Dear teachers,

Would you please tell me what is considered an obligatory adverbial?
Do you think that an adverbial that changes the meaning of a sentence if omitted is considered obligatory? Examples :

1) He saw the movie twice on Saturday.

2) Yesterday was the happiest day of the year for me.

3) The news about your illness reached me very late.

4) Will they be able to move the belongings by themselves?

Are "twice", "for me", "very late" and "by themselves" considered obligatory or not?

Thank you for your help and I wish you all a merry Christmas.
From good ol' Wikipedia:

Adverbials are typically divided into four classes:

adverbial complements (i.e. obligatory adverbial): adverbials that render a sentence ungrammatical and meaningless if removed. John put the flowers in a vase.

adjuncts: these are part of the core meaning of the sentence, but if omitted still leave a meaningful sentence.
John and Sophia helped me with my homework.

conjuncts: these link two sentences together.
John helped so I was, therefore, able to do my homework.

disjuncts: these make comments on the meaning of the rest of the sentence.
Surprisingly, he passed all of his exams.

According to that, none of your examples show obligatory adverbs; they are all adjuncts.
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How obligatory and optional adverbials can be indicated in a sentence

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patimo How can obligatory and optional adverbials can be indicated in a sentence?

They are not indicated in a sentence. "obligatory adverbial" is a grammatical term used to describe adverbials which must be present in a sentence in order to make a sentence correct. This information is not indicated in the sentence itself.

She put the flowers in a vase.

in a vase is an obligatory adverbial because She put the flowers is not a correct sentence, but there is nothing in the sentence that tells you that an expression like in a vase is obligatory. You know that only if you know English grammar, specifically how the verb put works.