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Normalization of Terms in Sharp Models of Logic of Proofs LP

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Moscow University Mathematics Bulletin Aims and scope

Abstract

A basic justification model is sharp when the evidence term constructors \(\cdot,+,!\) in it mean exactly the application of modus ponens rule, the union and the verification of evidences. We construct an example of a sharp model for the logic of proofs LP and establish that in any sharp model of LP every proof term is equivalent to some proof polynomial.

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Notes

  1. In the initial work [1] Artemov used specification containing all formulas of the given form, which sophisticates tracing the specific axioms in the inference.

REFERENCES

  1. S. N. Artemov, ‘‘Explicit provability and constructive semantics,’’ Bull. Symbolic Logic 7, 1–36 (2001). https://doi.org/10.2307/2687821

  2. A. Mkrtychev, ‘‘Models for the logic of proofs,’’ in Logical Foundations of Computer Science, Ed. by S. Adyan and A. Nerode, Lecture Notes in Computer Science, Vol. 1234 (Springer, Cham, 1997), pp. 266–275. https://doi.org/10.1007/3-540-63045-7_27

  3. S. Artemov and M. Fitting, Justification Logic: Reasoning with Reasons, Cambridge Tracts in Mathematics, Vol. 216 (Cambridge Univ. Press, Cambridge, 2019). https://doi.org/10.1017/9781108348034

  4. S. Artemov, ‘‘Justification awareness models,’’ in Logical Foundations of Computer Science, Ed. by S. Artemov and A. Nerode, Lecture Notes in Computer Science, Vol. 10703 (Springer, Cham, 2018), pp. 22–36. https://doi.org/10.1007/978-3-319-72056-2_2

  5. N. V. Krupski, ‘‘On the complexity of the reflected logic of proofs,’’ Theor. Comput. Sci. 357, 136–142 (2006). https://doi.org/10.1016/j.tcs.2006.03.015

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Chair of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    V. N. Krupski

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  1. V. N. Krupski
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Correspondence to V. N. Krupski.

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Translated by E. Oborin

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Krupski, V.N. Normalization of Terms in Sharp Models of Logic of Proofs LP. Moscow Univ. Math. Bull. 78, 309–312 (2023). https://doi.org/10.3103/S0027132223060049

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  • DOI: https://doi.org/10.3103/S0027132223060049

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