Linguistics 001     Lecture 10     Syntax I
"The structure of every sentence is a lesson in logic." (J.S. Mill)

BACKGROUND: the "cookbook problem"

We can communicate a lot without words, by the expressive use of eyes, face, hands, posture. We can draw pictures and diagrams, we can imitate sounds and shapes, and we can reason pretty acutely about what somebody probably meant by something they did (or didn't do).

Despite this, we spend a lot of time talking. Much of the reason for this love of palaver is no doubt the advantage of sharing words; using the right word often short-cuts a lot of gesticulating and guessing, and keeps life from being more like the game of charades than it is.

Given words, it's natural enough to want to put them together. Multiple "keywords'' in a library catalog listing can tell us more about the contents of a book than a single keyword could. We can see this effect by calculating the words whose frequency in a particular book is greatest, relative to their frequency in lots of books. Here are a few sample computer-calculated lists of the top-10 locally-frequent words, for each of a range of books on various topics:  

    "College: the Undergraduate Experience:" undergraduate faculty campus student college academic curriculum freshman classroom professor.

    "Earth and other Ethics:'' moral considerateness bison whale governance utilitarianism ethic entity preference utilitarian.

    "When Your Parents Grow Old:'' diabetes elderly appendix geriatric directory hospice arthritis parent dental rehabilitation

    "Madhur Jaffrey's Cookbook:'' peel teaspoon tablespoon fry finely salt pepper cumin freshly ginger

This is (half of) the secret of Google's effectiveness -- we get a very good idea about the content of a document from an index based on the words it contains.

In understanding such lists, we are making a kind of semantic stew in which the meanings of all the words are stirred up together in a mental cauldron. We get a clear impression of what the book is about, but there is a certain lack of structure.

For example, the last word list gives us a pretty good clue that we are dealing with a cookbook, and maybe even what kind of cuisine is at issue, but it doesn't tell us how to make any particular dish.

Just adding more words doesn't help: the next ten in order from the (Indian) cookbook  are:  

    stir lemon chicken juice sesame garlic broth slice sauce chili

This gives us some more information about ingredients and kitchen techniques, but it doesn't tell us how to make a vindaloo. To understand a recipe, we need more exact information about how the words (and ingredients!) combine.  

The principle of (recursive) compositionality

We don't normally communicate by trading lists of keywords. Children at a certain age (perhaps a year and a half or so) often create discourses by stringing together one-word sentences:
 

    "Juice. Shirt. Off!" (rough translation: "I spilled juice on my shirt. Could I have a clean shirt, please?")

However, when adults (and older children) communicate with words, they just about always put the words together in a hierarchical or recursive way, making bigger units repeatedly out of smaller ones. The meanings combine in a way that is not like the way that ingredients combine in a stew, but more like the combination of ingredients in an elaborate multilayered pastry, where things must go together in a very precise and specific way, or we get not a sachertorte but a funny sort of pudding.

This is the principle of compositionality: language is intricately structured, and linguistic messages are interpreted, layer by layer, in a way that depends on their structure.
 

Syntax-directed translation in logic and computer science

This strict sort of compositionality permits what is called "syntax-directed translation" in the terminology that computer scientists use to talk about compilers for computer languages. It means, for instance, that
 

    (1 + 2)  x 3
can be understood by first adding 1 and 2 and then multiplying the result by 3, whereas to understand
 
    1 + (2 x 3)
we first multiply 2 and 3, and then add 1 to the result. In this way the interpretation of arbitrarily complex expressions can be computed layer by layer, combining the interpretations of simpler parts.  A simple recursive calculation will determine the value of an arbitrarily complex arithmetic expression as a function of the values of its parts:
 
    ((23 x 5) + 2) / (3 + (9 x 4))
       (115   + 2) / (3 +    36)
             117   /    39
                   3

These ideas were first worked out by philosopher-logicians like Frege and Russell, long before computers were invented, in order to provide a formal way to define the meaning of mathematical expressions and mathematical reasoning.

This line of thinking gives us a first answer to the question "why bother with syntax?" The layered (recursive) structures of syntax allow us to communicate an infinity of complex and specific meanings, using a few general methods for building phrases with more complex meanings out of phrases with simpler ones.

This system is based on a marvelous foundation -- the tens of thousands of basic morphemes, words and idiomatic phrases of each human language. These are the "atoms" of meaning that syntactic combination starts with. Using syntax, we can specify not only the ingredients of a recipe, but also the exact order and method of their combination.
 

