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Feasible Operations on Proofs: The Logic of Proofs for Bounded Arithmetic

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Abstract

This paper presents a semantics for the logic of proofs \(\mathsf{LP}\) in which all the operations on proofs are realized by feasibly computable functions. More precisely, we will show that the completeness of \(\mathsf{LP}\) for the semantics of proofs of Peano Arithmetic extends to the semantics of proofs in Buss’ bounded arithmetic \(\mathsf{S}^{1}_{2}\) . In view of applications in epistemology of \(\mathsf{LP}\) in particular and justification logics in general this result shows that explicit knowledge in the propositional framework can be made computationally feasible.

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  1. The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Evan Goris

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  1. Evan Goris
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Correspondence to Evan Goris.

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This research supported by CUNY Community College Collaborative Incentive Research Grant 91639-0001 “Mathematical Foundations of Knowledge Representation”.

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Goris, E. Feasible Operations on Proofs: The Logic of Proofs for Bounded Arithmetic. Theory Comput Syst 43, 185–203 (2008). https://doi.org/10.1007/s00224-007-9058-x

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