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International Symposium on Logical Foundations of Computer Science

LFCS 2016: Logical Foundations of Computer Science pp 187–201Cite as

Sequent Calculus for Intuitionistic Epistemic Logic IEL

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9537))

Abstract

The formal system of intuitionistic epistemic logic IEL was proposed by S. Artemov and T. Protopopescu. It provides the formal foundation for the study of knowledge from an intuitionistic point of view based on Brouwer-Hayting-Kolmogorov semantics of intuitionism. We construct a cut-free sequent calculus for IEL and establish that polynomial space is sufficient for the proof search in it. We prove that IEL is PSPACE-complete.

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Notes

  1. 1.

    For example, it can be some trusted database that stores true facts without proofs or some zero-knowledge proof.

  2. 2.

    Sequents in [4] are classical (multiconclusion) and contain special labels denoting worlds of a Kripke structure, so this formalization can be considered as a classical formulation of the theory of forcing relation in a Kripke structure that corresponds to the intuitionistic bimodal epistemic logic.

  3. 3.

    This method was introduced by Kleene in the construction of his G3 systems, see [6].

References

  1. Artemov, S., Protopopescu, T.: Intuitionistic Epistemic Logic (2014). arXiv:1406.1582v2

  2. Williamson, T.: On intuitionistic modal epistemic logic. J. Philos. Log. 21(1), 63–89 (1992)

    MathSciNet  MATH  Google Scholar 

  3. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  4. Maffezioli, V., Naibo, A., Negri, S.: The Church-Fitch knowability paradox in the light of structural proof theory. Synthese 190, 2677–2716 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press, Cambridge (1996)

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  6. Kleene, S.C.: Introduction to Metamathematics. North-Holland Publ. Co., Amsterdam (1952)

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  7. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. Assoc. Comput. Mach. 28, 114–133 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  8. Statman, R.: Intuitionistic propositional logic is polynomial-space complete. Theor. Comput. Sci. 9, 67–72 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  9. Krupski, V.N.: Introduction to Computational Complexity. Factorial Press, Moscow (2006). (In Russian)

    Google Scholar 

  10. Kitaev, A., Shen, A., Vyalyi, M.: Classical and Quantum Computations. MCCME-CheRo, Moscow (1999). (In Russian)

    MATH  Google Scholar 

  11. Krupski, N.: Typing in reflective combinatory logic. Ann. Pure Appl. Log. 141, 243–256 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We are grateful to Sergey Artemov for inspiring discussions of intuitionistic epistemic logic. We thank the anonymous referees for their comments.

The research described in this paper was partially supported by Russian Foundation for Basic Research (grant 14-01-00127).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119992, Russia

    Vladimir N. Krupski & Alexey Yatmanov

Authors
  1. Vladimir N. Krupski
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  2. Alexey Yatmanov
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Corresponding author

Correspondence to Vladimir N. Krupski .

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Editors and Affiliations

  1. City University of New York , New York, New York, USA

    Sergei Artemov

  2. Cornell University , Ithaca, New York, USA

    Anil Nerode

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Krupski, V.N., Yatmanov, A. (2016). Sequent Calculus for Intuitionistic Epistemic Logic IEL. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2016. Lecture Notes in Computer Science(), vol 9537. Springer, Cham. https://doi.org/10.1007/978-3-319-27683-0_14

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  • DOI: https://doi.org/10.1007/978-3-319-27683-0_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27682-3

  • Online ISBN: 978-3-319-27683-0

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