Shakespearian Modal Logic: A Labelled Treatment of Modal Identity

In this paper we describe a modal proof system arising from the combination of a tableau-like classical system, which incorporates a restricted ("analytical") version of the cut rule, with a label formalism which allows for a specialised, logic dependant unification algorithm. The system provides a uniform proof-theoretical treatment of first-order (normal) modal logics with identity, with and without Barcan formula and/or its converse.