Operational logic of proofs with functionality condition on proof predicate
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.
Unable to display preview. Download preview PDF.
- 1.S. ArtËmov, Operational Modal Logic, Tech. Rep. 95-29, Mathematical Sciences Institute, Cornell University, December 1995.Google Scholar
- 2.K. Gödel, Eine Interpretation des intuitionistischen Aussagenkalküls, Ergebnisse Math. Colloq., Bd. 4 (1933). S. 39–40.Google Scholar
- 3.R.M. Solovay, Provability interpretations of modal logic, Israel J. Math., 25 (1976), pp. 287–304.Google Scholar
- 4.S. ArtËmov and T. Stra\en, Functionality in the basic logic of proofs, Tech. Rep. IAM 92–004, Department for Computer Science, University of Bern, Switzerland, Jan. 1993.Google Scholar
- 5.S. ArtËmov, Logic of proofs, Annals of Pure and Applied Logic, v. 67 (1994), pp. 29–59.Google Scholar
- 6.M.S. Paterson and M.N. Wegman, Linear unification, J. Comput. System Sci., v.16 (2) (1978), pp. 158–167.Google Scholar
- 7.D. Hilbert and P. Bernays, Grundlagen der Mathematik, Springer, 1934–1939.Google Scholar
- 8.D. van Dalen, Logic and Structure, Springer-Verlag, 1994.Google Scholar
- 9.H. Rogers, Theory of recursive functions and effective computability, McGraw-Hill Book Company, New York, 1967.Google Scholar
- 10.S. ArtËmov and V. Krupski, Referential data structures and labeled modal logic, Lecture Notes in Computer Science, v.813 (1994), pp. 23–33.Google Scholar
- 11.S. ArtËmov and V. Krupski, Data storage interpretation of labeled modal logic, Annals of Pure and Applied Logic, v.78 (1996), pp. 57–71.Google Scholar