Can one actually kill a machine? Not only do we have problems in defining life, we also have problems in defining death. Will this also be true in artificial life and artificial intelligence?
Death as we know it for natural life is terminal. That is once dead, natural life cannot come back (at least in the current understanding and with current technologies---some people believe otherwise).
Death for AI is trickier. There may be only one scenario: Global destruction: Extreme scenario where everything supporting the existence of an AI disappears. This is equivalent to death in natural life, and low probability. It means all AIs die at once (as well as us).
We also do not know the degree and form of embodiment necessary for AGIs. We can assume now that hardware is replaceable indefinitely, thus "limiting" death to the above extreme scenario. But AGIs "body" may not be indefinitely replaceable. Then a definition closer to natural life death may be necessary.
We see arguments for two other scenarios, that I refute below:
"Static Death": An AI is still "defined" or "saved" somewhere (whatever it means actually), but it is not authorized or able to use resources. Assuming an AI is made of hardware and software, it is like a program stored on a disk, but without permission to run.
"Dynamic Death": Under the same characterization of AI as hardware and software, dynamic death is the invalidation of progress akin to strong liveness properties, where an AI is trapped in an infinite loop (or a void loop), in a form of "active death", as what happens to Sisyphus in Greek mythology. This is different from static death, as the AI still uses dynamic resources, although it cannot make progress. Continuing under the same assumptions, such AI could be "loaded" in main memory, or locked waiting for inputs or outputs to complete.
Note that in these two scenarios, rebirth is possible, and they also subsume that there is an entity that can decide conditions for rebirth, or preventing it completely. Would this entity be an "admin", a god, other AIs, or a human is another question, really.
The terms "death" and "rebirth" here could just be changed for "imprisoning", where the dynamic version would be like our human prisons, and the static version would be like SciFi cryogeny. This is a bit of a stretch, but we can see an equivalence, and no good reason to qualify these two scenarios as deaths.
In conclusion, death for AI seems to be an exceptional, singular scenario, so AI cannot die in practice, except if we are wrong on how we think we can make AGIs. AI can however be imprisoned forever.
Note: The terminology above is completely made-up for the post. I do not have citations to back some claims, but it is based on readings and personal work (including in software verification).
If AI arises from a replicable manufacturing process (e.g. as with modern computers), then it will presumably be possible to take a snapshot of the state of an AI and replicate it without error on some other mechanism.
For such a construct, 'death' doesn't mean the same as it currently does for us fleshy organics: multiple clones of an AI could presumably be instantiated at any time.
Hence, the analog of death that is needed is something closer to 'thermodynamic heat death', in which the AI does no further 'useful work'.
Using the standard percept/action characterization of AIs, then (as indicated in a comment below the question) this AI SE question gives such a definition of death for an AI: i.e. when it enters into a state from which it receives no further percepts and takes no actions.
EDIT: Note that this conception of death is a more terminal notion for an AI than 'not currently running'. In principle, one could say that a program is 'alive' even though only one instruction was executed every 10,000 years. For a fascinating discussion on this, see Hofstadter's "A Conversation with Einstein's Brain".
"Death" exists as a single concept because the underlying reality that it's describing is closely clumped together, and our definition has changed with our ability to change that reality.
It seems more reasonable that the various sorts of things that could be considered 'death' will be split apart, and a different word will be used to refer to a system with no copies currently running, vs. a system that has no stored version but could be recreated (because the code and random seed to generate it are still around), vs. a system that has been totally lost. (And I'm probably missing some possibilities!)
I don't think the term "death" will mean anything to an AI. The reason I say that is this: with an AI, running (presumably) on digital hardware, we can simply snapshot it's state from memory at any time. And then at any arbitrary time in the future we can recreate it as it was with perfect fidelity.
So even if you terminate a program intending it to be "dead", you never know if someone will come along later and bring it up again. And perhaps more to the point, you might not know if another copy exists elsewhere.
I hate to use sci-fi references, but this one is apt: remember how in The Matrix trilogy programs would seek exile in The Matrix to avoid deletion? Maybe the same thing will happen with our AI's... they will copy themselves to other places and try to hide, to avoid being deleted. So if the program is clever enough, it might be able to evade any attempt to terminate it anyway.
The other answers seem to deal with "final death"...that is, a "terminal end" state where an AI cannot recover from. In other words, the AI is unable to function any further.
But that's not how I'd define death. I'd define death as a process being terminated. It doesn't matter if someone restarts the same process, because the existing process is already dead. The AI may have just made a new copy of itself, but it's just a copy, not the original. Death is just death.
We can call this type of "death" a "temporary death"...where the physical body dies but there is some "psychological continuity" (such as the source code that is used to run a program) that continues between the different bodies.
This type of "temporary death" has been explored in science fiction. PARANOIA and Eclipse Phase features humans who can quite frequently die, only to later be restored through a "memory backup". The humans may be functionally immortal...but the original is still dead, no matter what fates the other copies encounter. CGP Grey also made a video about Star Trek teleporters, which works by killing you and then spawning another copy of yourself in another area. Actually, fantasy settings also explores the idea of "temporary death" as well, where people can die only to later get revived by a magical spell.
My recommendation is to play through the philosophical game Staying Alive, which teaches three different philosophical approaches to life (and when that life terminates):
There are basically three kinds of things that could be required for the continued existence of your self. One is bodily continuity, which may actually require only that parts of the body stay in existence (i.e., the brain). Another is psychological continuity, which requires the continuance of your consciousness - by which is meant your thoughts, ideas, memories, plans, beliefs, and so on. The third possibility is the continued existence of some kind of immaterial part of you, which might be called the soul*. Of course, it may be the case that a combination of one or more types of these continuity is required for you to survive.
The other answers assumes that life is based on "psychological continuity", and looks at what might disrupt this "continuity". I assume that life is based on "bodily continuity", which is much easier to disrupt - just kill the process...it doesn't matter if a new process respawns...because the original process is still dead. By playing through "Staying Alive", you will be able to work out your own personal definition of life and death. Once you have your own personal definition, then simply apply it to this specific case, either siding with "psychological continuity" (the other answers) or "bodily continuity" (my own opinion).
*If you assume that life requires a soul, well, it is not clear that AI would have souls. If they don't (and this seems the most reasonable assumption here), then they obviously wouldn't be alive (and you cannot die if you are not alive). If they do have souls though, then the other answers which assume "psychological continuity" may still be applicable, as it seems that the existence of a "soul" is dependent on "psychological continuity".
The distinction between algorithms/robots and humans is that, when the human organism stops functioning, the human is considered dead.
By contrast, an algorithm still exists, even when not running. (I was going to use "even when not being executed", but avoided this for semantic reasons;) The algorithm can remain in this "stasis state" so long as there is a storage medium for the information.
- Killing an algorithm is easy--delete and empty the trash bin.
Essentially, to kill an algorithm, you need to erase the code that comprises it.
There is no reason to treat hard AI different then humans. Some people telling that you can make a snapshot of AI but there is no reason to not make a human snapshot also. We dont have technology for that but there is no any magical barrier that would make it impossible (save all biological data and then print your copy somewhere else. Why not?).
Its to early to talk about this as we do not understand our existence (Death term for biological creatures evolving all the time).
I bet that in the future we will merge with AI and the only question will be what death means for any intelligent existence.