The standard interpretation of this string is as conjunction: we expect to read as the sequent notation for Here we are taking the RHS Σ to be a single proposition C (which is the intuitionistic style of sequent); but everything applies equally to the general case, since all the manipulations are taking place to the left of the turnstile symbol
Since conjunction is a commutative and associative operation, the formal setting-up of sequent theory normally includes structural rules for rewriting the sequent Γ accordingly—for example for deducing from There are further structural rules corresponding to the idempotent and monotonic properties of conjunction: from we can deduce Also from one can deduce, for any B, Linear logic, in which duplicated hypotheses 'count' differently from single occurrences, leaves out both of these rules, while relevant (or relevance) logics merely leaves out the latter rule, on the ground that B is clearly irrelevant to the conclusion.
For example, in linear logic, since contraction fails, the premises must be composed in something at least as fine-grained as multisets.
The first conference on the topic was held in October 1990 in Tübingen, as "Logics with Restricted Structural Rules".
During the conference, Kosta Došen proposed the term "substructural logics", which is now in use today.