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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© 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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