Dynamic negation, the one and only (Q1288172)

Dynamic negation monoids (DNM) are introduced as algebraic models for the dynamic predicate logic studied by J. Groenendijk and M. Stokhof in 1991. These are monoids \((M,;,\text{id})\) together with a zero element \(\perp\) and a unary operation \(\sim\) (called dynamic negation) satisfying a finite set of axioms that we do not specify here. The authors show that: 1. not every monoid with zero is the reduct of a DNM, and 2. in a DNM \((M,;,\text{id},\perp, \sim)\) the composition ; uniquely characterises id, \(\perp\) and \(\sim\).