CONUNDRUM OF COMBINATORIAL COMPLEXITY

This paper examines fundamental problems underlying difficulties encou ntered by pattern recognition algorithms, neural networks, and rule sy stems. These problems are manifested as combinatorial complexity of al gorithms, of their computational or training requirements. The paper r elates particular types of complexity problems to the roles of a prior i knowledge and adaptive learning. Paradigms based on adaptive learnin g lead to the complexity of training procedures, while nonadaptive rul e-based paradigms lead to complexity of rule systems. Model-based appr oaches to combining adaptivity with a priori knowledge lead to computa tional complexity. Arguments are presented for the Aristotelian logic being culpable for the difficulty of combining adaptivity and a priori ty. The potential role of the fuzzy logic in overcoming current diffic ulties is discussed. Current mathematical difficulties are related to philosophical debates of the past.