Models, similarity and complexity

Internal models are an essential element of intelligent systems. Utilization of internal models requires establishing a correspondence between the model components and the world. Three types of similarity measures are defined and analyzed, which are related to the Aristotelian formal logic, fuzzy logic, and adaptive fuzzy logic. The author shows that formal logic can be used for adaptation, but leads to combinatorial complexity. Fuzzy logic is noncombinatorial, but also nonadaptive and may lead to unacceptably coarse granulation. Adaptive fuzzy logic combines the advantages of the previous two: it is noncombinatorial and adaptive. It requires that the a priori model is a fuzzy model: it is inherently uncertain. In the process of adaptation, an a priori fuzzy model is transformed into a crisp model corresponding to an individual crisp concept-object. The theory developed is compared to concepts of classical semiotics and philosophy