Ordered logic: Defeasible reasoning for multiple agents

Our goal is to provide a theoretical foundation for knowledge based applications which support nonmonotonic or defeasible reasoning and which incorporate the knowledge of multiple experts in a principled way. We present a generalized proof theory for defeasible reasoning and briefly explain the relationship of this system to other nonmonotonic formalisms. Then we present a proof theory and semantics for a logic that allows us to explicitly model internal perspectives or multiple agents. This ordered logic properly extends defeasible logic by allowing more complex precedence structure on rules. It provides a mechanism for resolving conflicts between competing perspectives without obscuring the opinions of those perspectives. We show which defeasible theories can be transformed into an equivalent theory in the new logic for multiagent reasoning and how a theory in the logic for multiagent reasoning can be transformed into an equivalent set of defeasible theories, one for each perspective or agent. We present a proof theory for quantified ordered logic and introduce the concept of a curtain which shields the cognitive resources of one agents from another agent. Finally, we consider some examples and discuss how it is possible to specify the relative superiority of some experts over others in a natural way using ordered logic.