kneecap soreness

Practice taekwando often about twice a week, stretch half an hour before and after exercise
my job requires me to sit in front of computer for extended period of time per day, and my main source of entertainment is also my computer.
me knee has this soreness when I about to stand up from sitting, standing up from kneeling down, or going downstairs, this usually happens the first time I do these movements, but as I do them in more repetitions the soreness becomes less apparent.

is this a sign of arthritis?

Not necessarily. Pain after moving prolonged positions which eases on moving around is a typical arthritic pattern but there could be a no. of reasons for your symptoms...could be something to do with your patella tendon(the tendon that passes across the front of your knee from your thigh)/quads or kneecap. Have you had any previous injuries? Do you get your symptoms at any other times e.g. getting out of bed / first thing in the morning? Seems unlikely it's arthritis.

Sounds very patello-femoral pain like, I suspect the kneecap bone's not running smoothly over the bone below it. Have you had any period of bedrest before its onset, even for a few days (I'm thinking maybe Quads wasting...) or a previous injury (+/- swelling) to the general area, do the muscles on both thighs look alike?

it seems to have patello femoral dysfunction because of weakness of quadriceps and that all because of your lifestyle. so start doing activities (outdoor) and strengthening of lower limb.

It sounds like a kneecap problem, known as Runners Knee (aka Anterior Knee Pain). It is common in active people, and also causes pain after prolonged inactivity ie sitting at the computer and going down stairs, and eases as you get going.
It is usually caused by muscle weakness and/or tightness, or can be due to anatomical features eg flat feet.
See Runners Knee for more info.
Hope that helps