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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