GENERAL APPROACH TO MANY VALUED KRIPKE MODELS
Szymon Frankowski · 2006
Main investigations concerning Kripke models refer to two valued case. The papers devoted to many-valued modal logics ([1], [2], [3], [4], [5], [6], [7]) do not contain even elementary theory of appropriate models. This paper provides very general notion of many valued Kripke model for every standard multimodality, and displays the suitable generalizations of the ideas known from the classical case: disjoint sum of Kripke models, bounded morphism (sometimes called pmorphism), bisimulation. Kripke models based on relational structures is one of the most important tool of semantical characterization of modal logics. In the past Kripke models, similarly like logics deflned by them, had only classical (two valued) character. However, for example in [1],[2] and [3] the many valued models appear which are a natural generalization of the classical one. They difier from it in that the propositional variables, and consequently all formulas, can be valued valued other than the two element Boolean algebra. The approach of Fitting [5], [6], [7] is more general: many-valued relations are : ; i i @ @ »» »»» :::