Sahlqvist-Type Completeness Theory for Hybrid Logic with Binder

07/04/2022

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by   Zhiguang Zhao, et al.

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In the present paper, we continue the research in <cit.> 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 <cit.>, 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 <cit.>.