What is the resource interpretation of $A \to B$ in linear logic? Linear logic seems to have two forms of implication.
$$A \multimap B$$
With resource interpretation of "consuming A yields B".
And the usual
$$A \rightarrow B$$
What is the resource interpretation of regular implication in linear logic?
For example, I've seen $A \rightarrow B$ sometimes re-interpreted as:
$$A! \multimap B$$
 A: I would say it is not a reliable way to translate classical logical formulas to resource-sensitive essence of linear logic just over semantic instructions. Thus, many interpretations are ex post facto attempts to make sense of formal results.
Presuming your intention by "regular implication" is "material implication" ($A \rightarrow B$) in classical logic, I think we can reason as follows:
We may think of propositions as place-holders for resources. Material implication tells that either we do not have, and thus, demand a resource A, or else, we have got a resource B available. In other words, we have either the absence of resource (i.e., to be supplied) A or the presence of resource (to be consumed) B.
Since these are "classical" resources; we can freely restore or dispose of them over and over again on demand. So we have the alternatives
$$!A \multimap !B$$ and
$$?A \multimap ?B$$
We supply either ?A to be consumed some amount and yield proportionately ?B, hence
$$!?A \multimap ?B$$
or we consume !B some amount and need proportionately !A, hence
$$!A \multimap ?!B$$
which are the expressions for material implication in LL.
