Characterization, definability and separation via saturated models

• Autores: Areces, Carlos Eduardo; Carreiro, Facundo Matias; Figueira, Santiago
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Modal Logics; Model Theory; Simulation; Characterization; Definability; Separation; Saturation
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Carreiro, Facundo Matias. University of Amsterdam; Países Bajos
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina