Consider the sentences
(1) All dogs bark.
(2) All dogs bark loudly.
In event semantics the logical form of (1) is (∃e,x) every(x) & dog(x) & bark(e,x). As for (2), one would add the conjunct loud(e). The latter formula implies the former, as one would expect. Now consider
(3) Few dogs bark.
(4) Few dogs bark loudly.
Again, the logical form of (4) implies that of (3) (since A & B ⊃ A). But in this case, (3) entails (4) because "few" is a decreasing quantifier. Is there a simple solution to this "paradox"?
Update: a note on the notation (to avoid confusion): In Davidsonian event semantics, sentences are represented as (existential closures of) conjunctions of literals. In dog(x), x can be a dog or a set of dogs (or some others individual that can be lexically described as dog). In this so-called conjunctivist approach, every(x) implies that x isn't a specific dog, but - as some put it - a typical/generic individual defined by the eventuality dog(e,x). There's one axiom in the theory that say that if something holds of a generic element of a set, there's an eventuality with the same predicate for every member of that set. Formally, genericel(x,s) & y∈s & P(e,x) ⊃ (∃e′)P(e′,y). This technique is widely used in commonsense reasoning, but as one can see, there are problems with some quantifiers.