William Elliot <ma... at (no spam) rdrop.remove.com> wrote:
But even in natural language "Obama, not Hillary" has no meaning out of
context.

Bah, "Food, not bombs!"

 But we understand a meaning for "Food, not bombs!" because we
recognize it as a popular slogan for those who *want* food, not bombs.
But it could also mean:

  Speaker A: What should we stop producing?
  Speaker B: Food, not bombs!

 So I suggest that what you're pointing to is modeled with lambda
abstraction over sets of entities and binary operators such that we'd
abstract upward from statement 1 to 3 as such:

1. Wants(a,food) & -(Wants(a,bombs))  = "a wants food and not bombs."

2. lambda.Y(lambda.x( Y(x,food) & -(Y(x,bombs))))

  = "food and not bombs"

3. lambda.X(lambda.Y(lambda.x( Y(x,food) X -(Y(x,bombs)))))

  = "food not bombs"

So 3 is then the meaning of "Food, not bombs." And in given contexts
listeners who understand that expression understand which members of
the sets over which we've abstracted are arguments in that
three-parameter function in line 3.

That would in fact define what it
means to understand any "x not y" statement.