Some years ago (in 2003) I wrote my first paper in collaboration with Cristiano Castelfranchi who at that time was the supervisor of my Master project in Cognitive Science. The work was aimed at providing a logical formalization of the notion of expectation and of expectation-based emotions such as hope, fear, disappointment and relief. In this paper I will revisit and extend the analysis we did in 2003. I will propose a refinement of the notion of expectation by formalizing its two primitive components: the value of the goal and the strength of the belief. Thanks to this refinement, I will provide a formal analysis of the intensity of hope and fear.