Abstract

In one of its possible formulations, the principle of the excluded middle says that, from two propositions A and ¬A , one is true. A paracomplete logic is a logic which can be the basis of theories in which there are propositions A such that A and ¬A are both false. So, we may assert that in a paracomplete logic the law of the excluded middle fails. For a discussion of such kind of logic, as well as for the study of some paracomplete systems, see da Costa and Marconi 1987a and 1987b. In the first of these papers, the authors investigate a hierarchy Pn, l ≤ n ≤ ω, of paracomplete propositional calculi; these calculi are the “duals” of the paraconsistent propositional logics Cn, l ≤ n ≤ ω, introduced be da Costa . In this note we present an algebraization of P1, developing some ideas of da Costa and Marconi 1987a, and study some of the main properties of the resulting algebraic system. It is not difficult to verify that the negation operator, in such an algebraic system, is not compatible with the basis equivalence relation. Thus, our algebraic systems constitute Curry algebras in the sense of da Costa 1966