论文标题
BCK-Elgebras的满意度
Satisfiability degrees for BCK-algebras
论文作者
论文摘要
我们研究了有限BCK-Elgebras中某些方程的满意度；也就是说，给定有限的bck-algebra和BCK-Elgebras语言中的方程式，元素随机选择以替换的方式随机选择的概率是什么？ 具体而言，我们考虑了排除的中间，双重否定，通勤，积极的含义和含义的方程。我们为方程提供了足够的条件，可以在交换性的BCK-elgebras之间具有有限的满足性差距，并证明排除中间的定律的差距为$ \ frac {1} {3} $，而积极的隐含和隐含方程则具有GAP $ \ frac $ \ frac \ frac {1}} {9} $。但是，更笼统地说，用BCK-Elgebras的语言，我们表明双重否定，换算性，积极的含义和含义都无法具有有限的满足性差距。在这些情况下，我们为概率提供了界限。
We investigate the satisfiability degree of some equations in finite BCK-algebras; that is, given a finite BCK-algebra and an equation in the language of BCK-algebras, what is the probability that elements chosen uniformly randomly with replacement satisfy that equation? Specifically we consider the equations for the excluded middle, double negation, commutativity, positive implicativity, and implicativity. We give a sufficient condition for an equation to have a finite satisfiability gap among commutative BCK-algebras, and prove that the law of the excluded middle has a gap of $\frac{1}{3}$, while the positive implicative and implicative equations have gap $\frac{1}{9}$. More generally, though, in the language of BCK-algebras, we show that double negation, commutativity, positive implicativity, and implicativity all fail to have finite satisfiability gap. We provide bounds for the probabilities in these cases.
