May 2019 A Modal Logic of Supervenience
Jie Fan
Notre Dame J. Formal Logic 60(2): 283-309 (May 2019). DOI: 10.1215/00294527-2019-0006


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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Jie Fan. "A Modal Logic of Supervenience." Notre Dame J. Formal Logic 60 (2) 283 - 309, May 2019.


Received: 19 January 2017; Accepted: 9 March 2017; Published: May 2019
First available in Project Euclid: 6 May 2019

zbMATH: 07096539
MathSciNet: MR3952234
Digital Object Identifier: 10.1215/00294527-2019-0006

Primary: 03B45

Keywords: axiomatizations , determinacy , expressivity , noncontingency , supervenience

Rights: Copyright © 2019 University of Notre Dame


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Vol.60 • No. 2 • May 2019
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