Linguistics 522

Lecture 3

Phrase-markers

Structure-dependence is the theme of our course. We have been arguing for it in terms of the trees we draw for sentences, which capture information of two kinds:

First phrasehood.

Second, categoriality.

The trees we'll be using then embody two notions, constituency (phrasehood) and categoriality. Radford doesn't call these structures trees. He calls them phrase-markers. The term tree is actually more popular among linguists and computer scientists alike. But is isn't more popular with one very important guy, Noam Chomsky. For some reason never made particularly clear to me, Noam Chomsky never talks about trees. He always talks about phrase markers.

Radford follows Chomsky here.

Defining basic Terms

graph, node, root node: Whether you say tree or phrase-marker, the structure can be formally thought of as a graph, a mathematical term that's particularly important in computer science. A graph is just any structure with points and lines between them, and a tree is just a special kind of graph with a fussier definition. The points in a graph are also called nodes and that is the term linguists use for the points in a phrase markers or a tree. Some of the nodes in tree (1) on p. 110 are the S-node (called the root node, because it's the top), the VP node, the NP node and the P node.

immediately dominates, dominates, exhaustively dominates, mother, daughter, sister, precedes, immediately precedes

(1)
    immediately dominates: In tree (1) on the left, TP immediately dominates NP1, T, and VP. NP immediate dominates D, V1 and N. VP immediately dominates V3 and NP2.
    mother, daughter, sister: used to describe nodes in an immediate dominance relation. A node M is the mother of a node D, if and only if M immediately dominates D. In the same situation we say D is a daughter of M. That is, a node D is the daughter of a node M if and only if M immediately dominates D. Two nodes that have the same mother are sisters. In tree (1), NP1 is the mother of D, V1 and N2, and D, V1 and N2 are the daughters of NP1. NP1 is NOT the mother of V2 because NP1 does not immediately dominate V2. In fact, NP1 is what you might call the grandmother of V2 (the mother of its mother).
    exhaustively dominates: A node M exhaustively dominates a set of nodes D1 through Dn if and only if M is the mother of each D' and there are no other nodes M is the mother of. In other words, the set of nodes a mother dominates must include all her daughters. In tree tree (1) on the left, TP does not exhaustively dominate NP and VP. It exhaustively dominates NP, T, and VP.
    dominates: Dominates is defined as follows:
    • A node A dominates a node B if A immediately dominates B
    • A node A dominates a node B if there is a node C such C dominates B and A dominates C.
      So this brings inheritance in. A dominates B not just when A is the mother of B, but also when it's the grandmother, or the great-great grandmother, or the great-great-great grandmother, and so on. In tree tree (1) on the left, TP dominates NP, T, and VP (because it immediately dominates them), but it also dominates D, N1, V1, V2, and V3 (among other nodes).
    immediately precedes: A node A immediately precedes a node B if it is immediately to the left of B. In tree (1) on the left, NP1 immediately precedes T and T immediately precedes VP, but NP1 does not immediately precede VP. T also immediately precedes V3 M in tree (1). And T also immediately precedes VP and it also immediately precedes V.
    precedes: Precedes is defined as follows:
    • A node A precedes a node B if A immediately precedes B
    • A node A precedes a node B if there is a node C such C precedes B and A precedes C.
      So NP1 precedes T because it immediately precedes T in tree (1), but it also precedes VP, V3, and NP2.

    Note that dominance and precedence are mutually exclusive. A node X cannot both dominate and precede another node Y.

    Essentially what this terminology does is break phrasehood down into two parts, dominance and precedence. A phrase is series of elements (words or phrases), dominated by a single node, which come in a fixed order.

Constituent, constituent of, immediate constituent of:

The following table summarizes these points:
A (immediately) dominates C
  iff  
C is a(n immediate) constituent of A
(2)

Observation We now have four ways of expressing the relation between nodes that is exemplified in tree (2):

These all mean the same thing.

Defining traditional grammatical terms, pp. 112, 113

Not important at this stage

C-Command

We've talked about mothers, grandmothers, great grandmothers, and so on, which I'll write great ... grand mothers. Now it's time to talk about nieces and great ... nieces.

