Peirce’s Sequent Proofs of Distributivity

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10119)


Peirce’s 1880 work on the algebra of logic resulted in a successful calculus (\(\mathbf {PC}\)) for Boolean algebra. Its leading principle (Peirce’s Rule) is that of residuation. We show how the law of distributivity, which Peirce states but does not prove in 1880, can be proved using Peirce’s Rule in \(\mathbf {PC}\). The system \(\mathbf {PC}\) is here presented as a sequent calculus, which was also Peirce’s preferred method. We then give a shorter proof in his 1896 graphical alpha system, and remark on the main findings also of historical importance.


Peirce’s rule Distributivity Sequent calculus Alpha graphs 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Logic and CognitionSun Yat-Sen UniversityGuangzhouChina
  2. 2.Chair of PhilosophyTallinn University of TechnologyTallinnEstonia

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