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Making copies: Insights from computation
Greg Kobele
Reduplicative Processes in Grammar
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 1
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CTM
provides means of understanding copy constructions
Makes particularly salient
External syntaxdistribution in clause
Doesn’t have much to say
about internal syntax of copies, or about how copies are made
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The question
What is the internal syntax of copies?what do copies look likewhat kinds of things can be copied. . . and what kind of mechanism makes copies
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Not all formalisms can describe copying
In phonology
FSOTSPE (à la Kaplan & Kay)
In syntax
GPSGGB (à la Rogers)WG
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Copying doesn’t come for free
What mechanisms can generate copies at all?separate this question from:
hierarchies of functional projections
the ‘right’ structure
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How to tell?
wcw
{wcw : w 2 {a, b}⇤}
a sentence is in this language iff1 it has exactly one c
2 the material to the left of c is identical to the material to its right
if you cannot describe this language
you cannot describe copying
if you can describe this language
I’m interested in what you can do
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(Some) mechanisms
AdjunctionIndexed rewritingMovementCopy movement
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Adjunction
Lexicon
S
c
S
a S
S� aS
b S
S� b
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Adjunction
Lexicon
S
c
S
a S
S� aS
b S
S� b
S
c
S
a S
S� a
S
b S
S� b
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Adjunction
Lexicon
S
c
S
a S
S� aS
b S
S� b
S
a S
S
c
a
S
b S
S� b
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Adjunction
Lexicon
S
c
S
a S
S� aS
b S
S� b
S
a S
b S
S
S
c
a
b
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Indexed rewriting
Rules
S[↵] ! xS[x↵]
S[↵] ! T[↵]
T[x↵] ! T[↵]x
T[] ! c
S[]
a S[a]
b S[ba]
T[ba]
T[a]
T[]
c
a
b
Derivation
S[] ) aS[a] ) abS[ba] ) abT[ba] ) abT[a]b ) abT[]ab ) abcab
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Reduplicative Processes in Grammar 9
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
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Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
� :: x z ya :: ⇤ x ⇤ z A z
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
<
a :: ⇤ z A z � :: z y
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
� :: y <
a :: A z t
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
� :: y <
a :: A z t
a :: ⇤ A ⇤ y x y
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
<
a :: ⇤ y x y >
� :: y <
a :: z t
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
� :: <
a :: x y >
t <
a :: z t
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
� :: <
a :: x y >
t <
a :: z t
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
� :: <
a :: x y
a :: z
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
b :: ⇤ x ⇤ z B z >
� :: <
a :: x y
a :: z
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
<
b :: ⇤ z B z >
� :: <
a :: y
a :: z
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
<
b :: ⇤ z B z >
� :: <
a :: y t
a :: z
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
<
b :: B z >
� :: <
a :: y t
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
<
b :: B z
a :: y
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
b :: ⇤ B ⇤ y x y >
<
b :: B z
a :: y
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
/ 25
Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
<
b :: ⇤ y x y >
<
b :: z
a :: y
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
<
b :: x y >
<
b :: z t
a ::
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
/ 25
Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
� :: ⇤ x ⇤ z w >
<
b :: x y >
<
b :: z t
a ::
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
/ 25
Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
<
� :: ⇤ z w >
<
b :: y >
<
b :: z t
a ::
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
/ 25
Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
>
<
b :: t
<
� :: w >
<
b :: y t
a ::
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
/ 25
Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
<
c :: ⇤ y s >
>
<
b :: t
<
� :: >
<
b :: y t
a ::
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
/ 25
Movement
Lexicon
a :: ⇤ x ⇤ z A z a :: ⇤ A ⇤ y x y ✏ :: ⇤ x ⇤ z wb :: ⇤ x ⇤ z B z b :: ⇤ B ⇤ y x y c :: ⇤ w ⇤ y s
✏ :: x z y
>
>
<
b :: t
<
c :: s >
>
<
b :: t
<
� :: ta ::
a ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 10
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Copying
Lexicon
a :: ⇤ x x ✏ :: xb :: ⇤ x x ✏ :: ⇤ x s z
c ::⇤ s ⇤ z s
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 11
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Copying
Lexicon
a :: ⇤ x x ✏ :: xb :: ⇤ x x ✏ :: ⇤ x s z
c ::⇤ s ⇤ z s
<
c :: ⇤ z s <
� :: z <
a :: <
b :: � ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 11
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Copying
Lexicon
a :: ⇤ x x ✏ :: xb :: ⇤ x x ✏ :: ⇤ x s z
c ::⇤ s ⇤ z s
>
<
� :: <
a :: <
b :: � ::
<
c :: s <
� :: <
a :: <
b :: � ::
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 11
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2-MCFLwn
Different mechanisms, same patterns
TAGCCGTree-local MCTAGMCFTGLIG
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 12
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MCFLwn
Different mechanisms, same patterns
ACG(2,3)CFTG
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 13
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MCFL
Different mechanisms, same patterns
MGSet-local MCTAGACG(2,>3)MCFGSTR(CFHG)MSOT(REG)
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 14
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PMCFL
Different mechanisms, same patterns
CMGalmost-linear ACG(2,>3)PMCFG
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 15
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Take home message
Patterns are real
grammars are a mode of presentation of underlying patterns
Meaningful to ask
which patterns are instantiated in NL?
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 16
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Inclusion diagram
CFL = 1-MCFL = 1-MCFLwn
2-MCFL
1-PMCFL2-MCFLwn
3-MCFL
2-PMCFL3-MCFLwn
3-PMCFL
...
...
...
MCFL
PMCFL
MCFLwn
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 17
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Separating MCFLwn from MCFL
The copying theorem (Kanazawa & Salvati, 2010)
if L = {wcw | w 2 L0} is a MCFLwn then L0 is generable by anon-branching MCFG
Translation: only simple things (L0) can be copied
L0 cannot necessarily involve branching structures⇤give [a good book] [to a nice student]
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 18
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The first question
Question 1
Are only structurally trivial things copyable?gk conjectures: no!
A no answer means
TAG, CCG, etc are wrong
A yes answer means
Huge confirmation of a deep prediction of TAG, CCG
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 19
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Separating MCFL from PMCFL
Semilinearity
intuition: Operations add a fixed, finite amount of structural elements
Translation: copies cannot be copied
a ) aa 6) aaaa
Exponential growth is just recursive doubling
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 20
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The second question
Question 2
Can copies be made of copies (of copies . . . )?gk conjectures: yes!
A no answer means
Huge confirmation of mild-context sensitivity hypothesis
A yes answer means
Hypothesis of mild-context sensitivity (Joshi, 85) is wrong. . . and with it most restrictive grammar formalisms
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 21
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The limits of full copying
Non-semilinear patterns
must involve exact copying
Translation: recursive copying must be exact
only recursive copying is truly copyingnon-recursive copying can just as easily generate opposite
‘copies’wcw = {aca, abcab, abbcabb, . . .}
let a = b and b = a; can’t have
a ! ba ! abba ! baababba ! abbabaabbaababba
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 22
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The third question
Question 3
Can we have non-exact (i.e. structure-only) copying in recursive copyconstructions?
gk conjectures: No!
Greg Kobele Making copies: Insights from computation
Reduplicative Processes in Grammar 23
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Conclusions
There are deep and fundamental questions that we need to askabout copying
is copying always small?
is copying only of simplexes?
is copying recursive?
The answers to these will sink various approaches to grammarOnce we know what patterns there are, we can focus on comingup with an elegant description language
Greg Kobele Making copies: Insights from computation
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