A Modal Logic of Supervenience

Notre Dame Journal of Formal Logic 60 (2):283-309 (2019)

Abstract

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.

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References found in this work

New Work for a Theory of Universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Concepts of Supervenience.Jaegwon Kim - 1984 - Philosophy and Phenomenological Research 45 (December):153-76.
Supervenience and Microphysics.Terence E. Horgan - 1982 - Pacific Philosophical Quarterly 63 (1):29-43.
Epiphenomenal and Supervenient Causation.Jaegwon Kim - 1984 - Midwest Studies in Philosophy 9 (1):257-70.

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Citations of this work

Supervenience, Dependence, Disjunction.Lloyd Humberstone - forthcoming - Logic and Logical Philosophy:1.
A Modal Logic of Supervenience.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (2):283-309.

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