Swap Kripke models for deontic LFIs

Abstract

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 Kripe 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 $C^{D}_n$ hierarchy, by use of the aforementioned mixed semantics with RNmatrices. This includes the historical system $C^{D}_1$ of da Costa-Carnielli (1986), the first deontic paraconsistent system proposed in the literature.