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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