Vitninu ber að útskýra orsökina og afleiðinguna.

Ber að is a common Icelandic expression meaning something like is obliged to, must, or is required to.

It comes from the verb bera, which often means to carry or to bear, but in this construction it has a more abstract meaning: it is incumbent on someone to do something.

So:

• e-m ber að gera e-ð = someone is obliged to do something

This expression is especially common in formal, legal, or official language.

Because this construction takes the person involved in the dative case, not the nominative.

• vitnið = the witness in the nominative
• vitninu = the witness in the dative

With bera að, Icelandic uses:

• e-m ber að ...

where e-m means to someone / on someone in the dative.

So Vitninu ber að ... literally works like It falls to the witness to ... or The witness is required to ...

Yes, ber is the present tense form of bera.

But verbs often develop idiomatic meanings in certain constructions. Here, bera is not being used literally. In e-m ber að + infinitive, it means something like:

• it is incumbent on
• it is required of
• one must

So even though bera often means carry/bear, that is not the meaning you should hear in this sentence.

Here að is the infinitive marker, like English to in to explain.

So:

• útskýra = explain
• að útskýra = to explain

It is not a preposition here. It simply introduces the infinitive after ber in this construction.

They are both direct objects of útskýra, so they are in the accusative case.

The verb útskýra takes an accusative object:

• útskýra eitthvað = to explain something

So:

• orsökina = accusative singular definite of orsök
• afleiðinguna = accusative singular definite of afleiðing

Both mean the ... because Icelandic usually attaches the definite article to the end of the noun.

Because Icelandic nouns belong to different declension patterns.

Both orsök and afleiðing are feminine nouns, but they do not form all cases in exactly the same way. The definite accusative singular endings reflect the noun’s declension class and stem shape.

So the difference is not because one is definite and the other is not; they are both definite. It is just normal noun inflection:

• orsök → orsökina
• afleiðing → afleiðinguna

This is something learners usually have to get used to noun by noun.

Because Icelandic main clauses normally follow the V2 rule: the finite verb tends to come in the second position.

Here the first element is Vitninu, so the finite verb ber comes next:

• Vitninu | ber | að útskýra orsökina og afleiðinguna

This is normal Icelandic word order.

If you changed the order, the meaning or sentence type might change. For example, Ber vitninu ...? would sound like the start of a question.

They are definite because the sentence is talking about a specific cause and a specific effect already understood from the context.

Icelandic uses a suffixed article:

• orsök = cause
• orsökin / orsökina = the cause
• afleiðing = effect/consequence
• afleiðingin / afleiðinguna = the effect/consequence

If the sentence were speaking more generally or indefinitely, the article might be omitted.

Yes. e-m ber að + infinitive sounds fairly formal, official, or legal.

A more everyday way might be:

• Vitnið á að útskýra ...
• Vitnið þarf að útskýra ...

These are more common in ordinary speech, though they are not exactly identical in tone:

• á að = is supposed to / should
• þarf að = needs to / has to
• ber að = is required to / is obliged to

Also notice that with á að or þarf að, you would normally use the nominative:

• Vitnið á að ... not
• Vitninu á að ...

To negate it, put ekki after the finite verb:

• Vitninu ber ekki að útskýra orsökina og afleiðinguna.

To put it in the past, use bar, the past tense of bera in this construction:

• Vitninu bar að útskýra orsökina og afleiðinguna.

So:

• ber = present
• bar = past

The dative vitninu stays the same because the construction itself still requires dative.