Abstract

In most modal logics, atomic propositional symbols are directly representing the meaning of sentences (such as sets of possible worlds). In other words, they use only rigid propositional designators. This means they are not able to handle uncertainty in meaning directly at the sentential level. In this paper, we offer a modal language involving non-rigid propositional designators which can also carefully distinguish de re and de dicto use of these designators. Then, we axiomatize the logics in this language with respect to all Kripke models with multiple modalities and with respect to S5 Kripke models with a single modality.