Are binary relations the same as "1-dimensional"?

Question

Halford et al. (2010) claims discusses binary relations and that humans can process up to a quaternary relation. Are these equivalent to "0-dimensional," "1-dimensional" relational reasoning problems discussed elsewhere?

For example, a binary relation discussed in that paper, taller(Bob, Tom) involves comparing one dimension: height, so it could be a 1-dimensional problem, yet I can't find confirmation of the terminology.

• Halford, G. S., Wilson, W. H., & Phillips, S. (2010). Relational knowledge: The foundation of higher cognition. Trends in Cognitive Sciences, 14(11), 497–505. https://doi.org/10.1016/j.tics.2010.08.005

Answer 1

In Short:

I am not sure what "0-dimensional" relational reasoning problems would be, but in mathematics, a binary relation is usually referred to as two-dimensional, a ternary one as tri-dimensional, etc, mostly because of their matrix representation in the same dimension.

Longer answer:

A binary relation associates elements from two domains ('domain' and 'co domain') via a set of ordered pairs. You can represent it as a two dimensional array of boolean value where one writes True in row $i$ and column $j$ if and only if $(i,j)$ is in the relation.

By extension, a ternary relation or any finitary relation (of which a quartenary relation would be a particular case) associates elements from $t$ domains (where $t=3$ for a ternary relation) via a set of $t$-uples, and you can represent them as $t$-dimensional arrays of boolean values