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Taming "McKinsey-like" formula: An Extended Correspondence and Completeness Theory for Hybrid Logic H(@) (2210.04433v1)
Published 10 Oct 2022 in math.LO and cs.LO
Abstract: In the present article, we extend the fragment of inductive formulas for the hybrid language L(@) in [8] including a McKinsey-like formula, and show that every formula in the extended class has a first-order correspondent, by modifying the algorithm hybrid-ALBA in [8]. We also identify a subclass of this extended inductive fragment, namely the extended skeletal formulas, which extend the class of skeletal formulas in [8], each formula in which axiomatize a 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].