# Syntax I

A weblog for CAS LX 522

## September 12, 2005

### Privative vs. binary

Filed under: Homework notes — Paul Hagstrom @ 3:01 pm

Let me see if I can clarify the distinction between binary and privative features.

So, downtown, the light atop the Berkeley Building provides a course-grained weather forecasting service. The light can be either blue or red, and it can either flash or not. The possible light configurations (and the conditions under which they appear) are summed up in this saying: steady blue, clear view; flashing blue, clouds due; steady red, rain ahead; flashing red, snow instead. During baseball season, a cancelled baseball game counts as “snow”, incidentally.

So, let’s try to model this light. It has four states. We can describe all and only those states by using two binary features. What we call the features doesn’t matter. We could, for example use the features [+/−precipitation] and [+/−good]. Naming the features as such allows us to describe the outward appearance of the light as follows: if the state is [+precipitation], the light is red, and if the state is [−precipitation], the light is blue. Supposing that [+good] states are better than [−good] states, and that rain is better than snow, and that clear skies are better than clouds, we can say that if the state is [−good], the light flashes, and if the state is [+good], the light is steady.

All this boils down to a model that we can write like this:

[+/−precipitation, +/−good]

And if we like,we can also write the correspondence between the four states that this model predicts will exist and the four states that are observed in the world:

[−precipitation, −good] = flashing blue
[+precipitation, −good] = flashing red

We could instead model this in terms of privative features, as well. Whereas a binary feature has a value (it is either + or −, it is like a switch that can either be in one position or another), a privative feature is a property that something can either have or lack.

To model these four states with privative features, we might use the features [precipitation] and [good].

[precipitation], [good]

The correspondence between the states that this model predicts and the four observed states would be written as follows:

[] = flashing blue
[precipitation] = flashing red.

Thus, when the state has the feature [precipitation], the light is red (and it is blue otherwise). And when the state has the feature [good], the light is steady (and it is flashing otherwise).

So, by looking at the examples above, you should see how you can move between binary and privative features. Generally speaking, the + value of the binary feature will correspond to a privative feature being there, and the − value will correspond to the privative feature not being there.

To continue along in parallel with the homework, suppose we wanted to describe the situations under which the light flashes. With the binary features, it’s easy. The light flashes when the state is [−good]. But how about with privative features? What is there in common between [] and [precipitation] (the two states that yield flashing)? It’s not easy to say. It’s basically the states in which [good] is missing.

Neither model above overgenerates (predicts states not attested in the world) or undergenerates (fails to predict the existence of states that are attested in the world).

1. Thanks a lot for this explanation — it helps a ton. I just think something that was/might still be confusing is that in most examples given so far (in the book, class, and here) there have been 2 possible features, while in the homework there are 3. But anyway, this does help.

Comment by Rachel Heller — September 12, 2005 @ 7:13 pm

2. Well, actually, the example in the book (with singular and plural) in the end just has one feature (either [+/-plural] or [plural]). And we could turn this example with the Berkeley building into an example with “three features” perhaps in a perhaps trivial (but, actually, sort of relevant to the homework problem) way by considering a model with the features [+/-precipitation, +/-good, +/-tall], where the meaning of [+tall] is “the light is far above the ground.” Of course, the light is always high above the ground. The fact that the light is [+tall] is not contributing anything to the predictions. So, we don’t need to include it in our model. A model like [+/-tall, +/-precipitation, +/-good] would overgenerate, because it predicts that there would also be four possible states (red/blue, flashing/steady) where the light is not high above the ground. But such states are not attested in the world.

Perhaps that’s more confusing than helpful, but if you see what I mean, you’ll see that it’s actually quite parallel to the homework problem at hand.

Comment by Paul Hagstrom — September 12, 2005 @ 7:49 pm

3. Right, right — that was much more helpful than confusing. Plus I see the post that came after the one I just commented on, which basically says the same thing. Great, I’m set. Thanks!

Comment by Rachel Heller — September 12, 2005 @ 7:57 pm