Indeed! I was speaking somewhat imprecisely - I was referring to logic in the sense of Bertrand Russel's work. I should rather say the major shortcoming of CLASSICAL logic is its inability to express uncertainty.

That being said, there are many flavours of non-classical logic and (paraconsistent, multivalued etc.) but their usage remains scarce outside of work in logic itself. Some intuitionistic, constructivist, and computational logics seem to be gaining popularity, especially in computer-related circles (computer-aided proof, numerical methods etc.)