The present paper is a sequel to Robles et al. (J Logic Lang Inf 29(3):349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property (vsp) and vsp-related properties.

中文翻译：

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Kleene强逻辑的一类隐式展开，通过Viaukasiewicz的三值逻辑Ł3的预完成性来显示其子类在功能上是完整的

本文是Robles等人的续集。（J Logic语言信息29（3）：349–374，2020. https://doi.org/10.1007/s10849-019-09306-2）。定义了功能上包括Łukasiewicz的逻辑Ł3的Kleene的三值逻辑的一类隐式展开式。研究了此类和/或其某些子类的一些属性。所考虑的属性包括3个值的真值集的功能完整性，自然条件的存在，变量共享属性（vsp）和vsp相关属性。