Paraconsistent Deontic Logic with Enforceable Rights
F. J. Ausín and Lorenzo Peña This paper is devoted to proposing a system of gradualistic (fuzzy) paraconsistent deontic logic, a logic which implements the idea not just of degrees of truth (and falseness) but also that of degrees of obligatoriness and licitness. The system we propose (transitive deontic logic) tries to implement a correct treatment of quantified deontic and juridical propositions, chiefly those concerning positive rights, which are couched in terms of existential quantifiers (the right to have a dwelling, a job, to enjoy medical care and so on). Even negative rights are expressed through universal quantifiers. Thus, without an adequate treatment of quantifiers, no system of deontic logic is satisfactory. However, standard systems of deontic logic make it extremely difficult, if not downright impossible, to implement quantifiers in any reasonable way. In order to achieve such a treatment, new postulates are put forward, but at the same time most of the usual axioms of standard systems of deontic logic are dropped. In fact, our approach departs from the common assimilation between deontic and modal notions. We start with three preliminary considerations.