Jeg må aflyse tiden.

Here må is the present tense of the modal verb at måtte.

In this sentence, må expresses necessity:

• I have to...
• I must...

So it is not mainly about permission here. Danish må can mean either:

• may / be allowed to
• must / have to

The context tells you which meaning is intended.

Both can sometimes be translated as must or have to, but they often feel slightly different.

• Jeg må aflyse tiden
  = I have to cancel the appointment
  This often suggests that circumstances make it necessary.

• Jeg skal aflyse tiden
  = I’m supposed to cancel the appointment / I’m going to cancel the appointment
  This can sound more like a plan, duty, or instruction.

So må often has a feeling of necessity, while skal often has a feeling of obligation, intention, or schedule.

Because må is a modal verb, and in Danish modal verbs are followed by the bare infinitive.

So you say:

• Jeg må aflyse tiden
• Jeg kan komme
• Jeg vil hjælpe

Not:

• Jeg må at aflyse tiden

This is similar to English:

• I must cancel
• not I must to cancel

Because tiden is the definite form of tid.

In Danish, definiteness is usually added to the end of the noun:

• en tid = an appointment / a time
• tiden = the appointment / the time

So tiden refers to a specific time or appointment, not just time in general.

Yes. In Danish, tid can mean ordinary time, but in the right context it can also mean an appointment or time slot.

This is especially common in situations like:

• doctors
• dentists
• hairdressers
• other booked appointments

So in a sentence like this, tiden is understood as the appointment rather than time in the abstract sense.

It is understandable, but many Danes would more naturally say:

• Jeg må aflyse min tid
• Jeg må aflyse aftalen

Why?

• min tid makes it clear that it is my appointment
• aftalen is often used for a more general appointment / arrangement / meeting

So Jeg må aflyse tiden is possible if the appointment is already clear from context, but Jeg må aflyse min tid often sounds more natural in everyday speech.

Because Danish usually puts the at the end of the noun as a suffix.

So instead of saying something like the time, Danish often does this:

• tid = time / appointment
• tiden = the time / the appointment

This is a very common feature of Danish nouns.

You put the verb first:

• Må jeg aflyse tiden?

This is normal Danish question word order for a yes/no question:

• statement: Jeg må aflyse tiden
• question: Må jeg aflyse tiden?

If må is interpreted as permission, that question means May I cancel the appointment?
If context makes it about necessity, it could also be understood differently, but permission is the more likely reading in question form.

No. Jeg må ikke aflyse tiden usually means:

• I must not cancel the appointment
• I am not allowed to cancel the appointment

That is a very important difference.

If you want to say I don’t have to cancel the appointment, Danish would more naturally use:

• Jeg behøver ikke at aflyse tiden
• Jeg behøver ikke aflyse tiden

So:

• må ikke = must not / may not
• behøver ikke = do not need to

The dictionary form is at aflyse, meaning to cancel.

You may see forms like:

• at aflyse = to cancel
• aflyser = cancels / am cancelling
• aflyste = cancelled
• har aflyst = have cancelled

In the sentence Jeg må aflyse tiden, the form aflyse stays in the infinitive because it follows the modal verb må.