论文标题
super-stulukasiewicz逻辑扩大了$δ$
Super-Łukasiewicz logics expanded by $Δ$
论文作者
论文摘要
Baaz的运营商$δ$是由Baaz引入的，以扩展Gödel逻辑，此后，该操作员被Hájek在其著名书籍中用于扩大模糊逻辑。这些逻辑称为$Δ$ -FUZZY逻辑。另一方面，研究了可能性操作员在olukasiewicz-Moisil代数的情况下进行了研究。奇怪的是，其中一位运营商与巴兹的一家相吻合。在本文中，我们在（$ n $值）super-couukasiewicz逻辑的背景下研究$δ$运算符。提出了对这些逻辑的代数研究，并给出了具有有限变量数量的Lindembaun-Tarski代数的基数。最后，作为副产品，我们提出了Hájek的lukasiwicz逻辑的替代公理化，并以$Δ$扩展。
Baaz's operator $Δ$ was introduced (by Baaz) in order to extend Gödel logics, after that this operator was used to expand fuzzy logics by Hájek in his celebrated book. These logics were called $Δ$-fuzzy logics. On the other hand, possibility operators were studied in the setting of Łukasiewicz-Moisil algebras; curiously, one of these operators coincide with the Baaz's one. In this paper, we study the $Δ$ operator in the context of ($n$-valued) Super-Łukasiewicz logics. An algebraic study of these logics is presented and the cardinality of Lindembaun-Tarski algebra with a finite number of variables is given. Finally, as a by-product, we present an alternative axiomatization of Hájek's Łukasiwicz logic expanded with $Δ$.
