Valency is closely related, though not identical, to transitivity. Transitivity refers to the number of core arguments of the verb that are not optional (giving intransitive verbs, transitive verbs, and * Newlyn lies. (valency of lie = 1, intransitive)

• John kicks the ball. (valency of kick = 2, transitive)
• John gives Mary a flower. (valency of give = 3, ditransitive)

The concept of valency is however undermined by the fact that non-optional or core meanings are hard to pin down. For example:

• Ask, and God will give.
• John kicks Mary the ball.
• The horse kicks.

And it becomes rather difficult to define what is non-optional. Modern trends such as cognitive grammars take the view that optionality is a gradation, i.e. different arguments have different degrees of co-occurrence, and this makes valency a moot issue.