Examination

Instead of leaving the brunt of the analysis to the lexical semantics, we can go right ahead and put it all in the extension of and. This gives us much simpler extensions for verbs while pulling the meaning more out into the open. We can expect to practically do this because there aren't really that many ways that verbs process their arguments. Let's look over the examples presented earlier.

In 1a, 1f, and 1g, we have a condensed form. That is, John and Mary voted is true exactly when John voted $\wedge$ Mary voted. Similarly, 2a, 2b, and 2c all expand the same way; there is no difference in extension between John bumped Mary and Bob and John bumped Mary $\wedge$ John bumped Bob.

The cases of 1b and 1c seem to need a more complicated interpretation. We can't just say that John and Mary kissed is true when John kissed $\wedge$ Mary kissed because each of those components is meaningless on its own. It makes no sense to say that a single person kissed. We need something more like John kissed Mary $\wedge$ Mary kissed John.

The cases of 3a, 3b, 3c, and 3d are complicated because they have at least two possible extensions. The first is that John and Mary met Bob and Sue is true exactly when John met Bob $\wedge$ John met Sue $\wedge$ Mary met Bob $\wedge$ Mary met Sue. The other is John met Bob $\wedge$ Mary met Sue.

The final, slightly troublesome, one is the case of 1e. If we want to treat it like the others we'd have to say John collided with Mary $\wedge$ Mary collided with John. What is distasteful about this is non only that we're adding words, but that collided seems somehow more natural in its original form while the collided with form sounds like a workaround to bend the verb to our will. Consider what happens if we say that collided - not collided with - is a verb that takes two arguments of equal status? Then we can just use the reflexive case of kissed in a slightly wasteful manner.