A Formalization of Viewpoints

We present a formalisation for the notion of viewpoint, a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends rst order predicate calculus through an axiomatization of provability and with the addition of proper reeection rules. The extension is not conservative, but consistency is granted. Viewpoints are deened as set of reiied meta-level sentences. A proof theory for viewponts is developed which enables to carry out proofs of sentences involving several viewpoints. A semantic account of viewpoints is provided, dealing with issues of self referential theories and paradoxes, and exploiting the notion of contextual entailment. Notions such as beliefs, knowledge, truth and situations can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints.