On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of Proofs
Abstract
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on proof terms and equality predicate on terms. Moreover, the completeness theorem and certain generalizations of Stone’s representation theorem are obtained for all proposed algebras.Author's Profile
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References found in this work
Explicit provability and constructive semantics.Sergei N. Artemov -2001 -Bulletin of Symbolic Logic 7 (1):1-36.
The logic of proofs, semantically.Melvin Fitting -2005 -Annals of Pure and Applied Logic 132 (1):1-25.
Justification logic: reasoning with reasons.S. N. Artemov -2019 - New York, NY: Cambridge University Press. Edited by Melvin Fitting.
Tracking reasons with extensions of relevant logics.Shawn Standefer -2019 -Logic Journal of the IGPL 27 (4):543-569.
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