论文标题
一致的posets
Consistent posets
论文作者
论文摘要
我们引入了所谓的一致posets，它们具有抗酮的限制posets，“ x，x”的下部锥和y，y'的下部圆锥提供了x，y是不同的形式为0,1，而且，如果x，y是不同的形式0，那么它们的下锥也是不同的形式0。我们表明，这些poset可以通过抗抗酮的交通式介绍对某些身份和含义的抗反应性表示来表示。在有限的分布或强模块化一致的poset的情况下，可以将其转换为残基结构，因此可以用作具有特定非古典逻辑的代数语义，并具有未陈出的结合和含义。最后，我们表明，一致的poset的Dedekind-Macneille完成是一个一致的晶格，即具有满足上述属性的抗酮相关的有界晶格。
We introduce so-called consistent posets which are bounded posets with an antitone involution ' where the lower cones of x,x' and of y,y' coincide provided x,y are different form 0,1 and, moreover, if x,y are different form 0 then their lower cone is different form 0, too. We show that these posets can be represented by means of commutative meet-directoids with an antitone involution satisfying certain identities and implications. In the case of a finite distributive or strongly modular consistent poset, this poset can be converted into a residuated structure and hence it can serve as an algebraic semantics of a certain non-classical logic with unsharp conjunction and implication. Finally we show that the Dedekind-MacNeille completion of a consistent poset is a consistent lattice, i.e. a bounded lattice with an antitone involution satisfying the above mentioned properties.
