Introduction to Binding

Dr. Hornstein asked that we review this stuff for his lecture tomorrow. See this PowerPoint from last year — text should help you follow along.

Basic Notations and Definitions

Transformation: We believe that we can apply transformations from sentences to create new sentences. For example, “you did buy what?” → “what did you buy?”

Traces: When a word moves, it leaves behind an unspoken word called a trace. For example, in “you did buy what?” → “whata did you buy ta?” the ta is the trace. Note that the second sentence gives you all the information that you need. So, by the we are lazy principle, we just don’t write out the first sentence.

Anaphora: An anaphor is a type of DP. Anaphora include reflexives (eg “himself”) and reciprocals (eg “each other”)

C c-commands D, F, and G, but E does not c-command anything.

Referential Expressions: (aka r-expression) Any DP that’s not an anaphor or a pronoun (eg “the man”)

Co-reference: Two DPs are coreferenced if they refer to the same object. For example, in “Jessicaa hurt herselfa“, Jessica and herself are coreferenced. The subscripts tell us which things are co-referenced. Notice that traces are always coindexed with their head.

C-command: A node c-commands everything in that is below its sibling. For example, in the image to the right, A c-commands all nodes except M.

PRO: PRO is the overt (non-spoken) subject in finite clauses. For example, in “I want [PRO to sleep]”, PRO is the subject of “to sleep”.

Basic Binding

The basic idea of behind binding (also called Government and Binding theory) is that there are three types of DPs: anaphora, pronouns, and referential expressions. Each type of DP can only be used in certain circumstances.

stgraph.png
1 a) Jessicaa gave herselfa cookies.

1 a) Jessicaa gave herselfa cookies.
1 *b) Jessicaa gave herselfb cookies.

2 a) Johna told Samb to help himc
2 b) Johna told Samb- to help hima

3 a) Hea thinks that theyb blame Johnc
3 *b) Hea thinks that theyb blame Johna

stgraph.png (1)
2 a) Johna told Samb help himc

3 a) Hea thinks that theyb blame Johnc
3 a) Hea thinks that theyb blame Johnc

In example 1, Jessica and herself must refer to the same person. Meanwhile, in sentence 3, he and John cannot be the same person. Sentence 2 seems lucky: him and John could be the same person, but it doesn’t have to be. It’s ambiguous.

To formalize these rules, we’re going to define a relationship called bind. Node A binds node B iff

  • A c-commands B
  • A co-references B

We then have three additional grammar rules regarding binding (spoiler alert: they’re incomplete):

  • Binding Condition A: Anaphora must be bound in a sentence
  • Binding Condition B: Pronouns do not have to be bound in a sentence
  • Binding Condition C: R-expression must be free (unbound)

Locality Constraints

Take a look at the following sentences:

*4. Roberta told [Samb to help himselfa]
*5. Jessicaa talked to hera

These sentences follow Binding Conditions A and B, but are ungrammatical. In 4, we co-reference “himself” with “Sam” and not “Robert”. In 5, we don’t co-reference “her” and “Jessica” together. The problem seems to have something to do with scope: anaphors must be bound in its “local domain”, which we’ll call the governing category. Pronouns can’t be bound in their local domain.

We’ll thus amend binding conditions A and B to read:

  • Binding Condition A: Anaphora must be bound in their governing category
  • Binding Condition B: Pronouns cannot be bound in their governing category

Government

Well, what exactly is a governing category? From the examples earlier, it seems that a governing category may just be the smallest containing IP (see 4 and 5 below). On closer inspection, it seems that DP can also be a governing category (see 6).

*4. [IP Roberta told [IP Samb help himselfa]]
*5. [IP Jessicaa talked to hera]
*6. [IP The coacha heard [DP (the player’s)b stories about (each other)a]]

But then, what about these sentences:

7. a) [IP The teama heard [DP [NP stories about (each other)a]]]
*7. b) [IP The teama heard [DP [the other team’s]b [NP stories about (each other)a]]]

8. a) [IP The teama wanted [IP [the other team]b to tell stories about thema]]
*8. b) [IP The teama wanted [IP to tell stories about thema]]

The only difference between between the 7a and 7b is the insertion of the subject “the other team’s”. Same with with 8a and 8b: the only difference is the “the other team”. So, our definition of a governing category:

The governing category of A is the smallest IP or DP which contains A and a subject (ie specifier).

Binding and Transformations

Astute readers may be confused. After all, binding’s obviously very important in linguistics (the theory’s called Government and Binding after all). But reflexives and other anaphora just don’t show up all that often.

The real reason why binding is so important is because they also apply to traces. For example, take the sentence below:

9. a) [IP [DPThe dog that is sleeping] will run].
9. b) [CP Willa [IP [DPThe dog that is sleeping] ta run]?
*9. c) [CP Isa [IP [DPThe dog that ta sleeping] will run]?

Why is the 9b grammatical while 9c is not? Well, as we’ve argued earlier, it could just be that yes-no question formation moves the highest auxiliary, without any reason why. Another, probably more elegant explanation is that in 9c, the trace isn’t bound in its GC (the DP).

10. Mistakesa were made ta

11. a) [IP Mistakesa were made ta [CP because [IP liesb were told tb]]]
*11. b) [IP Liesa were made mistakes [CP because [IP were told ta]]]

Binding constraints can also be seen in other transformations. For example, if believe that passive voice is caused by the movement of an object to an empty subject (10), then we can explain why 11a is grammatical while 11b is not. In 11a, the ta is bound in its GC by “mistakes”, while in 11b, ta is not bound in its GC.

Going into all the details of how binding constrains movement in sentences would probably take another entire post to even start, so I’ll stop here for now. Still, you can see how useful these binding constraints can be to explaining other phenomena.

Binding and PRO

About Alan Du

I'm one of the founders and co-presidents of this club. I also maintain this website. My main interests are all about cognition and intelligence. The idea that a bunch of atoms can combine and form something self-aware is absolutely fascinating. Linguistically, I'm interesting in integrating theoretical syntax with NLP, grammar inference, figuring out how the brain processes language, and creating a program with true artificial language capacities.

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