Clauses typically consist of at least one predicate - usually a verb, but sometimes an adjective or even a noun - and all of its dependents. Dependents that have to appear in a clause in order to express a complete thought are known as arguments. The argument-taking property of a predicate constitutes its argument structure. This property is inherently semantic since it provides information on how many and what semantic type of arguments a predicate takes. Argument structure, however, also relates to syntax and morphology because it contains information on how a given argument will be expressed in the clause (as a subject, object, etc.) and which morphology it will bear (e.g. nominative vs. accusative case). For instance, the verb bake in the sentence below takes two arguments, woman and sweet cake.
woman sweet cake bake
‘The woman baked a sweet cake.’
woman receives the thematic role agent and is expressed syntactically as the subject of the clause. sweet cake receives the theme role (it changes as a result of the verbal activity, more specifically, it comes into being) and is expressed as the syntactic object of the clause. Both arguments must be understood at least implicitly to form a complete thought, although the object in this case does not need to be expressed in the sentence. Still, even in the sentence woman bake we understand that the woman bakes something, which is due to the fact that bake has two semantic arguments and the second one bears a theme role. Compare this with yesterday in the sentence below. The time adverb is both semantically and syntactically optional and is therefore not an argument of the predicate but an adjunct.
yesterday woman sweet cake bake
‘Yesterday, the woman baked a sweet cake.’