some linguistics terminology

In linguistic, an argument is an expression that helps complete the meaning of a predicate, the latter referring in the context to a main verb and its auxiliaries. In this regard, the complement is a closely related concept. Most predicate take one, two or three arguments. A predicate and its arguments from a predicate-argument structure. The discussion of predicates and arguments is associated most with (content) verb and noun phrases (NPs), although other syntactic categories can also be construed as predicates and as arguments.

In linguistics, an adjunct is an optional, or structurally dispensable, part of a sentence, clause, or phrase that, if removed or discarded, will not otherwise affect the remainder of the sentence. Example: In the sentence John helped Bill in Central Park, the phrase in Central Park is an adjunct.

Arguments must be distinguished from adjuncts. Most theories of syntax and semantics acknowledge arguments and adjuncts, although the terminology varies, and the distinction is generally believed to exist in all languages.
The basic analysis of the syntax and semantics of clauses relies heavily on the distinction between arguments and adjuncts.The clause predicate, which is often a content verb, demands certain arguments. That is, the arguments are necessary in order to complete the meaning of the verb. The adjuncts that appear, in contrast, are not necessary in this sense. The subject phrase and object phrase are the two most frequently occurring arguments of verbal predicates.

For instance:
Jill likes Jack.
Sam fried the meat.
The old man helped the young man.
Each of these sentences contains two arguments (in bold), the first noun (phrase) being the subject argument, and the second the object argument.

When additional information is added to our three example sentences, one is dealing with adjuncts, e.g.
Jill really likes Jack.
Jill likes Jack most of the time.
Jill likes Jack when the sun shines.
Jill likes Jack because he’s friendly.

The added phrases (in bold) are adjuncts; they provide additional information that is not necessary to complete the meaning of the predicate likes. One key difference between arguments and adjuncts is that the appearance of a given argument is often obligatory, whereas adjuncts appear optionally. While typical verb arguments are subject or object nouns or noun phrases as in the examples above, they can also be prepositional phrases (PPs) (or even other categories). The PPs in bold in the following sentences are arguments:
Sam put the pen on the chair.
Larry does not put up with that.
Bill is getting on my case.

We know that these PPs are (or contain) arguments because when we attempt to omit them, the result is unacceptable:
Sam put the pen.
Larry does not put up.
*Bill is getting.

The area of grammar that explores the nature of predicates, their arguments, and adjuncts is called valency theory. Predicate have a valence; they determine the number and type of argument that can or must appear in their environment. The valence of predicates is also investigated in term of subcategorization.
In linguistics, verb valency or valence is 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.