The Algebra of Knowledge: Critique and Reformulation

The standard algebra of experessing knowledge and common knowledge in game theory is critically examines. It is argued that this algebra is flawed because it assumes implicitly that information partitions of individuals are common knowledge, and that all individuals know all the truths of science, medicine and other disciplines. A reformulation of the standard algebra is developed; and, in the context of this new algebra, it is demonstrated that the well-known formalization of Lewis' definition of common knowledge in terms of the meet of partitions is not an accurate depiction of Lewis' idea. The paper also comments on the meaning of 'states of the world' and on the agreeing-to-disagree type of claims.