A Hypersequent Approach to Modal Logic
The hypersequent approach to modal logic was first introduced by Pottinger (1983)
and developed by Avron (1996). More recently other approaches have been explored (see
Restall (2009), Lahav (2013), and Lellman (2014).) This talk offers an alternative
approach to modal logic in hypersequent systems. Of particular interest is that various
different systems of modal logic are not given by alterations in the operational
rules of the calculi (rules governing the necessity operator), but by altering
the external structural rules of hypersequents (such as external weakening, contraction,
and exchange). Philosophically, this account amounts to a way of holding that
modal terms vary in meaning because of the context in which they are embedded as opposed
to the behavior of the modal connectives. Several important formal results are proved
about the systems, including that the identity axiom need only be enforced in
the case of atomics, and that the cut rule is admissible for systems K, D,
and S5.
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