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Categories and constituents

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Title: Categories and constituents


1
Categories and constituents
2
Categories and constituents
  • Two goals first, to build up slowly the ideas of
    category and constituent in grammar, so that it
    does not seem obvious.
  • Second, to prepare the way to see the connection
    between constituents in a phrase-structure
    grammar and certain symbolic approaches to mind.

3
Two points of view
  • 1 Whats real and central in grammar are notions
    like Noun and Verb (and Noun Phrase and Verb
    Phrase). Then we find real nouns, like dog and
    John and Monday. Many of them are good nouns, but
    some of them are defective they dont do all
    the things that they should do.

4
2nd point of view
  • Whats real are sentences (or corpora)
  • John is leaving Wednesday with his dog.
  • When we look at a language, we find an enormous
    range of places where a given word can appear.
    (Places meaning environments, perhaps
    meanings). No two words are quite alike, but
    words do form clusters with regard to their
    grammatical behavior. For example, ...

5
  • The days of the week (MondaySunday) share a lot
    in common. We can simplify our description by
    generalizing over that set of words.
  • Likewise, Proper given names (John, Jerry, ).
  • As we form larger and larger classes, there are
    fewer things that they have in common.

6
  • Categories we have 4 things in mind when we make
    them
  • 1. (Lexical categories) Morphology
  • 2. Meaning (semantics)
  • 3. External distribution
  • 4. (Phrasal categories) internal distribution
  • ...

7
Morphology
  • What suffixes may appear with a given stem s,
    NULL, s
  • ed, s, ing, ed
  • er, est, ness

8
Meaning
  • Reference to objects in the world
  • Reference to n-ary predicates
  • unary tall, sleep
  • binary eat (human, food), saw (human, object)
  • ternary give (human, human, object)

9
External distribution
  • Roughly speaking this means, what this word (or
    phrase) can appear next to (before, after).
  • Nouns appear after articles (noun determiners,
    nominal determiners), after adjectives. before
    Prepositinal Phrase complements.
  • the dog, my dog, the taste of champagne, the war
    of the worlds

10
Internal distribution (phrases)
  • A noun phrase has three parts a determiner,
    followed by an adjective, followed by a noun.
  • Some of these are optional that is, we may
    still call something an noun phrase even if not
    all 3 are present.

11
Classical view of categories
  • Gardner (340f.) By the middle of this century, a
    certain position had become entrenched as the
    right way to think about categories, concepts,
    and classificationAnd yet in the past
    thirty-five years, during the very period when
    cognitive science has been in the ascenancy, this
    view of how we categorize the world has undergone
    the most severe attack, until today virtually no
    one holds it in its pure form.

12
Classical view
  • (Bruner) a category was arbitrarily defined
    (any set of attributes could have been targeted),
    and each item unambiguously fitted (or failed to)
    into that category. The traditional recipe a
    category and a set of defining features, just
    like the featherless biped.PhilosophersAnthropol
    ogistsnneuroscience, a search was on for
    detectors that registered unambiguously to all
    lines that were oriented in a certain direction
    but to none otherwise oriented. 341

13
  • Cf also Lakoff, Women, Fire, and Dangerous Things.

14
  • (Gardner) 1. Categories are arbitrary. Nothing
    in the world or in our nervous system determines
    how we must slice up our observations. Cutures
    and languages do this work. Items can be grouped
    together in any number of ways to form
    categories, and people can learn to identify or
    construct those categories defined by their
    culture.
  • 2. Categories have defining or critical
    attributes. All membersshare these defining
    attributes, no nonmembers share them, and there
    is no overlap between members and nonmembers.

15
  • 3. The intension (or set of attributes)
    determines the extension of a category (which
    items are members). Hence it makes no sense to
    talk about a category as having an internal
    structure, with some items standing out as better
    members than other items. Boundaries are sharp
    and not fuzzy.

16
  • When applied to categories, this meant that to
    know a category was to have an abstracted
    clear-cut, necessary, and sufficient criteria
    sic for category membership. If other thought
    processes, such as imagery, ostensive definition,
    reasoning by analogy to particular instances, or
    the use of metaphors were considered at all, they
    were usually relegated to lesser beings such as
    women, children, primitive people, or even to
    nonhumans. (Rosch and Lloyd, cited 342).

17
  • Rosch work on prototype categories
  • Berlin and Kay on color categories
  • Wittgenstein on family relations among
    categories, evolving into radial categories.

