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arXiv · 1611.04740

A Modal Logic of Supervenience

Jie Fan
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Abstract

Supervenience is an important philosophical concept. In this paper, 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 is very natural to 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 logic. We provide a sound proof system for our new logic. We also lift on to more general logics of supervenience. Related to this, we compare propositional logic of determinacy and non-contingency in expressive powers, and give axiomatizations of propositional logic of determinacy over various classes of frames, thereby resolving an open research direction listed in~\cite[Sec.~8.2]{Gorankoetal:2016}. As a corollary, we also present an alternative axiomatization for propositional logic of determinacy over universal models. We conclude with a lot of future work.

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Jie Fan. 2016-11-15. A Modal Logic of Supervenience. https://doi.org/10.1215/00294527-2019-0006

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