Abstract

In this paper, we contribute to the further development of non-deterministic semantics for propositional modality within the 8-valued framework. As our point of departure, we take MnD, a very weak modal logic where modal operators are inter-definable and uninterpreted. We study its extensions with respect to $\Box,\Diamond,\vee,\wedge,\rightarrow $ by means of simple refinements. We provide axiomatisations for all extensions obtained through these refinements. This systematic approach enables the exploration of a wide range of non-deterministic modal logics and hones our understanding of non-deterministic semantics for modality.