The logic of viewpoints

In this paper a propositional logic of viewpoints is presented. The language of this logic consists of the usual modal operatorsL (of necessity) andM (of possibility) as well as of two new operatorsA andR. The intuitive interpretations ofA andR are “from all viewpoints” and “from some viewpoint”, respectively. Semantically the language is interpreted by using Kripke models augmented with sets of “viewpoints” and with a new alternativeness relation for the operatorA. 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.