# 4.5 Direction of arrows

## Definiton

There is a convention for the direction of the arrows that go to and from a conceptual relation. In fact, this convention is part of the definition of a conceptual relation. The convention is this: For a conceptual relation with n arcs, the first n-1 arcs point towards the relation, while the last, or n-th, arc points away.

## Determining the last arc

How do we know which is the last arc? In other words, how do we know which arc should point away from the relation while all the rest should point towards the relation?

The answer is simple: We know from the signature of the relation. For example, the signature for the "Agnt" relation is:

```   <Act,Animate>
```

Therefore, the arc that points away must be the one that points to the concept denoting the animate entity:

```   [Sing]->(Agnt)->[Bird]
```

Thus when we say "first arc", "second arc", "third arc", etc., we are referring to their position within the signature.

## Special cases: 1 and 2 arcs

It follows from the definition that in the special case where there is only one arc (a monadic relation), the arc must point away from the relation. In the case of two arcs, the first points towards the relation while the second points away. For example:

```   (Past)->[Situation: [Sing]->(Agnt)->[Bird] ]
"A bird sang"
```

Notice how for the monadic relation (Past), the arc points away, while for the dyadic relation (Agnt), the first points towards the relation while the other points away.

## Next

Relations may have more than two arcs (have valence greater than 2). The next section discusses notation for dealing with this.

Prev: 4.4 Signature
Up: 4 Relations
Next: 4.6 Notation for more than two arcs