Syntax-directed translation in ordinary language?

However, in everyday talk, syntax-directed translated is not as easy to apply as it is (at least after Frege and Russell) in arithmetic. The relations between words and phrases do not seem to have meanings as simple and regular as "addition" and "multiplication," and the very structure of word sequences is often ambiguous.

Unlike in the arithemetic examples just given, ordinary language doesn't normally have explicit parentheses (although sometimes we modulate pitch and timing to try to indicate the grouping of words). This lack of vocalized parentheses sometimes leads to uncertainty about exactly what the structures are: thus a "stone traffic barrier'' is probably a kind of traffic barrier, and not a way of dealing with stone traffic, while ``steel bar prices'' are what you pay for steel bars. We know this because we know what interpretations make sense: just the fact that we have three English nouns in a row does not specify either the structure (1 (2 3)) or the structure ((1 2) 3).

The number of logically possible alternative structures, assuming each piece is made up of two elements, grows rapidly with phrase length. For instance, ``Pennsylvania state highway department public relations director'', which contains seven words, has 132 logically possible consituent structures, each of which has many possible meaning relationships between its elements. We understand it fairly easily, all the same, because we are already familiar with phrases like "public relations", "state highway", and so on.

In contrast, consider the phrase "process control block base register value,'' taken from the technical manual for a once-popular minicomputer. To those familiar with the jargon, this clearly means "the value of the base register for the block of memory dealing with process control," i.e. a structure like
 

    (((process control) block)((base register) value))

To most people, however, the structure of this compound is completely baffling. Manuals of style sensibly suggest that writers of English should avoid long noun compounds, because they are a lot of work for readers, and may be misunderstood if the reader is not as familiar as the writer is with the bits of jargon involved.

Ambiguity of constituent structure is not the only problem here. English noun compounds also suffer from semantic vagueness in the relations between the words, even when we know the constituent structure. Thus "peanut oil'' is oil made from peanuts, but "hair oil'' is not oil made from hair; a "snow shoe'' is a shoe to walk on snow with, but a "horse shoe'' is not a shoe to walk on horses with.

Some techniques for reducing ambiguity

In order to limit these various kinds of uncertainty, languages provide all sorts of (often optional) help to their users. For example, there are special words or endings for making structural or semantic relationships among other words explicit. We just used words like "for'' and "of'' and "dealing with'' to help make clarify the form and meaning of the phrase from the computer manual.

Languages also establish conventions about the interpretation of word order. For instance, although English compound nouns are about as loose a syntactic system as you ever see, English does regularly put the head (or dominant element) of noun compounds on the right, so that "dung beetle'' is a kind of beetle, while "beetle dung'' would be a kind of dung.

This is not logically necessary -- other languages, such as Welsh and Breton, make exactly the opposite choice. Thus Breton kaoc'h kezeg is literally the word for "manure'' followed by the word for "horse,'' i.e. "manure horse'' in a word-by-word translation. However,  Breton kaoc'h kezeg  means "horse manure,'' that is, manure produced by a horse, and not (say) a horse made of manure, or a horse dedicated to producing manure, or whatever "manure horse" in English might mean.

This situation is common: individual human languages often have quite regular patterns of word order in particular cases, even though these patterns may vary from language to language. Thus English expects determiners (words like "the'' and "a'') to come at the beginning of noun phrases, and adjectives to precede nouns they modify, so that we say "the big cow'' and not (for instance) "cow big the.''

As it happens, Mawu expects determiners to come at the end of noun phrases, and adjectives to follow the nouns that they modify, and so the equivalent phrase is Mawu is "nisi wo  o,'' which is literally "cow big the.''

Word order is more rigid in some languages than in others. Putting it another way, in some languages word order is more rigidly dependent on grammatical relations (roughly, the structures that specify who did what to whom), while in other languages, word endings do more work in expressing grammatical relations,  and word order can be used for other purposes, like indicating subtle gradations of discourse prominence.

Is syntax really necessary? The "dog bites postman" approach.

Are these ambiguity-reduction techniques really necessary?

Not always.

Let's  suppose that we knew what words mean, and a lot about how to put meanings together, but we had no particular constraints on syntactic structure. In this imaginary condition, we don't care about the order of adjectives and nouns, nor where verbs should go relative to their subjects and objects. There are some general principles that might help us, such as that semantically-related words will tend to be closer together than semantically-unrelated words are, but otherwise, we are back with the ``word stew'' we imagined earlier.

