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.
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