The logic of viewpoints (Q1060205)

In this paper a propositional logic of viewpoints is presented. The language of this logic consists of the usual modal operators L (of necessity) and M (of possibility) as well as of two new operators A and R. The intuitive interpretations of A and R are ''from all viewpoints'' and ''from some viewpoints'', respectively. Semantically the language is interpreted by using Kripke models augmented with sets of ''viewpoints'' and with a new alternativeness relation for the operator A. Truth values of formulas are evaluated with respect to a world and a viewpoint. Various axiomatizations of the logic of viewpoints are presented and proved complete. Finally, some applications are given.