Sahlqvist-Type Completeness Theory for Hybrid Logic with Binder

Abstract

In the present paper, we continue the research in [22] to develop the Sahlqvist-type completeness theory for hybrid logic with satisfaction operators and downarrow binders L(@, ↓). We define the class of skeletal Sahlqvist formulas for L(@, ↓) following the ideas in [10], but we follow a different proof strategy which is purely proof-theoretic, namely showing that for every skeletal Sahlqvist formula ϕ and its hybrid pure correspondence π, K H(@,↓) + ϕ proves π, therefore K H(@,↓) + ϕ is complete with respect to the class of frames defined by π, using a restricted version of the algorithm ALBA ↓ defined in [22].