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 L-models can be defined by a formula or a set of formu...

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Autores principales: Areces, Carlos Eduardo, Carreiro, Facundo, Figueira, Santiago
Formato: article
Lenguaje:Inglés
Publicado: 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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id I10-R14111086-20005
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Modal logics
Model theory
Simulation
Characterization
Definability
Separation
Saturation
spellingShingle Modal logics
Model theory
Simulation
Characterization
Definability
Separation
Saturation
Areces, Carlos Eduardo
Carreiro, Facundo
Figueira, Santiago
Characterization, definability and separation via saturated models
topic_facet Modal logics
Model theory
Simulation
Characterization
Definability
Separation
Saturation
description 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 L-models 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 L-models 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 ω-saturated models in question has the Hennessy-Milner 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.
format article
author Areces, Carlos Eduardo
Carreiro, Facundo
Figueira, Santiago
author_facet Areces, Carlos Eduardo
Carreiro, Facundo
Figueira, Santiago
author_sort Areces, Carlos Eduardo
title Characterization, definability and separation via saturated models
title_short Characterization, definability and separation via saturated models
title_full Characterization, definability and separation via saturated models
title_fullStr Characterization, definability and separation via saturated models
title_full_unstemmed Characterization, definability and separation via saturated models
title_sort characterization, definability and separation via saturated models
publishDate 2021
url http://hdl.handle.net/11086/20005
https://doi.org/10.1016/j.tcs.2014.02.047
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