Formal Semantics of Acknowledgements, Agreements and Disagreements

Acknowledgements, agreements, and disgreements are basic moves in communications among agents, since the moves form and revise shared information among the agents which is basic prerequisite of group-actions. This paper investigates formal semantics of the moves from the point of view of information sharing among agents, exploiting the circular objects assured by Hyperset Theory. Therefore, avoiding de nitions of shared information by in nite conjunctions of propositions with nested epistemic modalities, the actions are all interpreted as onestep (not in nite many step) formations of shared information by corecursive de nitions. As a result, we can provide a structure of inference between the actions, and de ne a process equivalence of dialogues with respect to their resulting shared information.