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On Two Models of Provability

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Mathematical Problems from Applied Logic II

Part of the book series: International Mathematical Series ((IMAT,volume 5))

Abstract

Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The first is the modal logic GL, also known as the Provability Logic, which was shown in 1979 by Solovay to be the logic of the formal provability predicate. The second is Gödel’s original modal logic of provability S4, together with its explicit counterpart, the Logic of Proofs LP, which was shown in 1995 by Artemov to provide an exact provability semantics for S4. These two models complement each other and cover a wide range of applications, from traditional proof theory to λ-calculi and formal epistemology.

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  1. CUNY Graduate Center, New York, USA

    Sergei Artemov

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  1. Department of Computer Science, King’s College London, Srand, London, WC2R 2LS, UK

    Dov M. Gabbay

  2. School of Computer Science and Information Systems, Birkbeck College, Malet Street, London, WC1E 7HX, UK

    Michael Zakharyaschev

  3. Sobolev Institute of Mathematics, SB Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Sergei S. Goncharov

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Artemov, S. (2007). On Two Models of Provability. In: Gabbay, D.M., Zakharyaschev, M., Goncharov, S.S. (eds) Mathematical Problems from Applied Logic II. International Mathematical Series, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-0-387-69245-6_1

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