Strong Kleene-Diense Logic: a variant of the infinite-valued Kleene-Diense Logic
"Strong Kleene-Diense Logic"
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Abstract
Kleene first investigated a three-valued system which follows the evaluations of the Łukasiewicz infinite-valued logic ŁC with respect to negation, conjunction, and disjunction, and treats → as material-like implication in the sense that A → B is defined as ～A∨B in its evaluation. Diense and Rescher extended it to many-valued logic and infinite-valued logic, respectively. This paper investigates a variant of the infinite-valued Kleene-Diense logic KD, which we shall call strong Kleene-Diense logic (sKD): sKD has the same evaluations as KD except that sKD takes a variant of Kleene-Diense implication. Following the idea of Dunn [2], we provide algebraic completeness for sKD together with its deduction theorem.
참고문헌 (12)
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