After the introduction of the Davidsonian framework, in which action verbs take an implicit argument corresponding to the event they describe, it has been argued that some sort of "negative events" should be considered in order to analyze, among others, examples of perceptual reports such as (1), causal statements such as (2), sentences such as (3) in which a temporal adverbial can scope over a negated verb phrase or the interaction of negation and distributivity as in (4). This position has always been highly controversial and so far, no formal account of these so-called negative events have been successfully proposed.
(1) Mary saw Fred not leave.
(2) I kept the kids awake by not turning of the light.
(3) John did not laugh for two hours.
(4) Mary and John each did not leave.
We analyze negation with a function Neg that turns a predicate of events P into an event Neg(P), that one can interpret as the not-P event. We will show how a simple and coherent logic for negation can be expressed with a single axiom and will present a small fragment of an English grammar with which it is possible to compositionally derive the meaning of all of the aforementioned examples.