<p><strong>In Short:</strong></p>
<p>I am not sure what &quot;0-dimensional&quot; 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.</p>
<p><strong>Longer answer:</strong></p>
<p>A <a href="https://en.wikipedia.org/wiki/Binary_relation" rel="nofollow noreferrer">binary relation</a> associates elements from two domains ('domain' and 'co domain') via a set of ordered pairs. You can represent it as a <strong>two dimensional array</strong> of boolean value where one writes <code>True</code> in row <span class="math-container">$i$</span> and column <span class="math-container">$j$</span> if and only if <span class="math-container">$(i,j)$</span> is in the relation.</p>
<p>By extension, a <a href="https://en.wikipedia.org/wiki/Ternary_relation" rel="nofollow noreferrer">ternary relation </a> or any <a href="https://en.wikipedia.org/wiki/Finitary_relation" rel="nofollow noreferrer">finitary relation</a> (of which a quartenary relation would be a particular case) associates elements from <span class="math-container">$t$</span> domains (where <span class="math-container">$t=3$</span> for a ternary relation) via a set of <span class="math-container">$t$</span>-uples, and you can represent them as <span class="math-container">$t$</span>-dimensional arrays of boolean values</p>

CC BY-SA 4.0
2022-08-16T09:20:28.430Z
2022-08-16T09:20:28.430Z
J.y B.y
<p>Halford et al. (2010) claims discusses binary relations and that humans can process up to a <em>quaternary</em>  relation. Are these equivalent to &quot;0-dimensional,&quot; &quot;1-dimensional&quot; relational reasoning problems discussed elsewhere?</p>
<p>For example, a binary relation discussed in that paper, <em>taller(Bob, Tom)</em> involves comparing one dimension: height, so it could be a 1-dimensional problem, yet I can't find confirmation of the terminology.</p>
<ul>
<li>Halford, G. S., Wilson, W. H., &amp; Phillips, S. (2010). Relational knowledge: The foundation of higher cognition. Trends in Cognitive Sciences, 14(11), 497–505. <a href="https://doi.org/10.1016/j.tics.2010.08.005" rel="nofollow noreferrer">https://doi.org/10.1016/j.tics.2010.08.005</a></li>
</ul>

<terminology>
Are binary relations the same as "1-dimensional"?
Azor Ahai -him-
# Are binary relations the same as "1-dimensional"?

(Asked by: username_0 on 2022-08-13)

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>

**Tags:** terminology


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## 1 answers

### Answer by username_1 on 2022-08-16. Score: 2

**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](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Ternary_relation)  or any [finitary relation](https://en.wikipedia.org/wiki/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


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