The Logic of Uncertainty and Geometry of the Worlds

The classical logic is built in an axiomatic way without containing any uncertainty. Over the years, many attempts have been made to extend the classical logic framework to incorporate uncertainties. This work has produced different and apparently conflicting definitions of uncertainties. Previously we have argued that an extended modal logic framework can provide a unifying formal language for many formalizations of uncertainty such as probability, approximate probability, evidence theory, fuzzy sets, and rough sets.