• DocumentCode
    3478277
  • Title

    Complete and independent sets of axioms of boolean algebra

  • Author

    Ninomiya, Tomoko ; Mukaidono, Masao

  • Author_Institution
    Dept. of international business Adm., Tamagawa Univ., Machida, Japan
  • fYear
    2003
  • fDate
    16-19 May 2003
  • Firstpage
    169
  • Lastpage
    174
  • Abstract
    We investigate fundamental properties of axioms of Boolean algebra in detail by using the method of indeterminate coefficients, which uses multiple-valued logic. We can prove that four axioms, one of the commutative laws, one of the complementary laws, one of the distributive laws and one of the least element(a), greatest element (b) and the absorption laws are independent from others in the set of fundamental axioms of Boolean algebra. Then we research candidates, including those four axioms and other smaller number of axioms and prove all of those candidates are indeed complete and independent sets of axioms of the algebra.
  • Keywords
    Boolean algebra; multivalued logic; set theory; Boolean algebra; absorption laws; commutative laws; complementary laws; distributive laws; independent axiom sets; multiple-valued logic; Absorption; Boolean algebra; Computer science; Logic functions;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Multiple-Valued Logic, 2003. Proceedings. 33rd International Symposium on
  • ISSN
    0195-623X
  • Print_ISBN
    0-7695-1918-0
  • Type

    conf

  • DOI
    10.1109/ISMVL.2003.1201402
  • Filename
    1201402