#3813. A Class of Implicative Expansions of Kleene’s Strong Logic, a Subclass of Which Is Shown Functionally Complete Via the Precompleteness of ?ukasiewicz’s 3-Valued Logic ?3

October 2026publication date
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Journal’s subject area:
Philosophy;
Linguistics and Language
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Abstract:
A class of implicative expansions of Kleene’s 3-valued logic functionally including Lukasiewicz’s logic 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.
Keywords:
3-Valued logic; Functional completeness; Kleene’s strong 3-valued logic; Natural conditionals; Variable-sharing property

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