Logic, Language, Information, and Computation (WoLLIC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9160))

Abstract

We define an Epistemic Separation Logic, called ESL, that allows us to consider epistemic possible worlds as resources that can be shared or separated, in the spirit of separation logics. After studying the semantics and the expressiveness of this logic, we provide a tableau calculus with labels and resource contraints that is sound and complete and then also study countermodel extraction.

Work partially supported by the ANR grant DynRes (project no. ANR-11-BS02-011) and by the EU ERC project EPS 313360. Hans van Ditmarsch is also affiliated to IMSc, Chennai, India, as research associate.

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References

  1. Balbiani, P., van Ditmarsch, H., Herzig, A., de Lima, T.: Tableaux for public announcement logics. J. Log. Comput. 20(1), 55–76 (2010)

    Article  MATH  Google Scholar 

  2. Baltag, A., Coecke, B., Sadrzadeh, M.: Algebra and sequent calculus for epistemic actions. Electron. Notes Theoret. Comput. Sci. 126, 27–52 (2005)

    Article  Google Scholar 

  3. Baltag, A., Coecke, B., Sadrzadeh, M.: Epistemic actions as resources. J. Log. Comput. 17(3), 555–585 (2006)

    Article  MathSciNet  Google Scholar 

  4. Biri, Nicolas, Galmiche, Didier: A separation logic for resource distribution. In: Pandya, Paritosh K., Radhakrishnan, Jaikumar (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 23–37. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Collinson, M., Pym, D.: Algebra and logic for resource-based systems modelling. Math. Struct. Comput. Sci. 19(5), 959–1027 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Courtault, J.R., Galmiche, D.: A modal extension of Boolean BI for resource transformations. In: International Workshop on Logics for Resources, Processes, and Programs, LRPP 2013, Nancy (2013)

    Google Scholar 

  7. Courtault, J.R., Galmiche, D.: A modal BI logic for dynamic resource properties. In: Artemov, Sergei, Nerode, Anil (eds.) LFCS 2013. LNCS, vol. 7734, pp. 134–148. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Galmiche, D., Méry, D., Pym, D.: The semantics of BI and resource tableaux. Math. Struct. in Comp. Sci. 15(6), 1033–1088 (2005)

    Article  MATH  Google Scholar 

  9. Gerbrandy, J.D.: Bisimulations on Planet Kripke. PhD thesis, University of Amsterdam, 1999. ILLC Dissertation Series DS-1999-01

    Google Scholar 

  10. Girard, J.Y.: Linear logic. Theoret. Comput. Sci. 50(1), 1–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  11. Herzig, Andreas: A simple separation logic. In: Libkin, Leonid, Kohlenbach, Ulrich, de Queiroz, Ruy (eds.) WoLLIC 2013. LNCS, vol. 8071, pp. 168–178. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Ishtiaq, S., O’Hearn, P.: BI as an assertion language for mutable data structures. In: 28th ACM Symposium on Principles of Programming Languages, POPL 2001, pp. 14–26, London (2001)

    Google Scholar 

  13. Meyer, J.-J., Van Der Hoek, W.: Epistemic Logic for AI and Computer Science. Tracts in Theoretical Computer Science 41. Cambridge University Press, New York (1995)

    Book  Google Scholar 

  14. Larchey-Wendling, D.: The formal strong completeness of partial monoidal Boolean BI. Journal of Logic and Computation, published online 2 June 2014, doi:10.1093/logcom/exu031

  15. Lenzen, W.: Recent work in epistemic logic. Acta Philosophia Fennica 30, 1–219 (1978)

    MathSciNet  Google Scholar 

  16. Marion, M., Sadrzadeh, M.: Reasoning about Knowledge in Linear Logic: Modalities and Complexity. In: Logic, Epistemology, and the Unity of Science, pp. 327–350. Kluwer Academic Publishers, Dordrecht (2003)

    Google Scholar 

  17. Plaza, J.A.: Logics of public communications. In: Proceedings of the 4th ISMIS, pp. 201–216. Oak Ridge National Laboratory (1989)

    Google Scholar 

  18. Pym, D.J.: The semantics and proof theory of the logic of bunched implications. Applied Logic Series, vol. 26. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  19. Moses, Y., Fagin, R., Halpern, J., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  20. Reynolds, J.: Separation logic: a logic for shared mutable data structures. In: IEEE Symposium on Logic in Computer Science, pp. 55–74. Copenhagen (2002)

    Google Scholar 

  21. van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. J. Appl. Non-Classical Log. 17(2), 157–182 (2007)

    Article  MATH  Google Scholar 

  22. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer Publishing Company, Netherlands (2007)

    Book  Google Scholar 

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Correspondence to Didier Galmiche .

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Courtault, JR., van Ditmarsch, H., Galmiche, D. (2015). An Epistemic Separation Logic. In: de Paiva, V., de Queiroz, R., Moss, L., Leivant, D., de Oliveira, A. (eds) Logic, Language, Information, and Computation. WoLLIC 2015. Lecture Notes in Computer Science(), vol 9160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47709-0_12

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  • DOI: https://doi.org/10.1007/978-3-662-47709-0_12

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