ELSJ Spring Forum 2017
April 24, 2017
Meiji Gakuin University

A Relabeling Analysis of*English Possessives
Jason Ginsburg
Osaka Kyoiku University

Sandiway Fong**
University of Arizonajginsbur@cc.osaka-kyoiku.ac.jp

sandiway@email.arizona.edu*Supported by Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research#16K02769**Currently on leave at Kyoto University

1Outline• Data• Core Assumptions• Combinatorics (the model)• Examples• Conclusion

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Data

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English possessive DPs• In English, of-insertion is regular but there is variation in thedeployment of the double genitive.
(1)
a. my friend/the friend of mine/*the friend of mine’s
b. your friend/*the friend of your/the friend of yoursc. his friend/the friend of his/*the friend of his’(s)d. her friend/*the friend of her/the friend of herse. their friend/*the friend of their/the friend of theirs
4English possessive DPs
How do possessives work?
(2) my friend• Assume that this is a DP with head ‘s. D needs Case (has uCase), but D also checks uCase on friend(3) the friend of mine
• friend is the underlying object of my• Why isn’t friend pronounced in object position?
• There is a possession-type relation between my and friend.
• Compare (4a-b) (cf. Barker 1998). In 4a, John owns the picture. In (4b), the picture is of John.
(4) a. a picture of John’s hangs in the gallery
b. a picture of John hangs in the gallery• Why don’t you say any of these:(5) a. *the friend of my’sb. *the friend of mine’s
5English possessive DPs• There is variation in the deployment of double genitives(6) the friend of mine vs. *the friend of mine’s(7) *the friend of your vs. the friend of yours(8) the friend of his vs. *the friend of his’s(9) *the friend of her vs. the friend of hers(10) *the friend of their vs. the friend of theirs• Assume that PF rules are at work.
• For example, in (6) mine blocks mine’s, in (7) yours blocks your• my + ‘s + friend = mine(my + ‘s + friend ≠ mine’s, my’s)6Core Assumptions

7Proposal• Theoretical underpinnings:• Minimalist framework of Chomsky (2013) – free Merge, labeling• Cecchetto and Donati’s (2015) relabeling proposal (for relative clauses)• Result:• We show how target examples (English possessives) can be computed

8Merge• Merge is free (Chomsky 2004, 2005, 2013, 2015)• no feature-driven movement• Internal Merge (IM) and External Merge (EM) are free
• IM and EM are both freely available*
External Merge of X with Y

Internal Merge of Y with X*A Chomsky 2017 lecture (University of Arizona) suggests IM is preferred over EM for minimal search reasons. Also see Shima (2000).

9Set Merge: Labeling(a) Head X labels(b) Head X is too weak to label
unless strengthened(c) No label(d) Y labels if XP moves out• Not all copies of XP are within
this Syntactic Object (SO)
• Y is not weak

• External Set Merge is free
• Internal Set Merge is free10

Strengthening• R is weak
• In (a), categorizer X labels• In (b), phase head y* transmits uPhi (and Case valuing) to R.
• Agree(R,XP) checks uPhi on R• <ɸ,ɸ> labels, as R and XP have identical ɸ-features• strengthened R may label {R,XP} (* represents strengthening)• In (c), n* strengthens R(a)

(b)

(c)

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Pair Merge
PM is asymmetric Merge
Y is on a separate plane (Y not visible to SELECT, nor AGREE, nor labeling).
(a) Y is externally PM’ed with ZP(b) Y is internally PM’ed with XP

Internal and external PM are free (cf. Richards 2009, Epstein, Kitahara, & Seely 2016) 12

Combinatorics (the model)

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Towards Efficient Computation• Recursive Free Merge can be a computational nightmare, but how
bad is it?

• free Merge means displacement is not feature-driven (old EPP/Edge feature)• Faculty of Language (3 factors), Chomsky (2005):• Genetic endowment: Merge, Labeling etc.
• Experience• Third Factor (incl. principle of efficient computation)• Possible limits on Merge• filtered by Labeling (CI interface transfer: triggered at a phase)• selection (root + categorizer)• efficient computation: e.g. no duplicate structures, no infinite loops, etc.
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Unrestricted Set Merge• Consider two heads r and n:
How many way to merge them?
recursively apply:
ESM: External Set Merge
Merge current SO withsome other SO in theworkspace
ISM: Internal Set Merge
SELECT a (proper) sub-SO of
the current SO to merge toitself

