Maximal contractions in Boolean algebras
Maximal contractions in Boolean algebras作者机构：Institute of Mathematics Shaanxi Normal University Xi’an China
出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))
年 卷 期：2012年第55卷第9期
页 面：2044-2055页
核心收录：
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金：supported by National Natural Science Foundation of China (Grant Nos. 11171200,61005046,61103133) Fundamental Research Funds for the Central Universities (Grant No. GK201004006)
主 题：deductive element consistency maximal contraction minimal subtraction basic element clause
摘 要：In the present paper,the concepts of deductive element and maximal contraction are introduced in Boolean algebras,and corresponding theories of consistency and maximal contractions are *** algorithm principle is proposed to compute all maximal contractions for a consistent set with respect to its refutation in Boolean *** is pointed out that the quotient algebra of the first-order language with respect to its provable equivalence relation constitutes a Boolean algebra,and hence the computation of R-contractions for closed formulas in first-order languages can be converted into the one in Boolean algebras proposed in this ***,the concept of basic element is introduced in Boolean algebras,which contributes to the definitions of clause and Horn clause transplanted from logic to a special type of Boolean algebras generated by basic *** is also pointed out that the computation of R-contractions for clauses in the classical propositional logic can be converted into the one in Boolean algebras generated by basic elements proposed in this paper.
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