Logic of proofs for bounded arithmetic

Authors:
Evan Goris
Affiliations:
The Graduate Center of the City University of New York, New York, NY
Venue:
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Year:
2006

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Abstract

The logic of proofs is known to be complete for the semantics of proofs in Peano Arithmetic PA. In this paper we present a refinement of this theorem, we will show that we can assure that all the operations on proofs can be realized by feasible, that is PTIME-computable, functions. In particular we will show that the logic of proofs is complete for the semantics of proofs in Buss' bounded arithmetic S$^{1}_{2}$ . In view of recent applications of the Logic of Proofs in epistemology this result shows that explicit knowledge in the propositional framework can be made computationally feasible.