By a strict logical interpretation, execution by death penalty is not murder. Dictionary definition of murder: "the _unlawful_ premeditated killing of one human being by another."

Violation of one's inalienable right to life (as written in the US declaration of independence, as well as the UN's universal declaration of human rights) is unlawful, regardless of any state legislation.

States can't legislate you out of your human rights.

One day the US federal courts will notice this error that they've made and fix the glitch.

As Churchill famously said, "You can always count on Americans to do the right thing - after they've tried everything else."

Someone who violates an innocent persons inalienable right to life, thereby forfeits their own right to life.

By that clown logic, any hostile forces can freely invade and conquer the United States, because it's universally illegal to kill human beings, including enemies.

No, it's not. Self defense is moral and justified. And some people are more dangerous alive than dead. Worse, some people develop a cult-of-personality and a following that they can even control or influence from jail. You telling me a mafia or gang leader or a former dictator guilty of genocide doesn't deserve the death penalty? Naive, to say the least. You know little of true evil, which does exist and no amount of corrective procedure will fix.

Someone held securely in prison does not pose an imminent threat to you, and thus an argument from self-defense is void.

The fact that you move on so deftly to the word "deserve" suggests that it's vengeance you seek.

An eye for an eye makes the whole world blind.

You are being disingenuous. A murderous psychopath is a danger to people. This is obvious and something that a five year old child can understand. Some people cross the line and forfeit their lives. The death penalty is absolutely justifiable unless you are a moral relativist, which is a logically inconsistent world view.

> Someone held securely in prison

I already mentioned the cult-of-personality example above and you breezed over it. Gang leaders are fully capable of executing kills from jail. They have influence that extends beyond the 4 walls they're contained to. Some of them have access to a vast array of money and dangerous people who they can delegate to. They can also actively influence or harm other prisoners in jail.

Treating true psychopaths with kid gloves won't make the world a better place.

If prisoners are able to lead criminal organizations whillst inside, that's very obviously a rather trivial-to-fix bug in the design of the jail, not a reason to murder someone for vengeance.

We have more than adequate technology to keep such hopeless cases from harming themselves or others.

It's not trivial to fix without introducing mechanisms that are worse than death, such as isolated confinement and other forms of torture.

I believe that this is a false dichotomy that you present; I can think of several different solutions to this problem in seconds, none of which are what you describe.

> Self defense is moral and justified.

To the extent that it is moral and justified, it does not extend to include intent to kill. To the extent intent to kill is present, it is not morally “self-defense”, though it may still be within the scope that law does not punish when the other moral elements of self-defense are present (which is, itself, right and proper despite allowing some immoral acts to go unpunished as criminal law should err on the side of nonpunishment and teasing out intent when the other elements of self-defense are present is more likely to result in the reverse error.)