For example, would an AI be able to own property, evict tenants, acquire debt, employ, vote, or marry? What are the legal structures in place to implement a strong AI into society?
Yes, to some of what you propose. No to some.
Today corporations are granted rights: to own property, earn income, pay taxes, contribute to political campaigns, offer opinion in public, ad more. Even now I see no reason why an AI should not be eligible to incorporate itself, thereby inheriting all these rights. Conversely, any corporation already in existence could become fully automated at any time (and some plausibly will). In doing so, they should not lose any of the rights and duties they currently employ.
However I suspect certain rights would be unavailable to an AI just as they are unavailable to a corporation now: marriage, draft or voluntary service in the military, rights due a parent or child or spouse, estate inheritance, etc.
Could this schizoid sense of human identity be resolved at some point? Sure. Already there have been numerous laws introduced and some passed elevating various nonhuman species to higher levels of civil rights that only humans heretofore enjoyed: chimpanzees, cetaceans, parrots and others have been identified as 'higher functioning' and longer lived, and so, are now protected from abuse in ways that food animals, pets, and lab animals are not.
Once AI 'beings' arise that operate for years and express intelligence and emotions that approach human-level and lifetime, I would expect a political will to arise to define, establish, and defend their civil rights. And as humans become more cybernetically augmented, especially cognitively, the line that separates us from creatures of pure silicon will begin to blur. In time it will become unconscionable to overlook the rights of beings simply because they contain 'too little flesh'.
Murray Shanahan, in his book The Technological Singularity, makes the case that the rights of any being are determined by its intelligence.
For instance, we value the life of a dog above that of an ant and likewise value human life above that of other animals.
From here one could argue that a general artificial intelligence of equal intelligence to a human should have equal rights to a human and a superior artificial intelligence should have more rights.
The question, of course, is whether our anthropocentric society would be willing to accept this fundamental shift in human rights and this idea of removing humanity from its pedestal of importance.
When it comes to legal frameworks, we really are entering into uncharted territory as AI is going to have to revolutionise the way we define many of the terms we take for granted today and question many of our usual assumptions.
AI is going to drive an important shift in our mindset well before it exceeds human intelligence.
No matter what rights it gets (as a company), it will still lack the right of not getting liquefied and all its properties transferred back to natural persons.
This is of course if no laws are changed.
To change the laws you will need to convince people that this machine is more "life" worthy than intelligent animals, and hope that people will deal with them better than they did with dolphins and chimps.
As I see it, machines can easily get the same or better rights then companies, but will always be under the mercy of the less intelligent man. (that is if things went peacefully :) )
Not only wouldn't a strong AI which came into existence today have the rights a human has, or any rights (see these discussions of the implementation of regulation for weak AIs at: The White House and The American Bar Association), but it seems unlikely the first one will.
Having rights implies that there are restrictions, which means there would have to be a system of control. However the control problem in AI is still unsolved.
Even assuming that problem is solvable, an AGI would then have to appear equivalent to natural humans. They don't yet (see Turing Test Passed?), and even after passing equivalence tests, are unlikely to remain that way, per the Singularity Hypothesis.
Further, if one or more AGIs were to be human-equivalent long enough to desire rights, lawmakers (in the US) would have to re-interpret the definition of personhood and grant them rights, as they did for corporations in 1886.
A sufficiently clever AGI, if self-interested, would pre-empt or co-opt existing legal structures, to seize whatever juridical rights it desired, as the opportunity arose. Thus it would render my opinions on the subject entirely moot.
Another way of putting this point: While current legal frameworks would not provide any rights to an artificial agent, current legal frameworks foreseeably will no longer be current, once an AI exists having attributes which imply the transformative change of those frameworks.
There is a legal difference between a "person" (which includes bodies corporate - corporations, incorporated associations, etc - and actual people) vs "natural person" (which is specifically a human being).
For an AI to marry, it would need to get the legal definition of "natural person" changed, and depending on the jurisdiction possibly also the definition of "man" or "woman".
For other things, such as owning property, evicting tenants, entering into contracts, etc, an AI would simply use a corporation. It may be that the corporation might need to have a minimum number of directors who are natural persons, but they could just be paid professionals, so no issue there.
With credit cards, it would depend on the policy of the issuing bank. There is no legal impediment to corporations having credit cards in their own right, but in practice banks often require a director's guarantee from a natural person that they can sue if the bill is not paid. They want to be sure they will get their money, even if the corporation is wound up.