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On modal logics of model-theoretic relations

Profile image of Denis I. SavelievDenis I. Saveliev

2018, arXiv (Cornell University)

https://doi.org/10.48550/ARXIV.1804.09810
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28 pages

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Abstract

Given a class C of models, a binary relation R between models, and a model-theoretic language L, we consider the modal logic and the modal algebra of the theory of C in L where the modal operator is interpreted via R. We discuss how modal theories of C and 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 quotient relations. We prove a downward Löwenheim-Skolem theorem for first-order language expanded with the modal operator for the extension relation between models.

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Related topics

  • Mathematics
  • Modal Logic
  • Model Theory
  • Philosophy and Religious Studies
  • Binary relation
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