A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘|$T$|-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions (i.e. expansions with a binary connective) of Kleene’s strong logic that are functionally complete for THREE.

中文翻译：

---

关于Kleene强三值逻辑二进制展开式的功能完备性的说明

Słupecki的经典结果指出，如果逻辑L在功能上包括Łukasiewicz的3值逻辑Ł3，并且他将“ | $ T $ | 在L中可以定义“函数”。通过依靠这一经典结果，我们证明了定义Kleene强逻辑的二进制展开式（即具有二进制连接式的展开式）的一般性定理，该逻辑在功能上是完整的。