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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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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I10-R141-11086-20005 |
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Universidad Nacional de Córdoba |
institution_str |
I-10 |
repository_str |
R-141 |
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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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AT arecescarloseduardo characterizationdefinabilityandseparationviasaturatedmodels AT carreirofacundo characterizationdefinabilityandseparationviasaturatedmodels AT figueirasantiago characterizationdefinabilityandseparationviasaturatedmodels |
bdutipo_str |
Repositorios |
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