We know that any "effectively computable" process is computable by a Turing machine (Turing-Church thesis).
Although it seems that "effectively computable" is still open to discussion, the intuitive interpretation is that any process that is "mechanical enough" can be computed by a Turing machine.
Turing's initial objective was to axiomatise how humans do reasoning. Now what do you need to reason? Non-ambiguous definitions (axioms) and non-ambiguous rules. Then you are good to go. So in effect if TM successfully modelise how humans think, that's all they should need and hence natural languages should be quite a close candidate to become regular languages as long as we impose that words have just one meaning.
My question is then, intuitively, is it enough for a language to be "non-ambiguous" to be computed by a Turing machine? Or is there more intuitive properties that the language need to respect?
(I am currently trying to figure out if the laws voted in a parliament, although written in mundane English, have enough of these characteristics to be computed by an automaton).