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Introduction Quantifier-based approach Computational background -NPIs -NPIs Discussion A quantifier-based approach to NPI-licensing typology: Empirical and computational investigations Dissertation defense Mai Ha Vu October 4, 2019

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

A quantifier-based approach to NPI-licensing typology: Empirical and computational investigations

Dissertation defense Mai Ha Vu October 4, 2019

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Outline

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Negative Polarity Items (NPIs)

Definition (Negative Polarity Item)

A negative polarity item α is an expression whose distribution is limited by sensitivity to some semantic property β. β must at least include negation. It shows the following contrast: (1) a. Nancy does not want anything. b. * Nancy wants anything.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

The questions addressed in the thesis

This thesis examines the Quantier-based approach to Negative Polarity Item licensing typology, from two perspectives:

  • Empirical: How adequate is this theory in explaining cross-linguistic dierences in

NPI-behavior?

  • Computational: How computationally complex are the constraints in this approach?

Today, I focus on my computational results.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Goals of this presentation

  • Introduce the quantier-based approach to NPI-licensing typology
  • Provide the necessary formal background
  • Demonstrate how a specic theory can be modeled with computational tools
  • Discuss the eects of choosing a theory on the computational results

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Outline

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Quantifier-based approach

  • In this thesis, I adopt a quantier-based approach to NPI-licensing following the ideas

in Giannakidou (2000).

  • Observation: a sentence like `I did not see anybody' could be expressed semantically

in one of two ways: (2) ∀x[person(x) → ¬ see(I, x)] (3) ¬∃x[person(x) ∧ see(I, x)]

  • Proposal: NPIs can be expressed with dierent quantiers, and that predicts their

syntactic behavior

▶ If they are universal quantiers (∀-NPI), they have to take scope above negation at

Logical Form (LF)

▶ If they are existential quantiers (∃-NPI), they have to take scope below negation (or

NPI-licensor) at LF

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∃-NPIs

  • Existentially quantied NPIs must be in the scope of their licensor at LF
  • Scope-domain is calculated through c-command
  • A node c-commands its sibling and all the nodes its sibling dominates → A node takes

scope over everything it c-commands

. . . . . . . . . NPI∃ . . . licensor

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∀-NPIs

  • ∀-NPIs must scope over negation at LF
  • They do so by undergoing Quantier Raising (QR) and attach to NegP

NegP Neg′ . . . . . . t . . . neg NPI∀

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Cross-linguistic differences in syntactic behavior

∃-NPIs ∀-NPIs Can appear higher than licensor no yes Long-distance licensing yes no Fragment answers no yes Sensitivity to islands no yes Examples English any-NPIs Hungarian se-NPIs ∀-NPIs must scope over negation → They can be higher on the surface then their licensor and not reconstruct: (4) a. * Anybody did not see the movie. b. Sen-ki npi-who nem neg ltta see-pst.3sg a the lm-et. movie-acc `Anybody did not see the movie. = Nobody saw the movie.'

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Cross-linguistic differences in syntactic behavior

∃-NPIs ∀-NPIs Can appear higher than licensor no yes Long-distance licensing yes no Fragment answers no yes Sensitivity to islands no yes Examples English any-NPIs Hungarian se-NPIs QR is clause-bounded → ∀-NPIs must be licensed by clause-mate negation: (11) Some man said every woman visited him. ∃ ≫ ∀, *∀ ≫ ∃ (12) a. Sue doesn't think that Joe would meet with anyone. b. * Sue Sue nem neg gondol-ta, think-pst.3sg hogy that Joe Joe tallkoz-na meet-cond.3sg sen-ki-vel. NPI-who-com `Sue doesn't think that Joe would meet with anyone.'

