Compu&ng)Minimalism)sandiway/mpp/cuny2012.pdf · 2012. 3. 15. · Compu&ng)Minimalism)...
Transcript of Compu&ng)Minimalism)sandiway/mpp/cuny2012.pdf · 2012. 3. 15. · Compu&ng)Minimalism)...
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Compu&ng Minimalism
Sandiway Fong Departments of Linguis&cs and Computer Science
University of Arizona
25th Annual CUNY Conference on Human Sentence Processing. March 14-‐16, 2012.
this work is in part jointly developed with Jason Ginsburg, U. of Aizu, Japan
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Minimal Computa&on (MC) Chomsky (2011) • language is a computa&onal system:
– Genera&ve Procedure (GP) – Parsing Procedure (PP)
• we should consider computa2onal efficiency, but… • when it comes to Minimal Computa&on (MC):
– conflicts between GP and PP are always resolved in favor of GP
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Minimal Computa&on (MC) • Chomsky (2011)
.. explore idea that the Genera&ve Procedure (GP) and Parsing Procedure (PP) share architecture PP can help GP minimize computa2on
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What cons&tutes an implementa&on?
• Minimalism: – (Chomsky 2001) and later papers
• Components of the theory: 1. Recursive Merge (internal/external) 2. Probe/Goal search (ac&ve/inac&ve) 3. Agreement (value Case, interpretable/
uninterpretable features) 4. Phases (limits on search)
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What cons&tutes an implementa&on?
excerpt from Deriva2on by Phase
Grammar formalisms e.g. Stabler (1998), (2011) (Lecomte & Retoré) 2001
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What cons&tutes an implementa&on?
agree(a,n) -‐ed: uφ, uCase n: φ, uCase
agree(tdef,n) tdef: uφ n: φ, uCase
①
①
②
②
agree(t,n) t: uφ, Nomina&ve n: uφ
agree(t,n) t: uφ, Nomina&ve n: φ, uCase
③
③
④
④
*actually, should need agree(t,a) as well to value Case on PRT
one probe, mul&ple goals: matrix T agrees with 3 goals
implementa&on op&mizes this away: uCase can be unified during agree
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What cons&tutes an implementa&on?
Numera'on: no pleonas&c there
probe [a!case ed] agrees with goal [n!case several prizes]�probe [tdef] agrees with goal [n!case several prizes]�probe [t] agrees with goal [n several prizes]�
same number of Merge steps as before
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Computa&on steps • Genera&ve Procedure (GP)
Spell-‐Out several prizes are likely several prizes to be awarded several prizes
Procedure: effec&vely determinis&c if we spoon feed the machine the numera&on
step-‐by-‐step examples @ hip://dingo.sbs.arizona.edu/~sandiway/mpp/dbyp/examples/
Computa'onal complexity? α #merge steps + β #nodes probed + …
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Minimal Computa&on • overriding condi&on of Minimal Computa'on (MC) means design for the Genera've Procedure (GP):
– “whenever efficiency of design and communica2on conflicts: design wins”
• no Parsing Procedure (PP) is specified – parsing need not be efficient
• Example: – several prizes are likely several prizes to be awarded several prizes
Chomsky (2011)
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Design Minimalism Genera&ve Procedure (GP) • Design minimalism:
– good for complexity, but what about data? • Limits on deriva&on
conserva&on of syntac&c objects (SO) – e.g. only copies, can’t create indices
• Problem for modules e.g. Binding theory (BT) – no Free Indexa&on – no theory-‐internal levels of representa&ons – no Binding Condi&ons A, B and C
assuming we s2ll want to have a syntac2c BT …
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Growing the implementa&on Binding theory (joint work with Jason Ginsburg, U. of Aizu, Japan) • Idea:
– doubling cons'tuent (DC), adapted from Kayne (2002) – e.g. [he John]
– Phases: derive distribu&onal differences between pronouns and anaphors
[TP John thinks [TP [he John] [v is [AP smart [he John]]]]]
uCase, iφ, theta Merge related work: Zwart (2002) Heinat (2003)
John thinks John he is smart John he
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Johni thinks hei is smart
scoreboard he John
lacks theta, Case theta, Case
licensed
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Johni thinks hei is smart
scoreboard he John
lacks Case theta, Case
licensed theta
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Johni thinks hei is smart
scoreboard he John
lacks Case theta, Case
licensed theta
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Johni thinks hei is smart
scoreboard he John
lacks theta, Case
licensed theta, Case
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Johni thinks hei is smart
scoreboard he John
lacks theta, Case
licensed theta, Case
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Johni thinks hei is smart
scoreboard he John
lacks theta, Case
licensed theta, Case
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Johni thinks hei is smart
scoreboard he John
lacks theta, Case
licensed theta, Case
phase boundary Essen'al idea: probe-‐goal search has limited range Suppose r-‐expr with unvalued uninterpretable feature at the limit of search is allowed to undergo theta Merge … obviously, 2ming is cri2cal
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Johni thinks hei is smart
scoreboard he John
lacks Case
licensed theta, Case theta
Last Resort (LR): theta Merge
Note: needed for all theories with a Doubling Cons&tuent (DC)
inaccessible
s2ll accessible
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Johni thinks hei is smart
scoreboard he John
lacks
licensed theta, Case theta, Case
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Johni thinks hei is smart
Spell-‐Out John John thinks he John is smart he John John thinks he is smart
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Data • Analysis of classic BT data:
– *Johni praises himi – Johni praises himselfi – Johni thinks hei is smart – *Hei thinks Johni is smart – *Johni thinks himselfi is smart – *Johni thinks that Mary likes himselfi – Johni considers himselfi to be intelligent – *Johni considers himi to be intelligent – Johni likes hisi dog – *Johni likes himselfi’s dog – ?*Hannahi found a picture of heri – Hannahi found a picture of herselfi – ?*Hannah found Peteri’s picture of himi – Hannah found Peteri’s picture of himselfi – Hannahi found Peter’s picture of heri – Hannahi found Peter’s picture of herselfi – etc.
