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Hypothetical Logic of Proofs

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Abstract

The logic of proofs is a refinement of modal logic introduced by Artemov in 1995 in which the modality ◻A is revisited as ⟦t⟧A where t is an expression that bears witness to the validity of A. It enjoys arithmetical soundness and completeness and is capable of reflecting its own proofs (⊦A implies ⊦ ⟦t⟧A, for some t). We develop the Hypothetical Logic of Proofs, a reformulation of LP based on judgemental reasoning.

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References

  1. Artemov, S.N., Beklemishev, L.D.: Provability logic. In: Handbook of Philosophical Logic, 2nd ed, 13, pp. 189–360. Springer, New York (2005)

  2. Sergei, N.: Artëmov and Eduardo Bonelli. The intensional lambda calculus. In: Artëmov, S.N., Nerode, A. (eds.) LFCS, vol. 4514 of Lecture Notes in Computer Science, pp. 12–25. Springer, New York (2007)

  3. Abadi, M., Fournet, C.: Access control based on execution history. In: In Proceedings of the 10th Annual Network and Distributed System Security Symposium, pp. 107–121, (2003)

  4. Sergei N.: Artëmov and Rosalie Iemhoff. The basic intuitionistic logic of proofs. J. Symb. Log. 72(2), 439– (2007)

    Article  MATH  Google Scholar 

  5. Artëmov, S.: Operational modal logic. Technical Report Technical Report MSI 95-29, Cornell University (1995)

  6. Sergei N.: Artëmov. Explicit provability and constructive semantics. Bull. Symbolic Logic 7(1), 1– (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bavera, F., Bonelli, E.: Justification logic and history based computation. In: Cavalcanti, A., Déharbe, D., Gaudel, M., Woodcock, J. (eds.) ICTAC, vol. 6255 of Lecture Notes in Computer Science, pp. 337–351. Springer, New York (2010)

  8. Bonelli E., Feller F.: Justification logic as a foundation for certifying mobile computation. Ann. Pure Appl. Logic 163(7), 935–950 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  9. Banerjee, A., Naumann, D.A.: History-based access control and secure information flow. In: Construction and Analysis of Safe, Secure, and Interoperable Smart Devices, International Workshop (CASSIS 2004), Revised Selected Papers, vol. 3362 of Lecture Notes in Computer Science, pp. 27–48. Springer-Verlag, Berlin (2005)

  10. Dashkov E.: Arithmetical completeness of the intuitionistic logic of proofs. J. Log. Comput. 21(4), 665–682 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  11. de Groote, P.: Strong normalization of classical natural deduction with disjunction. In: Typed Lambda Calculi and Applications, pp. 182–196. Springer, New York (2001)

  12. Davies, R., Pfenning, F.: A modal analysis of staged computation. In: Hans-Juergen B., Guy L.S. Jr. (eds.) POPL, pp. 258–270. ACM Press, New York (1996)

  13. Kuznets, R.: A note on the use of sum in the logic of proofs (2009)

  14. Lévy, J.-J.: Réductions correctes et optimales dans le lambda-calcul. PhD thesis, Paris 7 (1978)

  15. Nanevski, A., Pfenning, F., Pientka, B.: Contextual modal type theory. ACM Trans. Comput. Log. 9(3), 23:1–23:49 (2008)

    Google Scholar 

  16. Parigot, M.: Lambda-mu-calculus: an algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) LPAR, vol. 624 of Lecture Notes in Computer Science, pp. 190–201. Springer, New York (1992)

  17. Parigot M.: Proofs of strong normalisation for second order classical natural deduction. J. Symbolic Logic 62(4), 1461–1479 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pfenning F., Davies R.: A judgmental reconstruction of modal logic. Math. Struct. Comput. Sci. 11(4), 511–540 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Plotkin G.D.: Call-by-name, call-by-value and the lambda-calculus. Theor. Comput. Sci. 1(2), 125–159 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  20. Steren G., Bonelli E.: Intuitionistic hypothetical logic of proofs. Electr. Notes Theor. Comput. Sci. 300, 89–103 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. CONICET, UNQ and ITBA, Roque Sáenz Peña 352, Bernal, Buenos Aires, Argentina

    Eduardo Bonelli

  2. UBA, Buenos Aires, Argentina

    Gabriela Steren

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  1. Eduardo Bonelli
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  2. Gabriela Steren
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Correspondence to Eduardo Bonelli.

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Bonelli, E., Steren, G. Hypothetical Logic of Proofs. Log. Univers. 8, 103–140 (2014). https://doi.org/10.1007/s11787-014-0098-0

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  • DOI: https://doi.org/10.1007/s11787-014-0098-0

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