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In this comprehensive review, we describe a new mathematical problem inartificial intelligence (AI) from a mathematical modeling perspective,following the philosophy stated by Rudolf E. Kalman that "Once you get thephysics right, the rest is mathematics". The new problem is called "GeneralizedConstraints (GCs)", and we adopt GCs as a general term to describe any type ofprior information in modelings. To understand better about GCs to be a generalproblem, we compare them with the conventional constraints (CCs) and list theirextra challenges over CCs. In the construction of AI machines, we basicallyencounter 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 aboutmachines. We review the studies in relation to the GC problems although most ofthem do not take the notion of GCs. We demonstrate that if AI machines aresimplified by a coupling with both knowledge-driven submodel and data-drivensubmodel, GCs will play a critical role in a knowledge-driven submodel as wellas in the coupling form between the two submodels. Examples are given to showthat the studies in view of a generalized constraint problem will help usperceive and explore novel subjects in AI, or even in mathematics, such asgeneralized constraint learning (GCL).

Generalized Constraints as A New Mathematical Problem in Artificial Intelligence: A Review and Perspective