Modal logic with names
Journal of Philosophical Logic 22 (6):607 - 636 (1993)
| Abstract | We investigate an enrichment of the propositional modal language with a universal modality having semanticsx iff y(y ), and a countable set of names — a special kind of propositional variables ranging over singleton sets of worlds. The obtained language c proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment () of, where is an additional modality with the semanticsx iff y(y x y ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in c. Strong completeness of the normal c-logics is proved with respect to models in which all worlds are named. Every c-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from to c are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. | |||||||||
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