# On Modal Logics of Model-Theoretic Relations

@article{Saveliev2020OnML, title={On Modal Logics of Model-Theoretic Relations}, author={Denis I. Saveliev and Ilya Shapirovsky}, journal={Stud Logica}, year={2020}, volume={108}, pages={989-1017} }

Given a class $\mathcal C$ of models, a binary relation ${\mathcal R}$ between models, and a model-theoretic language $L$, we consider the modal logic and the modal algebra of the theory of $\mathcal C$ in $L$ where the modal operator is interpreted via $\mathcal R$. We discuss how modal theories of $\mathcal C$ and ${\mathcal R}$ depend on the model-theoretic language, their Kripke completeness, and expressibility of the modality inside $L$. We calculate such theories for the submodel and the… Expand

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