A cut-free sequent system for two-dimensional modal logic, and why it matters

Annals of Pure and Applied Logic 163 (11):1611-1623 (2012)
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The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness of the calculus for Davies–Humberstone models explains why those concepts have the structure described by those models. The result is yet another application of the completeness theorem.



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Greg Restall
University of Melbourne

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References found in this work

Two notions of necessity.Martin Davies & Lloyd Humberstone - 1980 - Philosophical Studies 38 (1):1-31.
Epistemic Two-Dimensional Semantics.David J. Chalmers - 2004 - Philosophical Studies 118 (1-2):153-226.
Worlds, times, and selves.A. N. Prior - 1977 - London: Duckworth. Edited by Kit Fine.
Multiple Conclusions.Greg Restall - 2005 - In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. College Publications.
Why We Need A - Intensions.Frank Jackson - 2004 - Philosophical Studies 118 (1-2):257-277.

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