On Hybrid Arrow Logic

We investigate hybridization of Arrow Logic. Hybridization is a general technique for increasing the power of modal logics. A hybrid extension of a given modal logic can be obtained in two stages: first adding a new sort of variables considered as formulas whose intended meaning is to denote points in the domains of the frames then introducing mechanisms for handling the now available information (e.g. the satisfiability operator @ and the down-arrow binder ↓). The hybrid language H(↓,@), obtained from the basic modal language following this construction, may be regarded as the “standard hybrid formalism”. In this paper, we study a system obtained from a hybridization of Arrow Logic much as H(↓,@) was obtained from the basic modal language.