Why the war on Hezbollah is justified

Israel's war was triggered by a raid into Israel by Hezbollah fighters killing 8 and kidnapping 2 Israeli soldiers. The justification for the war requires some history:

From the 1970's Israel's northern towns (like now) were intermittently attacked by terrorist forces from Lebanese territory. Israel counterattacked and had forces in southern Lebanon until May 2000 when Israel retreated to the international border (as acknowledged by the UN). Since then the Hezbollah or Lebanon have no legitimate claim that Israel is occupying their territory.

However during the 6 years since Israel's complete withdrawal, the Hezbollah (by their own admission and international estimates) have accumulated, with Syria and Iran's help, an incredible arsenal of over 12,000 rockets in southern Lebanon in defiance of UN Resolution 1559 http://www.mideastweb.org/1559.htm

In the past 3 weeks the Hezbollah has fired over 1600 of these rockets against Israel.

The Hezbollah organisation does not recognise the legitimicacy of the State of Israel - see
http://en.wikipedia.org/wiki/Hezbollah#Ideology
http://www.cfr.org/publication/9155/ and
http://www.globalsecurity.org/military/world/para/hizballah.htm

Israel is completely justified in defending its sovereignty against a ruthless terrorist organisation that is armed to the teeth and has repeatedly denied Israel's right to exist.