Initial workspace (WS): r, n
• 1 Merge:• {r,n}• 2 Merges• `{r,{r,n}}, {n,{r,n}}• 3 Merges• {{r,n},{r,{r,n}}}, {n,{r,{r,n}}},{r,{r,{r,n}}}, {{r,n},{n,{r,n}}},{n,{n,{r,n}}}, {r,{n,{r,n}}}• etc..
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Unrestricted Set Merge• Consider two heads r and n:
How many way to merge them?
• y-axis ☞: log10(#SOs)

1098

Syntactic Objects# Syntactic Objects (SO)log(#SOs)

4,000,000,000

73,500,000,000

63,000,000,000

52,500,000,000

Answer:without duplicates,#SOs = n!
(n=# Merges)

42,000,000,000
1,500,000,000

31,000,000,000

2500,000,000

100

246

# Merges permitted

8

10

120
12

34567

# Merges permitted

891016

Free Merge Constraints• In just three steps, Internal Set Merge(ISM) can create duplicates SOs• Example: in {r,{r,n}}by selecting either copy of r,
ISM can create same SO {r,{r,{r,n}}}A possible 3rd factor constraint: noduplicate SOs• can be eliminated cheaply• Memorization: i.e. must be able tospot duplicates locally• Derivation Tree:Start: SO: r, Input: [n]1.ESM, SO: {r,n}, Input: []1.1.ISM, SO: {r,{r,n}}, Input: []1.1.1.ISM, SO: {r,{r,{r,n}}}, Input: []1.1.2.ISM, SO: {{r,n},{r,{r,n}}}, Input: []1.1.3.ISM, SO: {r,{r,{r,n}}}, Input: []1.1.4.ISM, SO: {n,{r,{r,n}}}, Input: []1. 2.ISM, SO: {n,{r,n}}, Input: []1. 2. 1.ISM, SO: {n,{n,{r,n}}}, Input: []1.2.2.ISM, SO: {{r,n},{n,{r,n}}}, Input: []1.2.3.ISM, SO: {r,{n,{r,n}}}, Input: []1.2.4.ISM, SO: {n,{n,{r,n}}}, Input: []17

Free Merge Constraints• Eliminating duplicate SOs:

• X-axis: number of Set Merges (SM)• Y-axis ☟: number of SOs built• Y-axis ☞: log number of SOs built• Orange line: allowing duplicates• Blue line: with no duplicates

Number of SOs: logscale
12.00

10.00

No duplicates means aslightly more powerful
ISM proof system

8.00

6.00

10000000
9000000
8000000

4.00

7000000
6000000
2.00

5000000
4000000
3000000

0.00
12000000

234log(#SOs)

1000000567

8910log(#Nodups SOs)

01

2

34

5

67891018

Restrictions on Internal Merge• So far just one kind of restriction: no duplicate SOs• e.g. as shown earlier: {c,{a,{b,a}}} = 2 ways => {a,{c,{a,{b,a}}}}• of convenience to the proof system (only?)
Only one kind of repetition• Another kind: block repetitive operations (loops)• enlarge SO without bound (no decrease in WS size)• *𝜋𝜋 where 𝜋 is an IM sequence• e.g. ISM(a) ISM(a) or ISM(a) ISM(b) ISM(a) ISM(b) etc.

permitted (i.e. none),e.g. no rule *𝜋5+ (i.e. you canrepeat up to 4 times but notmore)• Suppose FL always (attempts to) block infinite loops (computational minimalism)• Yet another kind: lemmas: (can be applied proactively)• uF = unvalued feature F• e.g. can’t PM β[uF] to α forming <β, α>, where β is an adjunct• since β is no longer accessible to operations, β[uF] can never get valued
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Combinatorics: <{the,d},{book,n}>• Only convergent threadin the finite
computation tree!
• Statistics:• Nodes: 41• Loops detected: 13• Duplicates: 0• PMergeR: 15• MergeR: 53• Unlabeled: 17• Derivations: 1• Max # of merges: 8.
Derivations completed.