assume the DC for anaphors is different to begin with [D [D self][N he John]]
phase boundary
step-‐by-‐step examples @ hip://dingo.sbs.arizona.edu/~sandiway/mpp/binding/examples/ also paper
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More Data • double objects
– I showed John to himself in the mirror – *I showed himself to John in the mirror – I showed John himself in the mirror – *I showed himself John in the mirror
step-‐by-‐step examples @ hip://dingo.sbs.arizona.edu/~sandiway/mpp/binding2/examples/ also poster (TCP 2012) hip://dingo.sbs.arizona.edu/~sandiway/mpp/TCP2012.pdf
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Even More Data
DC for tough movement Hicks (2009) [Op John] (Op = empty operator) “smuggling opera2on”
step-‐by-‐step example @ hip://dingo.sbs.arizona.edu/~sandiway/mpp/hicks/examples/ tenta&ve analysis only …
Spell-‐Out John is tough [Op John] PRO to PRO please [Op John] John is tough to please
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Computa&onal Complexity Phases • Long distance:
– Johni thinks that Peter*i thinks that Mary thinks that Bill*i likes himi
• Cost of locality: – probe-‐goal search is local – iterated movement to the edge of a Phase
coreference possibili'es: [he John] preferred over [he Peter]
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Phases
without a Buffer, would need iterated movement to the edge of each marked phase
Computa'onal complexity α #merge steps + β #nodes probed + …
phase boundary
matrix T will airact John
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Computa&onal Complexity Phases • Long distance:
– Johni thinks that Peter*i thinks that Mary thinks that Bill*i likes himi
• Cost of locality: – probe-‐goal search is local – iterated movement to the edge of a Phase
coreference possibili'es: [he John] preferred over [he Peter]
comes with possible complica'ons: edge feature management order of goals: “tuck in”
• Alternate implementa'on – eliminate iterated movement of this sort (smaller trees) – use a Buffer (for theta Merge) – no extra ambiguity – Preference: external Merge < internal Merge < Buffer
where does this Buffer come from?
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Genera&ve and Parsing Procedures
• Idea: – Genera&ve Procedure (GP) and Parsing Procedure (PP) are not separate devices
GP PP
share grammar, data formats and memory devices
– but GP has priority over PP (Minimal Computa&on)
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Genera&ve and Parsing Procedures
GP
sequence of Merges can be had from an in-‐order traversal but repor&ng Merges on the way back up…
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Genera&ve and Parsing Procedures
PP In-‐order traversal: top down le� to right expansion
probe [a!case ed] agrees with goal [n!case several prizes]�probe [tdef] agrees with goal [n!case several prizes]�probe [t] agrees with goal [n several prizes]�
Two problems peculiar to parsing that must be dealt with
1. displacement without all copies being pronounced
2. empty heads (t,v and others)
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Parsing Procedure (PP)
• Implementa'on summary 1. le�-‐to-‐right, incremental expansion of the
covering grammar: • no need to recode GP
2. probe-‐goal: GP, PP nearly the same • 'ming issues: ac&ve/inac&ve goals
3. displacement: must put copies in gap posi&ons • need some memory device: Buffer • poten&al ambiguity (fill from input or Buffer)
4. empty heads: e.g T/Tdef, v/v* • PP (ambiguity), GP (no ambiguity, part of numera&on)
same traversal GP: report Merges on way back up PP: lazy evalua&on (freeze)
GP: Buffer = internal Merge
p g
c-‐command domain
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Several prizes are likely to be awarded
Note: introduced probe T its c-‐command domain doesn’t exist yet… freeze probe-‐goal search
At this point we know there is a copy of several prizes downstream but where exactly.. we don’t yet have enough informa2on
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Several prizes are likely to be awarded
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Several prizes are likely to be awarded
op&on 1: copy Buffer into open lower spec-‐T matrix T probe finds its goal
Note: introduced probe Tdef freeze probe-‐goal search
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Several prizes are likely to be awarded
alternate choice: don’t drop several prizes into subject posi&on
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Several prizes are likely to be awarded
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Several prizes are likely to be awarded
Note: introduced probe PRT –ed freeze probe-‐goal search
actually.. two out of the three probes are concurrently opera&ng
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Several prizes are likely to be awarded
copy Buffer into open object posi&on
probes Tdef and PRT find their goal
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Several prizes are likely to be awarded
alternate choice: don’t drop several prizes into open object posi&on
probes Tdef and PRT s&ll pending
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Several prizes are likely to be awarded
Local ambiguity
step-‐by-‐step examples @ hip://dingo.sbs.arizona.edu/~sandiway/mpp/cuny2012/examples/
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Summary
• theory: Chomsky (2001+ …) • implement: merge, agreement, probe-‐goal search, phases
• GP and PP share architecture: – traverse grammar in same way – same probe-‐goal algorithm – MC: we need a memory device to handle displacement – PP buffer shared
GP PP
GP: buffer used in DC analysis for pronoun binding
improves GP from the standpoint of MC
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Appendix
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Principles and Parameters Approach
parser opera&ons corresponding to linguis&c principles
PAPPI: Fong (1990)
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Principles and Parameters Approach
correct parse Generate and test: 33 candidate parses examined by the parser most are eliminated early by Case/Theta theory sub-‐system
Case/Theta
Binding Passed all constraints