Good.

Now, don't we have the same concern with "unless" as we had with "or": that both seem to be exclusive?

For example, one may say

(1) Sam is ten unless she's just turned eleven.

And, we've said that this means that either Sam is ten or she has just turned eleven. So far, no problem.

But doesn't this last "or" still seem like exclusive "or": she's ten or just turned eleven but not both? (The answer is going to be "No", so read on carefully!)

Contrast this with another example:

(2) We'll win unless the other team scores.

At first this may seem like an exclusive example. But really it is not. It may happen, of course, that they score, the match goes into overtime, and we score the winning goal. That is:

W	S		W	unless	S
T	T		T	T	T

just as inclusive "or" would have it.

So, (2) at least seems appropriately translated with the SL wedge.

But now notice that in (1), the word "unless" is no different from (1). The difference has to do with the two disjuncts: being 10 and being 11 are exclusive. But this is a matter independent of the translation of the "or", independent of the meaning of the word "or" and is only a matter of the meaning of "being 10 years old" and "being 11 years old".

So, how should we translate (1)? There are two possibilities both of which are reasonable.

The easiest way is

TvE

(where 'T' stands for "Sam is ten" and 'E' stands for "Sam has just turned eleven"). But does leave out a bit of meaning because the SL disjuncts 'T' and 'E' are independent (both can be true or both false or any combination thereof) whereas the English disjuncts are exclusive, i.e., if one is true then the other is false.

So, a more complete translation would be

(TvE)&~(T&E)

One or the other but not both. But keep in mind that the wedge is not an incomplete rendering of "unless". Rather, SL's problem is with 'T' and 'E': it treats them as both possibly true when they mean exclusive things.

So, what's the bottom line? How do I translate "or" and "unless"?