Combinatorics: the friend of mine
76lOG(#SOs)

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3

2

14 Operations

100

12

3

4

5

6

7

8

910

11

12

13

# Merges
Loops

Duplicates

PMergeR

MergeRCI Interface

Queue

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Combinatorics: the friend of mine
Merge #0

1

2

3

4

5

6

7

8

9

1
2

Branching factor

3
4
5
6
7
8

= Successful derivation(SO shown on previous slide)

910
11
12
13

Heads: [friend,n!case,[me,n!case,'s,d*],n*!case,[the,d]]

1011

12

13

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Examples23

Derivations• SM and PM are free• EM and IM are free• Labeling occurs at the phase level• Complement of phase head is transferred• Phase head transfers inflectional features to next lower head
• Rules of phonological form apply at transfer (after derivation iscomplete)• We assume no countercyclic operations (e.g. head-movement)• (some) head-movement phenomena can be relegated to Phonological Form (PF)24

Derivations• Merge Restrictions:(a) roots must be categorized (as soon as possible)(b) each categorizer must find its root (with no intervening heads)(c) categorizers can only categorize once
e.g. *{c,{R,{c,R}}} formed with only c and R (R=root, c=categorizer)(d) can’t PM β[uF] to α forming <β,α>, where β is an adjunctsince β is no longer accessible to operations, β[uF] can never get valued• CI Interface Restriction:(a) *<nP,nP>, *<dP,dP>• Interface expects <dP,nP>

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my friend• SM me (root) & n• SM ‘s (root)• SM (internal Set Merge) {me, n}

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my friend••••

SM me (root) & nSM ‘s (root)
SM (internal Set Merge) {me, n}
SM d*• uPhi and inherent Case are passed down to root ‘s• Agree(‘s,n)• uPhi checked on ‘s• uCase checked on n
• d* (phase head) triggers transfer• Labeling occurs• Shared ɸ label• Shared ɸ strengthen ‘s à ‘s*• SM friend & n• !case = uninterpretable Case
• n will label at transfer• PM my & friend• Spell-Out• me ‘s friend à my friend
27the friend of mine
• form my friend• PM my friend & friend• internal PM of friend• my friend = adjunct• SM n*• ability to assign inherent Case ispassed down to friend• Agree(friend,n) à n gets inherent
Case, pronounced as of• SM d & the• PM {the,d} & friend of my• {the,d} = adjunct28

the friend of mine
• Spell-Out is tricky• Note that the elements of the tree aren’tordered yet• n has inherent case – spelled out as ofpreceding my friend• me ‘s friend n = minethe d friend InherentCase me ‘s n friend = thefriend of mine

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Conclusions• An account of target possessive constructions in a featureless freeMerge system• A computer model computes all possible structures (perhaps a first)• However, overgeneration can cause issues:• Examples:(11) *the friend the(12) *the friend of the• Perhaps assume that the (and a) can never be stranded in English• Other puzzle:(13) #Mary’s friend of yours• on the intended reading: Mary’s friend & friend of yours• a problem to be resolved past CI Interface’s door?
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Spotted yesterday…

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References
Barker, C. 1998. Partitives, double genitives and anti-uniqueness. Natural Language and Linguistic Theory 16:679-717.
Bernstein, J.B. and C. Tortora 2005. Two types of possessive forms in English. Lingua 115:1221–1242.
Cecchetto, C. and C. Donati. 2015. (Re)labeling. Cambridge, MA: MIT Press.
Chomsky, N. 1986. Knowledge of Language. Westport, CT: Praeger.
Chomsky, N. 2004. Beyond explanatory adequacy. In Belletti, A. (ed.), Structures and beyond: The cartography of syntactic structures, vol. 3, 104-131.
Oxford: Oxford University Press.
Chomsky, N. 2005. Three factors in language design. Linguistic Inquiry 36: 1-22.
Chomsky, N. 2007. Approaching UG from below. In Sauerland, U. & Gartner, H.-M. (eds). Interfaces + Recursion = Language?, 1-29. New York: Mouton deGruyter.
Chomsky, N. 2013. Problems of projection. Lingua 130:33-49.
Chomsky, N. 2015. Problems of projection: Extensions. In Domenico, E. D., Hamann, C., Matteini, S. (eds.) Structures, strategies, and beyond – studies inhonor of Adrianna Belletti, 3-16. Amsterdam: John Benjamins.
Epstein, S. D., Kitahara, H., & Seely, D. 2016. Phase cancellation by external pair-merge of heads. The Linguistic Review 33: 87-102.
Oishi, M. 2015. The hunt for a label. In Egashira, H. et al (eds.) Untiring Pursuit of better alternatives, 222-334 Tokyo: Kaitakusha.
Richards. M. 2009. Internal pair-merge: The missing mode of movement. Catalan Journal of Linguistics 8: 55-73.
Shima, E. 2000. A preference for Move over Merge. Linguistic Inquiry 31: 375-285.

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