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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todo:paper_03043975_v537_nC_p72_Areces2023-10-03T15:20:28Z Characterization, definability and separation via saturated models Areces, C. Carreiro, F. Figueira, S. Characterization Definability Modal logics Model theory Saturation Separation Simulation Characterization Formal logic Saturation (materials composition) Separation Characterization theorems Definability First order logic Modal logic Model theory Observational equivalences Separation theorem Simulation Computer simulation 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. © 2014 Elsevier B.V. Fil:Areces, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Carreiro, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Figueira, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03043975_v537_nC_p72_Areces |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Characterization Definability Modal logics Model theory Saturation Separation Simulation Characterization Formal logic Saturation (materials composition) Separation Characterization theorems Definability First order logic Modal logic Model theory Observational equivalences Separation theorem Simulation Computer simulation |
| spellingShingle |
Characterization Definability Modal logics Model theory Saturation Separation Simulation Characterization Formal logic Saturation (materials composition) Separation Characterization theorems Definability First order logic Modal logic Model theory Observational equivalences Separation theorem Simulation Computer simulation Areces, C. Carreiro, F. Figueira, S. Characterization, definability and separation via saturated models |
| topic_facet |
Characterization Definability Modal logics Model theory Saturation Separation Simulation Characterization Formal logic Saturation (materials composition) Separation Characterization theorems Definability First order logic Modal logic Model theory Observational equivalences Separation theorem Simulation Computer simulation |
| 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. © 2014 Elsevier B.V. |
| format |
JOUR |
| author |
Areces, C. Carreiro, F. Figueira, S. |
| author_facet |
Areces, C. Carreiro, F. Figueira, S. |
| author_sort |
Areces, C. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_03043975_v537_nC_p72_Areces |
| work_keys_str_mv |
AT arecesc characterizationdefinabilityandseparationviasaturatedmodels AT carreirof characterizationdefinabilityandseparationviasaturatedmodels AT figueiras characterizationdefinabilityandseparationviasaturatedmodels |
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1782026450311839744 |