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This paper shows that there is a direct connection between dialogues and belief sharing. This connection is shown by proving a correspondence between observational equivalence between dialogues and epistemic bisimulation between Hyper-Discourse Representation Structures (Hyper-DRS) constructed from dialogues. An observational equivalence between dialogues is defined by a kind of similarity of resulting shared beliefs of the dialogues. The theory of Hyper-DRSs is defined by extending Kamp's Discourse Representation Theory (Kamp and Reyle 1993), a formal semantics of discourse or a dynamic semantics, which is exploiting the theory of hypersets (Aczel 1987;Barwise and Moss 1996) in order to solve the problem of the definition, formation and revision of circular objects like shared beliefs.

Formal Semantics of Dialogues Based on Belief Sharing and Observational Equivalence of Dialogues