Ninguem viu nada/
No one saw anything
Nem nunca ninguém disse nada a ninguém/
Never anyone said anything to anyone
A semantic negation may be entertained by no occurrence of any negative form:
Se Kennedy tivesse um carro blindado, teria
saído de Dallas com vida/
If Kennedy had a bullet proof car, he would
be alive when leaving Dallas.
(But) Kennedy had no bullet proof car.
For the first case, mainstream accounts tend to split into two views: (i) no negative expression expresses negation: single semantic negation is expressed by a phonetically null operator; (ii) all negative expressions express negation: multiple negations are factorized into a single one. The explicative appeal of these solutions is reduced: one ends up just rephrasing the empirical facts in terms of special-purpose stipulative mechanisms. In this talk, I would like to introduced you to a third type of solution I am working in, which is being developed, among other things, in our Nexing project. In this approach, downwards monotonicity properties are shown to play a decisive role in natural language.