Title :
Independence of each axiom in a set of axioms and complete sets of axioms of Boolean algebra
Author :
Ninomiya, Tomoko ; Mukaidono, Masao
Author_Institution :
Dept. of Int. Bus. Adm., Tamagawa Univ., Machida, Japan
Abstract :
We investigate fundamental properties of axioms of Boolean algebra in detail by using the Method of Indeterminate Coefficients. Three axioms, 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 essential for the algebra because those are independent from all other axioms of Boolean algebra. Then we research candidates, including those three axioms and other smaller size of axioms, for complete sets of axioms of Boolean algebra, and we can show some of those candidates are indeed complete sets of axioms of the algebra
Keywords :
Boolean algebra; logic design; multivalued logic; Boolean algebra; Method of Indeterminate Coefficients; absorption laws; axiom independence; complementary laws; distributive laws; multivalued logic; truth tables; Absorption; Boolean algebra; Computer science; Equations;
Conference_Titel :
Multiple-Valued Logic, 2002. ISMVL 2002. Proceedings 32nd IEEE International Symposium on
Conference_Location :
Boston, MA
Print_ISBN :
0-7695-1462-6
DOI :
10.1109/ISMVL.2002.1011088
