(From the chapter) Developed and evaluated a generative system for abstract reasoning items based on cognitive theory. The cognitive design system approach was applied to generate matrix completion problems. Study 1 involved developing the cognitive theory with 191 college students who were administered Set I and Set II of the Advanced Progressive Matrices. Study 2 examined item generation by cognitive theory. Study 3 explored the psychometric properties and construct representation of abstract reasoning test items with 728 young adults. Five structurally equivalent forms of Abstract Reasoning Test (ART) items were prepared from the generated item bank and administered to the Ss. In Study 4, the nomothetic span of construct validity of the generated items was examined with 728 young adults who were administered ART items, and 217 young adults who were administered ART items and the Advanced Progressive Matrices. Results indicate the matrix completion items were effectively generated by the cognitive design system approach. (PsycINFO Database Record (c) 2005 APA )