Representing Possibilities in Relation to Constraints and Agents

In this paper we describe a framework for overcoming agent ignorance within a setting for collaborative problem solving. As a result of privacy concerns, agents may not reveal information that could be of use in problem solving. In this case, under certain assumptions agents can still reason about this information in terms of the possibilities that are consistent with what they know. This is done using constraint-based reasoning in a framework consisting of an ordinary CSP, which is only partly known, and a system of "shadow CSPs" that represent various forms of possibilistic knowledge. This paper proposes some properties of good structure for this system and shows that a reasonable set of deductions used during the solving process preserves these properties. Extensions to the basic framework and relations to other work are also discussed.