An Epistemic Logic for Arbitration (Extended Abstract)

Arbitration is the process of settling a conflict between two or more persons[Liberatore and Schaerf, 1995; Revesz, 1993; 1997]. The first version of the arbitration operator between knowledge bases is proposed in [Revesz, 1993] via the socalled model-fitting operators. The postulates for modelfitting operators and the corresponding semantic characterization are presented. Arbitration is defined as a special kind of model-fitting operators. In [Revesz, 1997], the arbitration operator is further generalized to make it applicable to weighted knowledge bases. A set of postulates is also directly used in characterizing the arbitration between a weighted knowledge base and a regular knowledge base. A weighted knowledge base in [Revesz, 1997] is defined as a mapping from model sets to nonnegative real numbers and a regular knowledge base is just a finite set of prepositional sentences. A generalized loyal assignment is then defined as a function that assigns to each weighted knowledge base a pre-order between prepositional sentences so that some conditions are satisfied for the pre-orders. Finally, the arbitration of a weighted knowledge base by a regular knowledge base is defined as