# SUO: Re: maximum number of semantical relations

```In any kind of design or analysis, there are only three
numbers that require no further explanation:  zero, one,
and infinity.  Any number N greater than 1 is probably
an inadequate approximation to infinity -- unless there
is a convincing explanation of why N should be considered
a natural stopping point before infinity.  Following are
some sample explanations:

- Dichotomy:  If a distinction divides a class of
possibilities into A and not-A, then there are
exactly two classes.

- Trichotomy:  Peirce showed that it is possible to
transform any graph that contains a node with 4 or
more attached arcs into a graph that contains no
node with more than 3 attached arcs.  See the
diagram nodes.gif for a transformation that splits
the node X with four arcs into two nodes X1 and X2,
which have three arcs each; similar transformations
can be used to split nodes with any number of arcs
to additional nodes that have no more than 3.

-  Four-color theorem:  Any map of countries (i.e.,
connected areas) drawn on a plane can colored
with at most 4 colors so that no two contiguous
contries have the same color.

Any claim that some number N is a maximum should be
supported with such an explanation.  Otherwise, we
should regard N as merely the point at which somebody
stopped counting.

> I want to estimate a maximum number of relations that can
> be used in a knowledge representation in an ontology.  I

Meena responded:

> To my knowledge the semantic relations are --- inclusion,
> possession, attachment, attribution, antonym, synonym, case.
> The inclusion is further divided as class inclusion, meronymic
> inclusion, and spatial inclusion. (Winston, Chaffin, Hermann, 1987).

Winston, Chaffin, and Hermann had a good analysis and
classification of relations, which is well worth reading.
But I would regard any of those numbers -- 16, 7, 3, or
whatever -- as inadequate approximations to infinity
unless or until somebody can provide a good explanation
of why that subdivision should be considered exhaustive.

John Sowa

```