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Operational logic of proofs with functionality condition on proof predicate

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Book cover Logical Foundations of Computer Science (LFCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1234))

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Abstract

The extended operational (term-labeled modal) language is used to give the axiomatic description for functional proof predicate supplied with effective operations on proofs induced by modus ponens and necessitation rules. An additional operation is involved which restores a statement from its proof. The arithmetical completeness and decidability theorems are proved. The cut-elimination property for Gentzen style reformulation of corresponding logic is established.

Partially supported by Grant INTAS-RFBR No. 95-0095 and by Grant RFBR No.96-01-01470.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia

    Vladimir N. Krupski

Authors
  1. Vladimir N. Krupski
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Sergei Adian Anil Nerode

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© 1997 Springer-Verlag Berlin Heidelberg

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Krupski, V.N. (1997). Operational logic of proofs with functionality condition on proof predicate. In: Adian, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 1997. Lecture Notes in Computer Science, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63045-7_18

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  • DOI: https://doi.org/10.1007/3-540-63045-7_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63045-6

  • Online ISBN: 978-3-540-69065-8

  • eBook Packages: Springer Book Archive

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