Measuring relational complexity in oddity discrimination tasks

A relation-based theory of cognition proposes that cognitive capacity is limited, in part, by the maximum arity of a relation that can be processed in working memory (Halford, 1993; Halford, Wilson, & Phillips, submitted). Children below age five are limited to binary relations, hence have great difficulty on transitive inference tasks, which require integration of two binary relations into a ternary relation. This theory attempts to integrate cognitive and developmental data on the basic of a single metric - relational arity (number of related arguments). However, the lack of formal analysis into relational information involved in cognitive tasks threatens to undermine its utility. I propose using Natural language Information Analysis Method from relational database theory to analyze relational information in cognitive tasks. To demonstrate the utility of this method, I analyze two tasks: (1) simple oddity; and (2) dimension abstracted oddity. The analysis identifies the peak arity of simple oddity as binary and dimension abstracted oddity (like transitive inference) as ternary. Therefore, the relational theory predicts that dimension abstracted oddity cannot be performed until the median age of five years, while simple oddity can be performed earlier. The analysis also suggests variations on these tasks, and the peak arity for each variation is examined