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á, í, undir, yfir

The four prepositions á, í, undir and yfir share a common set of rules about when they govern the accusative or dative:

  • 🏃‍♂️ If there is movement or a change of state, they govern the accusative;
  • 🛑 If there is no movement or change of state, they govern the dative.

á and í​

The basic meaning of á and í is “on” and “in” respectively:

Bókin liggur á borðinu.
Það eru íspinnar í frystinum.

They are also used to talk about being “at” a place:

Hittumst á kaffihúsinu.
Fimm kennarar vinna í skólanum.

The use of á and í to mean “at” is highly idiomatic. It’s almost impossible to draw up a list of rules for when to use which preposition – there is not any particular logic. See here for a searchable list of the most common places and Icelandic placenames and their preposition.

In all of the examples above, there is no motion or change of state. Therefore, the dative case is used.

Movement or change of state​

If used with a verb that implies some kind of motion to a place, then the complement (object) of á, í, undir or yfir will be in the accusative:

Sibba fer í skólann.
Settu bókina í hilluna.
Kennarinn varpaði kvikmyndinni á vegginn.
Á ég að millifæra peningana á þig?

This use of the accusative is in lieu of using a preposition that means “to”, such as að or til. Til is only used for large towns or cities, countries or people. Every other kind of place uses á or í + accusative.

By extension, when á or í is used with a verb that involves a change into a state, the accusative is also used:

Um nótt breytist Skallagrímur í varúlf.
Höfundurinn þýddi bókina á lélega íslensku.
Hann fór úr því að vera rólegur í það að vera brjálaður.

undir and yfir​

The rules above about motion or lack of motion also apply to undir “under” and yfir “over”. Compare these two sets of sentences:

1️⃣
Flugvélin flaug yfir Ísland.
Kisan skríður undir borðið.

2️⃣
Flugvélin flaug yfir Íslandi.
Kisan skríður undir borðinu.

  • 1️⃣ Accusative – The plane flew over Iceland and passed it by. The cat crawled under the table from somewhere else.
  • 2️⃣ Dative – The plane flew above Iceland, but didn’t leave its airspace. The cat crawled around underneath the table, but didn’t leave its confines.