Notice that in
the suggested translation of "I will wake up unless my alarm clock
breaks" was "[My alarm clock will break Ú
I will wake up]"; it was not "[I will wake up Ú my alarm clock breaks]. The latter would certainly be wrong.
The reason is that, when "My alarm clock breaks" is used on
its own it means something like my alarm clock is given to breaking.
And this is the meaning it will bear in "[I will wake up Ú
my alarm clock breaks]". But this is not, of course, what
it means in "I will wake up unless my alarm clock breaks", when
that sentence is taken in its natural way. So, when translating using
one of the new truth-functors, always consider what the proposed constituent
sentences would mean on their own.
fact the safest thing, to avoid mistakes, is to use as constituent sentences
only stand-alone sentences: that is, sentences which can be understood
(in the right way!) without reference to the linguistic context. So translate
"John is English and so is Mary" as "[John is English Ù
Mary is English]". And translate "John likes David and David
likes him" as "[John likes David Ù
David likes John]". That it is say, avoid cross-reference.