In this chapter, we introduce, firstly, the concepts and terminologies of necessarily-type, possibly-type, and flexible possibly type modal propositionsPossibly-type modal proposition and rules and presents a representation with believability-degreeBelievability-degree of (possibly-type) modal propositions and rules; Next, we present the definition and computation formulasComputation formula of truth values of modal propositions; present a reasoning method with modal propositions and rules; and derive a transitive formula of believability-degrees and present a model of relational inference with believability-degrees; Then we analyze and reveal the origin of possibly-type modal propositions, and then reveal also an origin of uncertain information; Finally, we introduce flexibly-quantified propositionsFlexibly-quantified proposition and their formal representation, and then reveal a correlation between imprecise informationImprecise information and uncertain informationUncertain information.