The completeness and compactness of a three-valued first-order logic

Abstract

The strong completeness and the compactness of a three-valued first order predicate calculus with two distinguished truth-values are obtained. The system was introduced in Sur un prcb leme de Jaskowski, I .M.L. D.'Ottaviano and N.C. A. da Costa, C.R. Acad.Sc. Paris 270A (1970) , pp.1349-1353, and has several applications, especially in paraconsistent logics.