In linguistics, verb valency or valence refers to the number of arguments controlled by a verbal predicate. It is related, though not identical, to verb transitivity, which counts only object arguments of the verbal predicate. Verb valency, on the other hand, includes all arguments, including the subject of the verb. The linguistic meaning of valence derives from the definition of valency in chemistry. This scientific metaphor is due to Lucien Tesnière, who developed verb valency into a major component of his (what would later become known as) dependency grammar theory of syntax and grammar. The notion of valency first appeared as a comprehensive concept in Tesnière's posthumously published book (1959) Éléments de syntaxe structurale (Elements of structural syntax).
Types of valency 
There are several types of valency: impersonal (=avalent), intransitive (=monovalent), transitive (=divalent) and ditransitive (=trivalent):
- an impersonal 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 - it has no concrete referent. No other subject can replace it. In many other languages, there would be no subject at all. In Spanish, for example, it is raining could be expressed as simply llueve.)
- an intransitive verb takes one argument, e.g. He1 sleeps.
- a transitive verb takes two, e.g. He1 kicked the ball2.
- a ditransitive verb takes three, e.g. He1 gave her2 a flower3.
- There are a few verbs that take four arguments. Sometimes bet is considered to have four arguments in English, as in the examples I1 bet him2 five quid3 on ”The Daily Arabian”4 and I1 bet you2 two dollars3 it will rain4.
The term valence also refers to the syntactic category of these elements. Verbs show considerable variety in this respect. In the examples above, the arguments are noun phrases (NPs). But arguments can in many cases be other categories, e.g.
- Winning the prize made our training worthwhile. - Subject is a non-finite verb phrase
- That he came late did not surprise us. - Subject is a clause
- Sam persuaded us to contribute to the cause. - Object is a non-finite verb phrase
- The president mentioned that she would veto this bill. - Object is a clause
Many of these patterns can appear in a form rather different from the ones just shown above. For example, they can also be expressed using the passive voice:
- Our training was made worthwhile (by winning the prize).
- We were not surprised (by the fact that he came late).
- We were persuaded to contribute (by Sam).
- That she would veto this bill was mentioned (by the president).
The above examples show some of the most common valence patterns in English, but do not begin to exhaust them. Other linguists have examined the patterns of more than three thousand verbs and place them in one or more of several dozen groups.
The verb requires all of its 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. In the southeastern United States, an emphatic trivalent form of eat is in use, as in I'll eat myself some supper. Verbs that are usually monovalent, like 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.
Valency vs. subcategorization 
Tesnière 1959 expresses the idea of valence as follows (translation from French):
- "One can therefore compare the verb to a sort of atom with hooks, susceptible to exercising attraction on a greater or lesser number of actants. For these actants, the verb has a greater or lesser number of hooks that maintain the actants as dependents. The number of hooks that a verb has constitutes what we will call the valence of the verb."
Tesnière used the word actants to mean what are now widely called arguments (and sometimes complements). An important aspect of Tesnière's understanding of valency was that the subject is an actant (=argument, complement) of the verb in the same manner that the object is. The concept of subcategorization, which is related to valency but associated more with phrase structure grammars than with the dependency grammar that Tesnière developed, did not originally view the subject as part of the subcategorization frame, although the more modern understanding of subcategorization seems to be almost synonymous with valency.
Valency in syntactic theory 
Valence plays an important role in a number of the syntactic frameworks that have been developed in the last few decades. In Generalized Phrase Structure Grammar (GPSG), many of the phrase structure rules generate the class of verbs with a particular valence. For example, the following rule generates the class of transitive verbs:
- VP → H NP [love]
H stands for the head of the VP, that is the part which shares the same category as the VP, in this case, the verb. Some linguists objected that there would be one such rule for every valence pattern. Such a list would miss the fact that all such rules have certain properties in common. Work in Government and Binding (GB) takes the approach of generating all such structures with a single schema, called the X-bar schema:
- X' → X, Y’’…
X and Y can stand for a number of different lexical categories, and each instance of the symbol ’ stands for a bar. So A’, for instance, would be a kind of AP (adjective phrase). Two bars, used here for the complements, is thought by some linguists to be a maximal projection of a lexical category. Such a schema is meant to be combined with specific lexical rules and the projection principle to distinguish the various patterns of specific verbs.
Head-Driven Phrase Structure Grammar (HPSG) introduces a handful of such schemata which aim to subsume all such valence related rules as well as other rules not related to valence. A network is developed for information related to specific lexical items. The network and one of the schemata aims to subsume the large number of specific rules defining the valence of particular lexical items.
Notice that the rule (VP → H NP [love]) and the schema (X’ → X, Y’’…) deal only with non-subject complements. This is because all of the above syntactic frameworks use a totally separate rule (or schema) to introduce the subject. This is a major difference between them and Tesnière's original understanding of valency, which included the subject, as mentioned above.
One of the most widely known versions of Construction Grammar (CxG) also treats the subject like other complements, but this may be because the emphasis is more on semantic roles and compatibility with work in cognitive science than on syntax.
See also 
- For a discussion of valency from the traditional perspective of dependency grammar, see Fischer and Ágel (2010).
- Concerning the valency patterns, see Levin (1993).
- The quotation is from Tesnière (1959/69:238).
- Tesnière (1959/69:109) emphasizes that the subject is a complement just like the object in chapter 51, paragraph 109.
- Concerning an early and prominent account of subcategorization, see Chomsky (1965).
- Concerning GPSG, see Gazdar et al. (1985).
- The classical work in GB is Chomsky (1981).
- A classic work establishing the X-bar schema is Jackendoff (1977).
- The classic work of HPSG is Pollard and Sag (1994).
- A seminal work for the development of CxG is Goldberg (1995).
- Chomsky, N. 1965. Aspects of the theory of syntax. Cambridge, MA: MIT Press.
- Chomsky, N. 1981. Lectures on Government and Binding. Dordrecht: Foris.
- Fischer, K. and V. Ágel. 2010. Dependency grammar and valency theory. In: The Oxford handbook of linguistic analysis, 223-255. Oxford: Oxford University Press.
- Gazdar, G., E. Klein, G. Pullum, and I. Sag. 1984. Generalized Phrase Structure Grammar. Oxford: Basil Blackwell.
- Goldberg, A.. 1995. A Construction Grammar approach to argument structure. Chicago: University of Chicago Press.
- Jackendoff, R. 1977. X-bar syntax: A study of phrase structure. Cambridge, MA: MIT Press.
- Levin, B. 1993. English verb classes and alternations: A preliminary investigation. Chicago: University of Chicago Press.
- Pollard, C. and I. Sag. 1994. Head-Driven Phrase Structure Grammar. Chicago: University of Chicago Press.
- Tesnière, L. 1959. Éleménts de syntaxe structurale. Paris: Klincksieck.
- Tesnière, L. 1969. Éleménts de syntaxe structurale, 2nd edition. Paris: Klincksieck.