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Pillars of Computer Science pp 58–71Cite as

Symmetric Logic of Proofs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4800))

Abstract

The Logic of Proofs LP captures the invariant propositional properties of proof predicates t is a proof of F with a set of operations on proofs sufficient for realizing the whole modal logic S4 and hence the intuitionistic logic IPC. Some intuitive properties of proofs, however, are not invariant and hence not present in LP. For example, the choice function ‘+’ in LP, which is specified by the condition s:Fvt:F→(s + t):F, is not necessarily symmetric. In this paper, we introduce an extension of the Logic of Proofs, SLP, which incorporates natural properties of the standard proof predicate in Peano Arithmetic:

t is a code of a derivation containing F,

including the symmetry of Choice. We show that SLP produces Brouwer-Heyting-Kolmogorov proofs with a rich structure, which can be useful for applications in epistemic logic and other areas.

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Authors and Affiliations

  1. CUNY Graduate Center, 365 Fifth Ave., New York, NY 10016, USA

    Sergei Artemov

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  1. Sergei Artemov
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Arnon Avron Nachum Dershowitz Alexander Rabinovich

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Artemov, S. (2008). Symmetric Logic of Proofs. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds) Pillars of Computer Science. Lecture Notes in Computer Science, vol 4800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78127-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-78127-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78126-4

  • Online ISBN: 978-3-540-78127-1

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