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- Title
Sahlqvist completeness theory for hybrid logic with downarrow binder.
- Authors
Zhao, Zhiguang
- Abstract
In the present paper, we continue the research in Zhao (2021, Logic J. IGPL) to develop the Sahlqvist completeness theory for hybrid logic with satisfaction operators and downarrow binders |$\mathcal {L}(@, {\downarrow })$|. We define the class of restricted Sahlqvist formulas for |$\mathcal {L}(@, {\downarrow })$| following the ideas in Conradie and Robinson (2017, J. Logic Comput. , 27, 867–900), but we follow a different proof strategy which is purely proof-theoretic, namely showing that for every restricted Sahlqvist formula |$\varphi $| and its hybrid pure correspondence |$\pi $| , |$\textbf {K}_{\mathcal {H}(@, {\downarrow })}+\varphi $| proves |$\pi $| ; therefore, |$\textbf {K}_{\mathcal {H}(@, {\downarrow })}+\varphi $| is complete with respect to the class of frames defined by |$\pi $| , using a modified version |$\textsf {ALBA}^{{\downarrow }}_{\textsf {Modified}}$| of the algorithm |$\textsf {ALBA}^{{\downarrow }}$| defined in Zhao (2021, Logic J. IGPL).
- Subjects
LOGIC; SATISFACTION
- Publication
Logic Journal of the IGPL, 2024, Vol 32, Issue 3, p367
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzac079