Mahan Vaz

Paraconsistent deontic logics have been proposed to deal with deontic paradoxes. We argue that these systems have been misdirected when used to solve deontic paradoxes not grounded on deontic inconsistency. Although the solutions are a formally satisfactory way out of the paradoxes, philosophically they are unsatisfactory. As an example, we discuss how some paraconsistent deontic logics have dealt with Chisholm’s Paradox. A paraconsistent deontic logic should be used to solve paradoxes directly related to deontic inconsistency, as in the case of moral dilemmas. We show how some of these logics can model moral dilemmas while avoiding trivialization. We then consider the philosophical viability of their treatment of moral dilemmas. We argue that _DPI_ is a system that models moral dilemmas in a philosophically satisfactory way. We offer an interpretation for this system, which reads the operator \boxminus as formalizing non-dilemmatic situations. We discuss its philosophical consequences.

We present a construction of nondeterministic semantics for some deontic logics based on the class of paraconsistent logics known as Logics of Formal Inconsistency (LFIs), for the first time combining swap structures and Kripke models through the novel notion of swap Kripke models. We start by making use of Nmatrices to characterize systems based on LFIs that do not satisfy axiom (cl), while turning to RNmatrices when the latter is considered in the underlying LFIs. This paper also presents, for the first time, a full axiomatization and a semantics for the CDn hierarchy, utilizing the aforementioned mixed semantics with RN matrices. It includes the historical system CD1 of da Costa and Carnielli (1986), the first deontic paraconsistent system proposed in the literature.