The logic of proofs, semantically

Annals of Pure and Applied Logic 132 (1):1-25 (2005)
A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.
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DOI 10.1016/j.apal.2004.04.009
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Sergei Artemov (2008). The Logic of Justification. Review of Symbolic Logic 1 (4):477-513.
Melvin Fitting (2008). A Quantified Logic of Evidence. Annals of Pure and Applied Logic 152 (1):67-83.

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