A formula N is negative if and only if is positive.
A connective c of arity n is negative if for any negative formulas N1,...,Nn, is negative.
Proposition (Negative connectives)
More generally, is negative for any formula A.
The notion of negative connective is related with but different from the notion of synchronous connective.
Generalized structural rules
Negative formulas admit generalized right structural rules corresponding to a structure of -monoid: and . The following rule is derivable:
Negative formulas are also acceptable in the context of the promotion rule. The following rule is derivable: