Just a couple more clarifying comments, with respect to the one actually difficult question on the homework.
First of all, let me state succinctly what the constraints are:
Structural Parallelism requires that the overt pronoun and the elided pronoun are interpreted as being the same type. So, it is satisfied when both pronouns are interpreted as bound, or when both pronouns are interpreted as referential. It is not satisfied if one pronoun is interpreted as bound and the other is interpreted as referential.
Referential Parallelism only comes into play when both pronouns are interpreted as referential; so, if either or both of the pronouns are interpreted as bound, Referential Parallelism is irrelevant. But when it is relevant, it says that both pronouns should be interpreted as referring to the same individual.
Principle B regulates binding relations, so it will only be relevant when one or both of the pronouns is interpreted as a bound variable. If a pronoun is interpreted as a bound variable, then its binder must be “far enough away” in the usual sense (the binder has to be outside the smallest DP or IP that properly contains the bound pronoun).
Principle P (or Rule I, Rule I*, etc.) says that bound variable interpretations are preferred. Or, put another way, you don’t use more indices than you have to. This is the principle that can be overridden by adults in special contexts (the “identity debates” or the “Evans-style” contexts, etc.).
Now, you are given a particular scene and a sentence, and you’re asked to determine whether kids will (at least sometimes) agree that the sentence describes the scene. An adult would not, but the question is whether there is an interpretation of the sentence that the kid might allow that would come out as true in that scene.
The evidence (Thornton & Wexler’s study) is that kids always respect Principle B and Structural Parallelism, but are relatively willing to violate Principle P and Referential Parallelism.
Back to the problem at hand, you have a sentence. On its own, this sentence has many, many possible interpretations. Each pronoun might be a bound variable, or it might be referential. If it’s referential, it might refer to Mama Bear, Goldilocks, or someone else. The other pronoun has the same options, and there’s the additional question of whether, when the two pronouns are referential, they refer to the same individual. So, many, many possible interpretations.
However, you also have a scene, and so you can narrow down your focus to just the interpretations that might come out “true” for that scene. The scene is one in which MB is washing herself, and GL is washing herself. So, how might that come about?
Here’s a little head start on how the thinking goes…
One possibility would be:
MB λx[x touches x], GL λx[x touches x]
Here, both pronouns are interpreted as bound variables. The sentence would evaluate as true of the scene. It satisfies Structural Parallelism, and Referential Parallelism is irrelevant. It satisfies Principle P. But it violates Principle B. And kids always respect Principle B, so they would not consider this a possible representation. So, if the kid is going to agree that this sentence accurately describes the scene, it will not be on the basis of the interpretation given above.
Another possibility would be
MB λx[x touches x], GL touches GL
Here, the overt pronoun is interpreted as a bound variable, and the second one is interpreted as referential, referring to GL. But this violates Structural Parallelism (the two pronouns are not interpreted as being the same type), and the overt pronoun violates Principle B. So, this one is also not among the representations a kid will be considering.
And so forth…
If at the end, you’ve considered all of the ways this sentence might come out “true” of the scene in question, and none of them would have been considered by a kid (who obeys Principle B and Structural Parallelism, but can at least sometimes disregard Principle P and Referential Parallelism), then the prediction is that the kid would not accept the sentence. If, however, at least one of the interpretations is possible given the constraints that kids obey and ignore, then the kid might sometimes accept the sentence.