On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of Proofs

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Studia Logica 111 (4):573-613 (2023)
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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.

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10.1007/s11225-022-10033-2

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Meghdad Ghari
University Of Isfahan

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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.Sergei Artemov - forthcoming - Stanford Encyclopedia of Philosophy.
Tracking reasons with extensions of relevant logics.Shawn Standefer - 2019 - Logic Journal of the IGPL 27 (4):543-569.

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