Journal of Automated Reasoning

, Volume 29, Issue 1, pp 1–16 | Cite as

Short Single Axioms for Boolean Algebra

  • William McCune
  • Robert Veroff
  • Branden Fitelson
  • Kenneth Harris
  • Andrew Feist
  • Larry Wos

Abstract

We present short single equational axioms for Boolean algebra in terms of disjunction and negation and in terms of the Sheffer stroke. Previously known single axioms for these theories are much longer than the ones we present. We show that there is no shorter axiom in terms of the Sheffer stroke. Automated deduction techniques were used in several parts of the work.

Boolean algebra Sheffer stroke single axiom 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • William McCune
    • 1
  • Robert Veroff
    • 2
  • Branden Fitelson
    • 3
  • Kenneth Harris
    • 4
  • Andrew Feist
    • 5
  • Larry Wos
    • 6
  1. 1.Mathematics & Computer Science DivisionArgonne National LaboratoryUSA
  2. 2.Computer Science DepartmentUniversity of New MexicoUSA
  3. 3.Philosophy DepartmentStanford University, and Mathematics & Computer Science Division, Argonne National LaboratoryUSA
  4. 4.Madison, Wisconsin, and Mathematics & Computer Science DivisionArgonne National LaboratoryUSA
  5. 5.Mathematics DepartmentDuke UniversityUSA
  6. 6.Mathematics & Computer Science DivisionArgonne National LaboratoryUSA

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