Obtaining desired AI behavior

Looks like you're making distinctions between how you're going to build something that has the desired behavior. That how would be the specification.

These concepts could be explicitly specified set theoretically as concepts, or specified by defining boundaries in some conceptual space, or more generally, specified algorithmically as the product of information processing system with learning behavior and learning environment, without initially explicitly creating a conceptual representation.

It's not that one way is rigorous, and one is not, but that they are different ways of creating something with the desired behavior, or in your particular case, different ways between creating the concepts you want to use in producing the desired behavior. The distinction between a conceptual specification and an algorithmic specification seems meaningful and useful to me,

I think this works as a drop in replacement for the first two sentences:

Sophisticated autonomous AI may need to base its behavior on fuzzy concepts such as well-being or rights to obtain desired AI behavior. These concepts are notoriously difficult to explicitly define conceptually, but we explore implicitly defining those concepts by algorithmically generating those concepts.

I assumed that the type of AI design you're exploring is structurally committed to creating those concepts, instead of simply creating algorithms with the desired behavior, or I would have made more general statements about functionality.

Whatever you think of my proposed wording, and even if you don't like the distinctions I've made, the crucial word that I've added is but - an adversity conjuction. But, while, instead, ... a word to balance the things you're trying to make the distinction between, thereby identifying them. The meaning you intended in the first two sentences was a tension or conflict, but the grammar and sentence structure didn't reflect that.