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. © 2023, Springer Nature B.V.