4.3 Valence


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.


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".

n-adic, monadic, dyadic, triadic

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:

  1. monadic is a synonym for 1-adic,
  2. dyadic is a synonym for 2-adic,
  3. triadic is a synonym for 3-adic.

Examples of the first three valences

Examples of monadic relations

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

   (Past)->[Situation: [Bird]<-(Agnt)<-[Sing] ]
   "In the past, there was this situation: A bird was singing."

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

Examples of dyadic relations

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]
                 <-2-[Person: Brad]
   "Julia is between Tom and Brad"
   Example of a triadic relation.

Note the special multi-line notation. We will discuss this in detail later.


To summarize: the valence of a relation is determined by the relation type, is always constant, and signifies the number of arcs that belong to the relation.

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Next: 4.4 Signature