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 definitions of shared information by infinite conjunctions of propositions with nested epistemic modalities, the actions are all interpreted as one-step (not infinite many step) formations of shared information by corecursive definitions. As a result, we can provide a structure of inference between the actions, and define a process equivalence of dialogues with respect to their resulting shared information.