A theory of the graceful complexification of concepts and their learnability

Conceptual complexity is assessed by a multi-agent system which is tested experimentally. In this model, where each agent represents a working memory unit, concept learning is an inter-agent communication process that promotes the elaboration of common knowledge from distributed knowledge. Our hypothesis is that a concept’s level of difficulty is determined by that of the multi-agent communication protocol. Three versions of the model, which differ according to how they compute entropy, are tested and compared to Feldman’s model (Nature, 2000), where logical complexity (i.e., the maximal Boolean compression of the disjunctive normal form) is the best possible measure of conceptual complexity. All three models proved superior to Feldman’s: the serial version is ahead by 5.5 points of variance in explaining adult inter-concept performance. Computational complexity theories (Johnson, 1990; Lassaigne & Rougemont, 1996) provide a measure of complexity in terms of the computation load associated with a program’s execution time. In this approach, called the structural approach, problems are grouped into classes on the basis of the machine time and space required by the algorithms used to solve them. A program is a function or a combination of functions. In view of developing psychological models, it can be likened to a concept, especially when y’s domain [y = f(x)] is confined to the values 0 and 1. A neighboring perspective (Delahaye, 1994) aimed at describing the complexity of objects (and not at solving problems) is useful for distinguishing between the“orderless, irregular, random, chaotic, random” complexity (this quantity is called algorithmic complexity, algorithmic randomness, algorithmic information content or Chaitin-Kolmogorov complexity; Chaitin,