Inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic operator of supervenience as a sole modality. The semantics of supervenience modality very naturally correspond to the supervenience-determined consequence relation, in a quite similar way that the strict implication corresponds to the inference-determined consequence relation. We show that this new logic is more expressive than the modal logic of agreement, by proposing a notion of bisimulation for the latter. We provide a sound proof system for the new logic. We lift onto more general logics of supervenience. Related to this, we address an interesting open research direction listed in the literature, by comparing propositional logic of determinacy and noncontingency logic in expressive powers and axiomatizing propositional logic of determinacy over various classes of frames. We also obtain an alternative axiomatization for propositional logic of determinacy over universal models.
"A Modal Logic of Supervenience." Notre Dame J. Formal Logic 60 (2) 283 - 309, May 2019. https://doi.org/10.1215/00294527-2019-0006