Dialogue in Rough Context

Abstract

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.