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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