Awareness and partitional information structures

This is the first of two papers where we present a formal model of unawareness. We contrast unawareness with certainty and uncertainty. A subject is certain of something when he knows that thing; he is uncertain when he does not know it, but he knows he does not: he is consciously uncertain. On the other hand, he is unaware of something when he does not know it, and he does not know he does not know, and so on ad infinitum: he does not perceive, does not have in mind, the object of knowledge. The opposite of unawareness is awareness, which includes certainty and uncertainty. This paper has three main purposes. First, we formalize the concept of awareness, and introduce a symmetry axiom which states that a subject can be aware of something, φ{symbol} say, if and only if he is aware of its negation not-φ{symbol}; in other words, that φ{symbol} and not-φ{symbol} are perceived together, or neither is. We then derive the basic properties of awareness. The second purpose is to prove a different axiomatic characterization, based on the concept of awareness of the system which underlies the model of information with partitional structures (known as S5). The third purpose of this paper is to show that without a substantial weakening of the rules of inferences normally assumed in modal logic a satisfactory model of unawareness, which includes the symmetry axiom, is impossible. This alternative approach is developed in a second paper by the same authors.