Under these circumstances, we could still probably understand a lot of everyday language, because some ways of putting words together make more sense than others do.

We are in something like this condition when we try to read a word-for-word gloss of a passage in a language we don't know. Often such glosses can be understood: thus consider the following ancient Chinese proverb (tones have been omitted, but distinguish zhi "it" from zhi "know"):
 

    fu ching hu yu, mo  zhi zhi  zai;
    luck light than feather not it know carry
                   
    huo zhong  hu di,  mo  zhi zhi   bi.
    misfortune heavy than earth not it know avoid

This means something like ``although luck is lighter than a feather, we don't know how to carry it with us; although misfortune is heavier than the earth, we don't know how to avoid carrying it''

Most people can figure this out, at least approximately, despite the elliptical style that does not explicitly indicate the nature of the connections between clauses, and despite the un-English word order.  Few of us will have any trouble grasping that it is luck that is (not) being carried, and misfortune that is (not) being avoided, because that is the only connection that makes sense in this case.

A scholar will explain to us, if asked, that this proverb exemplifies a particular fact about ancient (pre-Qin) Chinese, namely that object pronouns ("it' in this case) precede the verb when it is negated. This syntactic fact would have helped us figure out that "it'' is the object of "avoid'' rather than the subject of "know''--but we guessed that anyway, because things made more sense that way.

Sometimes the nature of the ideas expressed doesn't make clear who did what to whom, and we (or modern Chinese speakers), expecting objects to follow verbs, might get confused. Thus the phrase

 
er wei  shi wo fei ye
but not ever I criticize

means "but (they) did not ever criticize me,'' not "but I did not ever criticize (anyone).''
 

A clinical parallel: neurological agrammatism

The task of trying to interpret glossed passages in a language we don't know may give us some appreciation for the situation of people whose ability to process syntactic structure is neurologically impaired, even though other aspects of their mental functioning, including their understanding of complex propositions, may be intact.

When there is a lesion in the frontal lobe of the left cerebral hemisphere, the result is often a syndrome called Broca's aphasia. The most important symptom is an output problem: people with Broca's aphasia cannot speak fluently, tend to omit grammatical morphemes such as articles and verbal auxiliaries, and sometimes can hardly speak at all. Their comprehension, by comparison, seems relatively intact.

However, under careful study their ability to understand sentences turns out to be deficient in systematic ways. They always do well when the nouns and verbs in the sentence go together in a way that is much more plausible than any alternative: "It was the mice that the cat chased,'' "The postman was bitten by the dog,'' and so forth. If more than one semantic arrangement is equally plausible, e.g. "It was the baker that the butcher insulted,'' or if a syntactically wrong arrangement is more plausible than the syntactically correct one, e.g. "The dog was bitten by the policemen,'' then they do not do so well.

Representations of syntactic structure

One common way to represent syntactic structure is in terms of a type of graph structure known as a "tree". This can be presented in the form of a "labelled bracketing", in which paired parentheses or brackets are used to represent the hierarchical structure; or equivalently as a tree diagram. You can explore these representations in the output of the online version of a recent parser from UC Berkeley.

An essentially equivalent representation is in terms of lexical "dependencies". The recentt Universal Dependencies project aims to provide a vocabulary of dependency-ggrammar types for all of the world's languages.

Here are a tree diagram and a dependency diagram illustrating essentially the same structure for the same sentence. The tree diagram comes from the Berkeley parser. The dependency diagram below it comes from a page illustrating the output of a Stanford-based software project. The differences underline the fact that there can be different conventions for representing the same structure, in whatever system.

We don't expect you to master the intricacies of these systems -- the point is to illustrate some of the ways that the basic idea of recursive message structure can be carried out systematically.

(ROOT
  (S
    (ADVP
      (NP (DT This) (NN time))
      (IN around))
    (, ,)
    (NP (PRP they))
    (VP (VBP 're)
      (VP (VBG moving)
        (ADVP (RB even) (RBR faster))))
    (. .)))

det(time-2, This-1)
nmod:npmod(around-3, time-2)
advmod(moving-7, around-3)
nsubj(moving-7, they-5)
aux(moving-7, 're-6)
root(ROOT-0, moving-7)
advmod(faster-9, even-8)
xcomp(moving-7, faster-9)


A popular open-source dependencyparser is spaCy, with a demo available here.

Online demos of a dependency parser and a constituency parser from the Allen Institute for AI are available at the links.

A constituency parser from CMU can be found here.



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