On understanding "except" ...
When we say "A except B" we normally mean that A and B are mutually exclusive. Either A is the case or B is the case but not both.
If you think in terms of sets then
All birds can fly except for penguins and ostriches or unless they have a broken wing
could be re-written as
In the universe of birds, there are exactly two distinct sets -- one in which every member of the set can fly and the other in which you find penguins and ostriches and birds with broken wings
.
(In passing, note the way the words "and" and "or" in English often need to be adjusted in a symbolic expression.)
Birds
+-----------+------------+
| | |
| Fly | Exceptions |
| | |
+-----------+------------+
Representing mutual exclusion in predicate logic is most easily handled by exclusive-or (XOR). We want to say fly XOR exceptions
.
In systems that allow quantifiers to limit the universe of discourse, we could write:
∀x∊birds (fly(x) XOR (penguin(x) v ostrich(x) v brokenWing(x)))
If quantifiers are unlimited, then:
∀x (bird(x) → (fly(x) XOR (penguin(x) v ostrich(x) v brokenWing(x))))
And if XOR is not in the set of allowed operators, then you might have to use the equivalence:
p XOR q ≡ ((p v q) & -(p & q))
There are a couple of other implications hiding in the English sentence that are not fully expressed in the suggestions above.
The sentence in predicate logic allows the case that there are
no birds, whereas the English sentence probably implies that there is
at least one bird.
"A except B" in English normally implies that there are at
least some instances of the exception. Not only is there at least one
bird, but there is at least one penguin that cannot fly. That could
be added to the predicate sentence via appropriate use of existential
quantifiers.
"A except B" in English nearly always
implies that A is the most common case and B is the exception. In the
absence of other evidence, we would assume A. In the universe of
birds, most can fly and only the listed exceptions cannot fly. There
is no easy construct in predicate logic to capture the sense of a
majority case.