Branching node:

C-Command:

In (10) on p. 115,

Consider the following example:

    (3)

      B C-Commands C, D, E, F, and G.

      C C-commands B [so C and B C-command each other.]

      C does NOT C-command D,E,F,G, because it dominates all of them.

Here is where the nieces and great ... nieces come in:

Anaphora and C-command

Reflexives and reciprocals are special forms that occur only in special syntactic contexts:

The claim made in the text is reflexives and reciprocals are dependent in a special way. Like pronouns they require antecedents. Unlike pronouns they require those antecedents to be in a special syntactic configuration:

Parallel facts for each other.

Words like reflexives and reciprocals that have this special dependency property are called anaphors. The following proposal is made for anaphors:

This accounts for all the ungrammatical examples above. For example: There is no semantically acceptable antecedent that both precedes and C-commands himself. Here there is a semantically acceptable antecedent that precedes himself but it does not C-command himself. The first branching node above John does not dominate himself. This example shows that precedence alone is not enough to predict the distribution of anaphors.

The following example shows that C-command alone is not anough:

The account also accounts for the ambiguity of examples like this

It could be that each arrow shooter is shooting at the other. Or it could be that they are shooting each arrow at the other's arrow. In other words, the antecedent of the reciprocal could be We or it could be arrows. Both NPs C-command and precede the reciprocal. Therefore both are candidate antecedents by our principle.

Questions to Think About

Now think about the following example:

Is there an analogous ambiguity? More importantly, is there a problem for Principle A? Think about the tree for this example.

Now think about this one:

Same question.

And finally:

Same question.

Phrase-Structure rules and lexicon

We now move to a more precise statement of what the grammar looks like.

We need a finite set of rules that can "generate" an infinite set of sentences.

We're going to have two kinds of "rules"

Phrase-structure rules state immediate dominance and precedence relations. The phrase-structure rule for TP says a TP can immediately dominate a VP preceded by an T preceded by an NP.

The lexical entry for "boy" says "boy" is a noun. We'll call the categories that belong to some lexical entry lexical categories.

We call the nodes in a tree that dominate words or nothing terminal nodes. Consider the following partial tree:

The nodes D,N,T, and VP are all terminal nodes in this tree.

Phrase structure-rules and phrase markers

A phrase-structure rule admits local trees:

admits A tree is well-formed with respect to a grammar G if and only if it meets two conditions:
  1. All the local trees are admitted by phrase-structure rules in G.
  2. All the terminal nodes dominate words of the appropriate lexical category as defined by the lexicon of G.

Definition of grammaticality

We call the words admitted by some well-formed tree the yield of that tree.

Now we can say what strings are generated by a grammar G.

A string is grammatical if and only if it it is the yield of some tree admitted by the grammar.

Determining when a sentence is grammatical accoding to a grammar

Our job in this course is not so much to find the right grammar of English as to find ways of evaluating candiadtre grammars. As a result, the most important skill you learn in this course will be determining whether or not some proposed grammar characterizes an example sentence as grammatical.

If the grammar says the sentence is grammatical and our intuitions tell us it's grammatical, good for the grammar.

If the grammar says the the sentence is grammatical and our intuitions tell us it's ungrammatical, we say the grammar overgenerates.

If the grammar says the the sentence is ungrammatical and our intuitions tell us it's grammatical, we say the grammar undergenerates.

It's pretty safe to safe all the grammars we consider in this course will do both. It will undergenerate because there are lots of constructions we won't consider. For example:

The italicized constituent begins with a determiner, like a noun phrase, but lacks a head noun. None of the rules we consider in this course will generate this sort of thing.

Our rules will overgenerate because even for the constructions we DO consider there are all kinds of constraints we are ignoring. For example:

(= 26, PS rule 6), p. 134, generates NPs like But it also allows So determiners and nouns have number, and they must agree, and we haven't yet found a way to account for this.

The skill we need for this course is to be able to take a set of rules and a set of data and decide whether the rules account for the data. If not, we need to be able to decide on the simplest change to our rules that will extend them to cover the data.

Execrcise V, p. 160 is about this.

Particles and conjunctions

The question raised is whether we need to recognize new lexical categories for particles and conjunctions.

