Building on work by Alfonseca et al. (2021), we study the conditions necessary for it to be logically possible to prove that an arbitrary artificially intelligent machine will exhibit certain behavior. To do this, we develop a formalism like -- but mathematically distinct from -- the theory of formal languages and their properties. Our formalism affords a precise means for not only talking about the traits we desire of machines (such as them being intelligent, contained, moral, and so forth), but also for detailing the conditions necessary for it to be logically possible to decide whether a given arbitrary machine possesses such a trait or not. Contrary to Alfonseca et al.'s (2021) results, we find that Rice's theorem from computability theory cannot in general be used to determine whether an arbitrary machine possesses a given trait or not. Therefore, it is not necessarily the case that deciding whether an arbitrary machine is intelligent, contained, moral, and so forth is logically impossible.

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