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