Opened Access Dynamic Topological Logic of Metric Spaces


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Autor: Fernández Duque, David
Departamento: Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial
Fecha: 2012
Publicado en: The Journal of Symbolic Logic, 77 (1), 308-328.
Tipo de documento: Artículo
Resumen: Dynamic Topological Logic (DT L) is a modal framework for reasoning about dynamical systems, that is, pairs hX; fi where X is a topological space and f : X ! X a continuous function. In this paper we consider the case where X is a metric space. We rst show that any formula which can be satis ed on an arbitrary dynamic topological system can be satis ed on one based on a metric space; in fact, this space can be taken to be countable and have no isolated points. Since any metric space with these properties is homeomorphic to the set of rational numbers, it follows that any formula can be satis ed on a system based on Q. We then show that the situation changes when considering complete metric spaces, by exhibiting a formula which is not valid in general but is valid on the class of systems based on a complete metric space. While we do not attempt to give a full characterization of the set of valid formulas on this class we do give a relative completeness result; any formul...
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Cita: Fernández Duque, D. (2012). Dynamic Topological Logic of Metric Spaces. The Journal of Symbolic Logic, 77 (1), 308-328.
Tamaño: 188.8Kb
Formato: PDF


DOI: 10.2178/jsl/1327068705

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