MV-algebras with internal states and probabilistic fuzzy logics

• Autores: Tommaso Flaminio, Franco Montagna
• Localización: International journal of approximate reasoning, ISSN 0888-613X, Vol. 50, Nº 1, 2009, págs. 138-152
• Idioma: inglés
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• Resumen

  • In this paper we enlarge the language of MV-algebras by a unary operation s equationally described so as to preserve the basic properties of a state in its original meaning. The resulting class of algebras will be called MV-algebras with internal state (or SMV-algebras for short). After discussing some basic algebraic properties of SMV-algebras, we apply them to the study of the coherence problem for rational assessments on many-valued events. Then we propose an algebraic treatment of the Lebesgue integral and we show that internal states defined on a divisible MV?-algebra can be represented by means of this more general notion of integral.