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) . 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 .
Some preliminary observations are made and future directions of work are indicated.
KeywordsApproximation Space Lower Satisfaction 14th European Conf Indian National Science Academy Indiscernibility Relation
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