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In the present article, we extend the fragment of inductive formulas for thehybrid language L(@) in [8] including a McKinsey-like formula, and show thatevery formula in the extended class has a first-order correspondent, bymodifying the algorithm hybrid-ALBA in [8]. We also identify a subclass of thisextended inductive fragment, namely the extended skeletal formulas, whichextend the class of skeletal formulas in [8], each formula in which axiomatizea complete hybrid logic. Our proof method here is proof-theoretic, following[10, 19] and [3, Chapter 14], in contrast to the algebraic proof in [8].

Taming "McKinsey-like" formula: An Extended Correspondence and Completeness Theory for Hybrid Logic H(@)