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

Studia Logica (2023)Cite this article

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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Acknowledgements

We would like to thank the referees for their comments. The presentation of the paper has been considerably improved as a result of those comments. We also wish to express our deep gratitude to Nicholas Pischke for reading an earlier draft of the paper and providing many precious suggestions. The research of the first author was in part supported by a grant from IPM and carried out in IPM-Isfahan Branch. The research of the second author was in part supported by a grant from IPM (No.99030420) and carried out in IPM-Isfahan Branch.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    Amir Farahmand Parsa & Meghdad Ghari

  2. Department of Philosophy, Faculty of Literature and Humanities, University of Isfahan, Isfahan, Iran

    Meghdad Ghari

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  1. Amir Farahmand Parsa
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  2. Meghdad Ghari
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Correspondence to Meghdad Ghari.

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Farahmand Parsa, A., Ghari, M. On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of Proofs. Stud Logica (2023). https://doi.org/10.1007/s11225-022-10033-2

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  • DOI: https://doi.org/10.1007/s11225-022-10033-2

Keywords

  • Logic of proofs
  • Algebraic semantics
  • Completeness
  • Representation theorem