On Paraconsistent Weak Kleene Logic and Involutive Bisemilattices - Part I
نویسندگان
چکیده
In his Introduction to Metamathematics [13, § 64], S.C. Kleene distinguishes between a “strong sense” and a “weak sense” of propositional connectives when partially defined predicates are present. Each of these meanings is made explicit via certain 3-valued truth tables, which have become widely known as strong Kleene tables and weak Kleene tables, respectively. If the elements of the base set are labelled as 0, 1 2 , 1, the strong tables for conjunction, disjunction and negation are given by a ∧ b = min{a, b}, a ∨ b = max{a, b}, ¬a = 1− a. The weak tables for the same connectives, on the other hand, are given by:
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