Invariant item ordering of transitive reasining tasks
Klaas Sijtsma, Brian W. Junker, Jürgen Rost, Rolf Langeheine · Data Archiving and Networked Services (DANS) · 1997
Transitive inference is a type of reasoning in which an order relation between two objects A and C is inferred from the observed relation between objects within at least two other pairs of objects, one of which contains A and the other C. For example, consider three objects (e.g., sticks, denoted A, B, and C) and the characteristic length (X), and assume that A is the shortest and C the longest: XA < XB < XC. A transitive inference has been drawn if the observations XA < XB and XB < XC, which provide the premise information, lead to the logical conclusion through abstract reasoning that XA < XC. Of course, the number of objects, the amount of available information, and the number of inferences can each be larger. Other examples of characteristics are weight, surface and temperature. Physical objects might be sticks, balls, discs, tubes, cubes, etc.