Characterization, definability and separation via saturated models
Three important results about the expressivity of a modal logic L are the Characterization Theorem (that identifies a modal logic L as a fragment of a better known logic), the Definability theorem (that provides conditions under which a class of Lmodels can be defined by a formula or a set of formu...
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Formato:  article 
Lenguaje:  Inglés 
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2021

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Acceso en línea:  http://hdl.handle.net/11086/20005 https://doi.org/10.1016/j.tcs.2014.02.047 
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Sumario:  Three important results about the expressivity of a modal logic L are the Characterization Theorem (that identifies a modal logic L as a fragment of a better known logic), the Definability theorem (that provides conditions under which a class of Lmodels can be defined by a formula or a set of formulas of L), and the Separation Theorem (that provides conditions under which two disjoint classes of Lmodels can be separated by a class definable in L). We provide general conditions under which these results can be established for a given choice of model class and modal language whose expressivity is below first order logic. Besides some basic constraints that most modal logics easily satisfy, the fundamental condition that we require is that the class of ωsaturated models in question has the HennessyMilner property with respect to the notion of observational equivalence under consideration. Given that the Characterization, Definability and Separation theorems are among the cornerstones in the model theory of L, this property can be seen as a test that identifies the adequate notion of observational equivalence for a particular modal logic. 
