Dialogue in rough context

Two agents Ag-1 and Ag-2 confront each other with their own perspectives represented by approximation spaces (U, R-1) and (U, R-2) [3]. They enter into a dialogue (negotiation) over either the extension of the same 'concept' or over two pieces of information or beliefs, A and B, the first for Ag-1, and the second for Ag-2 respectively, which are subsets of U. A combined approximation space (U, R) emerges out of the superimposition of the equivalence classes due to R-1 and R-2. Each agent performs some specified operations one at a time. After an operation by an agent the turn comes to the co-agent. Rounds and effects of rounds are then defined. A dialogue is a sequence of rounds. There are certain rules of the game that depend on the three approximation spaces. The result of a dialogue after n rounds starting with the initial sets A, B is a pair (A(n), B-n), A(n), B-n being supersets of A and B respectively. A dialogue is characterised depending on the various kinds of overlap of the sets A(n) and B-n and their lower and upper approximations. It is satisfactory if the sets A(n) and B-n turn out to be roughly equal with respect to the approximation space (U, R). Dialogues of lower satisfaction are not altogether rejected. This latter type generalizes the notion of Belief-Merging [2]. Some preliminary observations are made and future directions of work are indicated.