Single axioms for Boolean algebra.

McCune, W.

Argonne National Laboratory

关键词: Algebra;    Equations;    Mathematical Logic;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;   

DOI  :  10.2172/764208
RP-ID  :  ANL/MCS-TM-243
RP-ID  :  W-31109-ENG-38
RP-ID  :  764208

美国|英语

来源: UNT Digital Library

【 摘 要 】

Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.