de Morgan's Duality Law


For every proposition involving logical addition and multiplication ("or" and "and"), there is a corresponding proposition in which the words "addition" and "multiplication" are interchanged.


Weisstein, Eric W. "de Morgan's Duality Law." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/deMorgansDualityLaw.html

Types of valency
There are several types of valency:

an avalent verb takes no arguments, e.g. It rains. (Though it is technically the subject of the verb in English, it is only a dummy subject, that is a syntactic placeholder with no true meaning. No other subject can replace it.)
an monovalent verb takes one argument, e.g. He sleeps.
a divalent verb takes two, e.g. He kicks the ball.
a trivalent verb takes three, e.g. He gives her a flower.
a tetravalent verb takes four. They are uncommon, perhaps non-existent in English. Maybe for example: He sold you a shirt for 9 bucks.
The verb requires all of these arguments in a well-formed sentence, although they can sometimes undergo valency reduction or expansion.

For instance, to eat is naturally divalent, as in he eats an apple, but may be reduced to monovalency in he eats. This is called valency reduction.

Verbs that are usually monovalent, like to sleep, cannot take a direct object. However, there are cases where the valency of such verbs can be expanded, for instance in He sleeps the sleep of death. This is called valency expansion.

Verb valence can also be described in terms of syntactic versus semantic criteria. The syntactic valency of a verb refers to the number of dependent arguments that the verb can have, while semantic valence describes the thematic relations associated with a verb.