# Number sense

The Xapagy agent has a simple number sense which allows the representation of four classes of numbers: none, one, pair and many. In the following we will describe the semantics and representation of these concepts.

None: represents the absence of instances of a certain kind of objects in a certain context. For instance, we might say that there are no pencils in a box. This is represented through an |inexistent| instance as seen in the previous example.

```A box / exists.
The box / contains / an inexistent pencil.```

One: represents the existence of exactly one instance of a certain kind in a certain situation. For instance, we might say that there is one pencil in the box. This is represented as an instance directly mapping to the object.

```A box / exists.
The box / contains / a pencil.```

Pair: represents the existence of exactly two instances in a certain situation. This is represented through a group instance, which also has the |pair| attribute, with the two instances being members of the group.

```A box / exists.
The box / contains / a pair pencil.
A pencil red / becomes-right-of / pair.
A pencil blue / becomes-left-of / pair.```

Many: represents a large number of instances in a certain situation. This is represented through the a group instance which also has the |many| attribute. The semantics of the many groups is that they are not enumerated – it is generally assumed that not all the members are individually

```A box / exists.
The box / contains / a many pencil.
The many pencil / contains / a red pencil.```