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arXiv · 2210.04433

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

Zhiguang Zhao
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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].

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Zhiguang Zhao. 2022-10-10. Taming "McKinsey-like" formula: An Extended Correspondence and Completeness Theory for Hybrid Logic H(@). https://arxiv.org/abs/2210.04433

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