Generalized Constraints as A New Mathematical Problem in Artificial
  Intelligence: A Review and Perspective
  In this comprehensive review, we describe a new mathematical problem in
artificial intelligence (AI) from a mathematical modeling perspective,
following the philosophy stated by Rudolf E. Kalman that "Once you get the
physics right, the rest is mathematics". The new problem is called "Generalized
Constraints (GCs)", and we adopt GCs as a general term to describe any type of
prior information in modelings. To understand better about GCs to be a general
problem, we compare them with the conventional constraints (CCs) and list their
extra challenges over CCs. In the construction of AI machines, we basically
encounter more often GCs for modeling, rather than CCs with well-defined forms.
Furthermore, we discuss the ultimate goals of AI and redefine transparent,
interpretable, and explainable AI in terms of comprehension levels about
machines. We review the studies in relation to the GC problems although most of
them do not take the notion of GCs. We demonstrate that if AI machines are
simplified by a coupling with both knowledge-driven submodel and data-driven
submodel, GCs will play a critical role in a knowledge-driven submodel as well
as in the coupling form between the two submodels. Examples are given to show
that the studies in view of a generalized constraint problem will help us
perceive and explore novel subjects in AI, or even in mathematics, such as
generalized constraint learning (GCL).