Particles first:

What syntactic category that we already recognize seems like closest fit for these particles? Some argue they should be assimilated to prepositions, partly because they can (often) be replaced with PPs. Radford notes prepositions can also function as subordinating conjunctions:

And sometimes a single word can be a preposition, a particle, and a conjunction:

See also examples with after, before, p. 134.

So what Radford argues for (Emonds's analysis) is that there are three uses of prepositions, the canonical preposition use (where they take an NP complement), the conjunction use (they take a clause complement) and the particle use (they take no complement). This is just the kind of variation we see with verbs.

Some prepositions take only the transitive and transitive option and not sentential complements: Again there are verbs that show THIS pattern:

Another argument, essentially a distributional argument, is that prepopositions, conjunctions, and particles may all take the same modifiers:

Now what about restrictions on all this behavior?

Many prepositions cannot be used as particles:

Many conjunctions (what Emonds would call prepositions that take S complements) do not take NP complements:

But Emonds's story is going to be that these restrictions are not categorial. They are lexical restrictions. That is, these differences among what Emonds call prepositions are like the differenvces between ordinary verbs. Some verbs take S- but not NP-complements:

Some take NPs but not Ss: Some take no complement at all: So on the old analysis, Prepositions only took NP complements; they were a defective category. The new analysis makes Prepositions look much more like other categories.

Notice all the argumentation is about parsimony here. Let's have fewer lexical categoires, because overall that gives us a simpler picture of grammar.

Why is simpler better? Well if we constrain the class of grammars (by constraining the class of categories they can use), then maybe we are on the way to explaining why children learn them so easily.

We'll see.

Conflating categories

Continuing along the same lines. Now we try to constrain the class of categories by collapsing several categories together.

First we try to collapse adjectives and adverbs.

Arguments:

  1. Morphological: Both adjectives and adverbs have comparative and superlative forms
    1. Objection: Many adverbs form their comparative and superlative forms not with -er and -est but with more and most.
    2. Response: So do many adjectives like expensive and probable.
    3. Often the same comparative form will be shared by an adjective and its -ly counterpoart.
      • She was happier than he was.
      • * She works happilier than he does.
      • She works happier than he does.
  2. Syntactic: Adjectives and Adverbs have similar premodifiers like very, really, and extremely.

New official treatment: Adj and Adv get collapsed. We call the new category A (rather than advective or adjerb).

Questions to Think about

Now think of an objection to collapsing adverbs and adjectives. What's the first problem that comes to mind?

Not conflating categories

The argument for conflating Adj and Adv was really based on something you may have learned about in previous linguistics classes called complementary distribution. The idea is basically the Superman/ Clark Kent idea. If there are two entities you never see in the same place at the same time, then maybe underlyingly they're the same entity. It's just that sometimes they're wearing glasses. So the idea was that adverbs are just adjectives wearing glasses.

In this particular case, the idea was that there's one category which "surfaces" as an adjective when it's modifying a Noun, and as an Adverb everywhere else.

Compare this to the treatment of allomorphy in the case of plural s

  1. fox: /f aa k s/ + /ax z/
  2. dog: /d ao g/ + /z/
  3. duck: /d uh k/ + /s/
Three different ways of pronouncing plural s. These forms occur in complementary distribution. That is, they not only occur in environments that mutually exclude each other, but the environments taken together, exhaust the possibilities.

Why not do more of the same?

Why not collapse adjectives and determiners? There are a variety of facts that argue against this.

The basic morphological argument is that there is no shared morphology between determiners and adjectives:

  1. Adjectives have comparative and superlative forms; determiners do not
  2. Adjectives take -ly to become Adverbs; determiners do not
  3. Adjectives take -ness to become noun; determiners do not.
  4. And so on...

Distributional arguments:

  1. Different distributions. Determiner must always precede adjective in an NP:
  2. Adjectives can iterate or "stack up" to the left of a noun; determiners can not
  3. More important (in my book). Adding a determiner can an NP "complete". Adding an Adjective cannot:
  4. Determiners and Determiners can be conjoined; adjectives and adjectives can be conjoined; determiners and adjectives cannot.

Semantic arguments.

  1. Selection between Adjectives and Nouns on semantic grounds
  2. Selection between

Sample exercise answers

Excercise VI. Example answers.