# 4.3 Valence

## Definition

The valence n of a relation is the number of arcs that belong to it. For any relation type t, the valence n is always constant. That is, the number of arcs that belong to a relation is always the same.

## Example

For example, the number of arcs that belong to the relation "Dest" (destination) is always two, and the number of arcs that belong to the relation "Agnt" (agent) is also always two. This is because the valence of "Dest" is 2, and the valence of "Agnt" is also 2:

```   [Person: John]<-(Agnt)<-[Go]->(Dest)->[City: Aalborg]
```

This conceptual graph can be paraphrased as:

"A Person, John, is the agent of 'Go', and the destination of Go is a City, which is Aalborg".

In better English:

"John is going to Aalborg".

A relation with valence n is said to be n-adic. For example, a relation with valence 5 is said to be 5-adic. The first three valences have special names:

## Examples of the first three valences

Examples of monadic expressions include "Past" (past tense) and "Psbl" (possibility):

```   (Past)->[Situation: [Bird]<-(Agnt)<-[Sing] ]
```

```   (Psbl)->[Situation: [Bird]<-(Agnt)<-[Sing] ]
"It is possible that a bird is singing."
```

We have already seen numerous example of dyadic relations. For example, "Agnt" (agent), "Dest" (destination), and "On".

### Example of a triadic relation

An example of a triadic relation could be "Betw" or 'between'.

```   [Person: Julia]<-(Betw)-
<-1-[Person: Tom]
"Julia is between Tom and Brad"