How has belief modality contributed to formal semantics?

Looking back the history of formal treatment of linguistics, we cannot disregard the contribution of possible world semantics. Intensional logic of Montague semantics, DRT (Discourse Representation Theory), mental space, and situation theory are closely related to or compared with the notion of possible world. All these theories have commonly clarified the structure of belief context or uncertain knowledge, employing hypothesized worlds. In this talk, I firstly brief the pedigree of these theories. Next, I will introduce the recent development of modal logic for the representation of (i) knowledge and belief and (ii) time, in which belief modality is precisely discussed together with the accessibility among possible worlds. I will refer to BDI (belief-desire-intention) logic, CTL (computational tree logic), and sphere-based model in belief revision. Finally, I will discuss how these theories could be applied to the further development of analyses of natural language.