Logic of Proofs for Bounded Arithmetic

  • Evan Goris
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3967)


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.


Explicit Knowledge Propositional Variable Epistemic Logic Induction Scheme Provability Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Evan Goris
    • 1
  1. 1.The Graduate Center of the City University of New YorkNew YorkUSA

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