A formula P is positive if and only if is negative.
A connective c of arity n is positive if for any positive formulas P1,...,Pn, is positive.
Proposition (Positive connectives)
More generally, is positive for any formula A.
The notion of positive connective is related with but different from the notion of asynchronous connective.
Generalized structural rules
Positive formulas admit generalized left structural rules corresponding to a structure of -comonoid: and . The following rule is derivable:
Positive formulas are also acceptable in the left-hand side context of the promotion rule. The following rule is derivable: