If you sleep during the day, do you need less sleep at night? If, say, you sleep 2-3 hours during the day (in the afternoon) - Do you need less sleep at night?

After all, subjects feel less tired in the evening after sleeping during day.

Can sleep hours be accumulated in a linear fashion? For example: Will sleeping 3 hours during the day justify sleeping just 4-5 hours during the night?
Short answer: Yes, if you sleep 2--3 hours during the day, you generally need less sleep at night.

Important considerations: However, the short answer is not the full story. In particular, in answer to your question about whether or not sleep hours can be accumulated in a linear fashion, the answer is strictly no, but approximately yes. 

To understand the problem with assuming linearity of sleep, consider the extreme example of "sleeping" for one minute, and then being awake the next, and keep doing this for the entire day. In theory, you would have spent 12 hours awake, and 12 hours asleep. But of course, you'll feel exhausted, and would be in desperate need of some good sleep.

What's important to keep in mind, is the different stages of sleep. See http://www.helpguide.org/articles/sleep/how-much-sleep-do-you-need.htm for a good overview.

The Stages of Sleep:


  Non-REM sleep
  
  Stage N1 (Transition to sleep) – This stage lasts about five minutes.
  Your eyes move slowly under the eyelids, muscle activity slows down,
  and you are easily awakened.
  
  Stage N2 (Light sleep) – This is the first stage of true sleep,
  lasting from 10 to 25 minutes. Your eye movement stops, heart rate
  slows, and body temperature decreases.
  
  Stage N3 (Deep sleep) – You’re difficult to awaken, and if you are
  awakened, you do not adjust immediately and often feel groggy and
  disoriented for several minutes. In this deepest stage of sleep, your
  brain waves are extremely slow. Blood flow is directed away from your
  brain and towards your muscles, restoring physical energy.
  
  REM sleep
  
  REM sleep (Dream sleep) – About 70 to 90 minutes after falling asleep,
  you enter REM sleep, where dreaming occurs. Your eyes move rapidly,
  your breathing shallows, and your heart rate and blood pressure
  increase. Also during this stage, your arm and leg muscles are
  paralyzed.


In Conclusion: Sleep hours can be thought of as accumulating linearly in blocks of sleep cycles. That is, as long as you hit the right sleep stages during your nap, it counts! Generally, a complete sleep cycle lasts about 90 minutes, so sleep in multiples of 90 minutes would be ideal...