However, though the word "demonstrative" may be the best word, the primary desire was to connect the notion of analyticity
with the kind of soundness proof which is conducted usually for a formal system to show (inter alia) its consistency.
In this context the axioms are shown true with respect to the semantics, and the inference rules are shown to respect the
semantics, with the effect that all the theorems are known to be true under the semantics, and hence analytic.
It is the (rather elementary) connection between proof in sound deductive systems and the semantic notion of analyticity that
is the target of the exercise, and therefore the defined concept of "demonstrative" is wholly semantic, does not talk about
necessity, and might be thought to differ from the Aristotelian notion on that account.

A further difficulty arised from incompleteness.
There is no single (r.e.) deductive system which proves all the analytic truths.
In these models, the only constraint on axioms is that they are analytic, and the only constraint on inference rules is that
they preserve truth under the relevant semantics.
This does yeild the desired identity, but certainly represents a more liberal deductive regime than that in Locke and Hume,
who require that the axioms and rules be intuitively certain.
To get the identity I am in effect permitting sound deductive systems in which the most tenuous and obscure (but true) large
cardinal axioms are employed, and it is doubtful that Locke would have thought these intuitively certain.

So far as Aristotle is concerned, the rules are syllogistic, and he has no conception of the linguistically pluralistic world
inhabited by modern logicians, so again our notion of demonstrative is on the generous side.