The use of rational agents for modelling real world problems has both been heavily investigated and become well accepted, with BDI (Beliefs, Desires, and Intentions) Logic being a widely used architecture to represent and reason about rational agency. However, in the real world, we often have to deal with different levels of confidence in the beliefs we hold, desires we have, and intentions that we commit to. This paper extends our previous framework that integrated qualitative levels of beliefs, desires, and intentions into BDI Logic. We describe an expanded set of axioms and properties of the extended logic. We present a modular structure for the semantics which involves a non-normal Kripke type semantics that may be used for other agent systems. Further, we demonstrate the usefulness of our framework with a scheduling task example.