Five-year-olds can figure out things pretty well

The researchers used an established branch of maths called Category Theory to develop the new theory, which shows that these reasoning skills have similar profiles of development because they involve related sorts of processes.
Around five years of age, children begin to understand that if X is taller than Y and Y is taller than Z, then X is also taller than Z, or the process of transitive inference.
They also begin to understand that there are other fruits than apples in a grocery store - the technique of class inclusion.
Despite decades of previous experiments, the causes of the remarkably similar profiles of mental growth across such seemingly dissimilar paradigms of reasoning have largely been a mystery.
Steven Phillips, at the National Institute of Advanced Industrial Science and Technology (AIST-Japan), and colleagues have shown that both transitive inference and class inclusion develop around five years of age.

They involve the ability to apply two lines of thinking about a problem at the same time, whereas younger children are limited to one.
In the category theory, the emphasis is on the relations (maps) between objects, rather than their contents, said a Public Library of Science (PLoS) release.
In a transitive inference example, children must think about a person (Mary) who is both taller than John and shorter than Sue to make the inference.
These findings were published in the latest issue of PLoS Computational Biology.