Sentences of the form, “A thinks B thinks ,” arise in the analysis of game-like situations and in the sociology of knowledge. These are modeled by a Boolean algebra with operators, where “A believes x,” is written Ax. Operators ∩j=1 (∞i, Ai)j representing complete consensus or “common opinion” are defined. Properties of these epistemic operators are derived from postulates. Sociological features of content, stability and change of shared awareness are discussed. Finally, the model is used to solve a class of 2-person 0-sum games in which the conventional requirements for mutual knowledge are relaxed.
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