论文信息 - Independence of each axiom in a set of axioms and complete sets of axioms of Boolean algebra

Independence of each axiom in a set of axioms and complete sets of axioms of Boolean algebra

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.

Masao Mukaidono | Tomoko Ninomiya

[1] Raymond E Miller. Switching theory , 1979 .

[2] Masao Mukaidono,et al. Independence of the axioms of Boolean algebra in multiple-valued logic , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[3] Masao Mukaidono,et al. Fundamental Properties on Axioms of Kleene Algebra , 2000, ISMIS.

[4] M. Mukaidono. A set of independent and complete axioms for a fuzzy algebra (Kleene algebra) , 1981 .

[5] Masao Mukaidono,et al. Clarifying the axioms of Kleene algebra based on the method of indeterminate coefficients , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[6] Louis Couturat,et al. The Algebra Of Logic , 1914 .

[7] T. Ninomiya,et al. Synthesis of Axiom Systems for the Three-Valued Predicate Logic by Means of the Special Four-Valued Logic, , 1983 .