We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix (with both only one and two designated values) and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova (Rep Math Log 47:173–182, 2012).

中文翻译：

---

Kleene 强逻辑的全自然蕴涵展开的类在功能上等价于 Łkasiewicz 的 3 值逻辑 Ł3

我们考虑由 Kleene 强 3 值矩阵（只有一个和两个指定值）的所有自然蕴涵展开的集合确定的逻辑，并选择在功能上与 Łukasiewicz 的 3 值逻辑 Ł3 等价的所有逻辑类。“自然蕴涵矩阵”的概念基于 Tomova (Rep Math Log 47:173–182, 2012) 中定义的“自然条件”概念。