18
Back to categories for words (etc)
  • Noun properties (?English)
  • Takes articles
  • Takes preceding adjectives
  • May appear as subject of a sentence
  • May appear as object of a preposition
  • Has singular and plural form plural is realized
    as /s/
  • Refers to an object or set of objects
  • May take possessive s
  • May serve as antecedent to a pronoun

19
  • Verb
  • Has present-tense form (-s in 3rd singular)
  • Has past-tense form (-ed)
  • Agrees with its subject noun phrase
  • Refers to a predicate (1 or more arguments)
  • Follows the subject immediately
  • Appears at the beginning of a verb-phrase

20
Where this is heading...
  • We may think of behaviors of a word and not
    just words as a vast set of attributes, each of
    them a value along a dimension. Lets say there
    are n dimensions (n is a number). Then a given
    word is a set of specifications for those n
    attributes.
  • Categories are clusters of such points, or
    regions in that space.

21
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22
Hypostatization
  • taking the color of the wine bottle for the color
    of the wine.
  • In this case, our goal is to see that we develop
    categories like lexical category and constituent
    in order to better understand linguistic facts,
    like distribution then we take category and
    constituent to be real, and forget where they
    came from.

23
Is that wrong? bad?
  • Probably. The jurys still out. Its not expected
    back soon.
  • A big issue -- one that separates the first and
    second cognitive revolutions -- is whether there
    is a role to be played by cognitive
    representations in this case, syntactic
    representations -- our beloved trees.

24
The first cognitive revolution
  • thoroughly endorsed syntactic trees

S
VP
NP
PP
N
V
det
P det N
the cat is on the mat
25
  • and said that somehow or other, trees like this
    are in the mind.
  • Whatever that might mean.

26
Connectionist-style models
  • do not (appear to?) fare well with
    representations of this sort.
  • So ultimately one must choose between the models
    and the representations.
  • Maybe its good enough for the connectionist
    models to deal with the facts that the
    representations were invented to deal with.

27
  • Were a bit in the same state that Einstein and
    his cohort had to deal with with regard to
    old-style Newtonian time do you keep to it, or
    do you (following Mach) say that time is just one
    way to organize the facts, and the facts are what
    we really care about organizing?

28
Words, Categories, Languages
  • There are many ways to think about sentences in a
    language.
  • Even trying to classify different ways to think
    about language is hard.
  • One great divide separates those focusing on
    given corpora (singular corpus), and those on a
    grammar abstracted away from any given corpus.

29
Whats real?
  • Is it the corpus -- the utterances?
  • Or is it something more abstract that (perhaps)
    gave rise to the utterances -- perhaps an
    ability, a capacity?
  • Mach, of course, would choose the first of these.
  • Is that choice liberating or repressive?

30
  • Its liberating if you think it means you can use
    any description that you want, since no one is
    more real or less real than any other.
  • Its repressive if you think it means that no
    theory is worth developing.

31
Lets take Mach seriously...
  • and ask what linguistic science can do to
    compress or abbreviate the observed data.
  • First of all, there are words...

32
Words, first
  • There are many words in a language
    (10,000-100,000). How complex or how simple is a
    description going to be that tells us what
    combinations will be encountered in English (or
    another language)?

33
Categories, first
  • We may start with a pretheoretic idea that words
    fall into a small number of groups, and the
    behavior of words in each group is pretty much
    the same.
  • Behavior means the decision whether a word can
    appear in a given context or not.

34
Constituents
  • Constituents are useful constructs to help us
    define what contexts means in the preceding
    slide (in a given context).
  • But how, exactly?

35
If we think of words as events in time...
  • we will be very tempted to think of each word as
    being the cause of the next, since causality
    generally seems to go from past to the future in
    this world.
  • This leads us to a model like this

36
1st word...
Emitter
The
37
next word...
Emitter
dog
The
38
Emitter
dog
is
The
39
Emitter
is
on
dog
The
Eventually, The dog is on the mat.
40
  • But sentences are not sequences where each word
    is independent of what precedes it.
  • We could try the hypothesis that the emitter is
    in a particular state after it emits a particular
    word, and that state is responsible for emitting
    the next word, and then transitioning to the next
    state.

41
Here is a view
  • At any given moment, a speaker has uttered a
    certain number of words, and that leaves open
    certain choices for the next word, and closes off
    other choices.
  • Lets let grammar be the study of that.

42
  • Lets say that a person (or speaker, or grammar)

43
Grammatical and lexical words
  • Closed class grammatical, open class lexical.
  • Again, this is an easy intuition to begin with
    well challenge it in a moment. But lets stick
    to it at first.

44
Category
  • Our first intuition is that some simplicity will
    emerge out of the fact that some statements will
    hold for many different words.
  • Templates, simple patterns

45
How many words can be substituted there? Many.
Does that tell us that cat, dog, spot, box, ,
comprise a single category?
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