KLEENE’S THREE VALUED LOGICS AND THEIR CHILDREN

Article type: Research Article

Authors: Fitting, Melvin

Affiliations: Dept. Mathematics and Computer Science, Lehman College (CUNY), Bronx, NY 10468, Depts. Computer Science, Philosophy, Mathematics Graduate Center (CUNY), 33 West 42nd Street, NYC, NY 10036, [email protected]

Note: [] Research partly supported by NSF Grant CCR-9104015.

Abstract: Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences.

DOI: 10.3233/FI-1994-201234

Journal: Fundamenta Informaticae, vol. 20, no. 1,2,3, pp. 113-131, 1994