A boolean model of role discrimination

This article analyzes, based on Boolean approach by C.C. Ragin, how the subjective internal structure of social roles conditions the possibility of discrimination of role performance (role discrimination). I postulate, in an actor's image, a role consists of some role elements, which make up the internal hierarchical structure (role image) according to each element's importance for the role. After introducing a set of definitions and assumptions, the role discrimination is formulated as a Boolean equation, taking the role elements as independent variables and the role discrimination itself as a dependent variable. Suppose role X, and suppose a performer and an observer interact each other on role performing, each having his/her own image. In general, between such two given actors, the performance of X by the performer can be discriminated by the observer under the condition that the pattern of practicing role elements included in each image ("practical profile") coincides with each other, at least partially. Taking up a simple case of two elements and introducing the judgment rule, I examine the possibility of role discrimination for all possible combinations of the images. After that, some general propositions as to the possibility of role discrimination, that hold regardless of the number of role elements, are discussed.