Abstract

Da Costa's paraconsistent systems of the series Cm (for finite m) (see [C1], [C2], and esp. [C3], pp. 237ff.) share important features with transitive logic, TL (which has been gone into in [P1] and [P2]), namely, they all coincide in that: (c1) they possess a strong negation, `¬', a conditional, `⊃', a conjunction, `∧', and a disjunction, `∨', with respect to which they are conservative extensions of CL or Classical Logic; (c2) they possess a non strong negation, `N' (notations are different for systems C) which does not possess all properties of classical negation, but for which the following schemata are theorematic (I use the letters `p', `q', etc as schematic letters; my notational conventions are basically Church's: associativity leftwards; a dot stands for..