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Cross-linguistic differences in syntactic behavior

∃-NPIs ∀-NPIs Can appear higher than licensor no yes Long-distance licensing yes no Fragment answers no yes Sensitivity to islands no yes Examples English any-NPIs Hungarian se-NPIs ∀-NPIs can raise above negation, and have the rest of the sentence elided for fragment answers: (19)

  • a. Who did you see? *Anyone I did not see .
  • b. Ki-t

who-acc lt-tl? see-pst.2sg Sen-ki-t NPI-who-acc nem neg lt-t-am . see-pst-1sg `Who did you see? Nobody.'

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Cross-linguistic differences in syntactic behavior

∃-NPIs ∀-NPIs Can appear higher than licensor no yes Long-distance licensing yes no Fragment answers no yes Sensitivity to islands no yes Examples English any-NPIs Hungarian se-NPIs Island sensitivity indicates movement (including QR) → ∀-NPIs are sensitive to islands, because they undergo QR: (26) A student ate a slice of pizza <and/or every slice of cake>. ∃ ≫ ∀, ∗∀ ≫ ∃ (27)

  • a. Sam didn't eat <beans or anything>.
  • b. Most people eat beans and rice and beans and toast, but he doesn't eat <beans

and anything>! (p.c. Bruening) c. * Jancsi Jancsi nem neg eszik eat <bab-ot bean-acc s/vagy and/or sem-mi-t>. NPI-what-acc `Jancsi doesn't eat beans and/or anything.'

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Locality of QR revisited

  • Newer experimental evidence suggests that QR is not actually clause-bound, but

might be a processing eect (Wurmbrand, 2018)

  • Hungarian shows constrast between covert and overt movement:

(28) * Sue Sue nem neg gondol-ta, think-pst.3sg hogy that Joe Joe tallkoz-na meet-cond.3sg sen-ki-vel. NPI-who-com `Sue doesn't think that Joe would meet with anyone.' (29) Sue Sue sen-ki-veli NPI-who-com nem neg gondol-ta, think-pst.3sg hogy that Joe Joe tallkoz-na meet-cond.3sg ti. `Sue doesn't think that Joe would meet with anyone.' (30) Anna Anna sen-ki-veli NPI-who-com nem neg hall-otta, hear-pst.3sg hogy that Sue Sue meg prt gr-te, promise-pst.3sg hogy that tallkoz-na meet-cond.3sg ti. `Anna didn't hear that Sue promised that she would meet with anyone.'

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Overview of the constraints

  • ∃-NPIs: must be c-commanded by negation
  • ∀-NPIs: must c-command negation through movement, AND covert-movement is

clause-bound

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Outline

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Computational complexity

  • A computer uses an algorithm to generate an output
  • If the human cognitive faculty is a type of computer, then it uses grammar to

generate strings in natural language

  • Computational complexity measures the complexity of the grammar: how

mathematically powerful are the tools needed to describe it?

  • The actual grammar of natural language is unobservable directly → we have to rely
  • n the output to infer the grammar, and the output is a string

→ Overarching question: Based on the string outputs, how complex are the most complex patterns in dierent modules of natural language?

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

How complex is natural language?

Finite Regular Context-free Mildly context-sensitive Context-sensitive Recursively-enumerable Syntax Morphology Phonology

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Syntax is mildly context-sensitive?

Joshi's (1985) conjecture, based on Shieber's (1985) observation:

  • Swiss German cross-serial dependency is a mildly context-sensitive pattern

(anbmcndm) (31) ...mer ...we em Hans Hans-dat es the huus house hlfed helped aastriche paint (Shieber, 1985) `We helped Hans paint the house.'

  • Syntax must be powerful enough to generate such patterns
  • BUT: this assumes that the relevant data structure output by the syntax is a string

the string output of syntax is mildly context sensitive

  • What if the we take the relevant data structure to be trees?

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

The complexity of syntactic trees

  • Thatcher (1967): Regular tree languages yield Context-Free string-languages

▶ This brings down the complexity of most syntactic constraints to the regular class of

languages

▶ But, it still does not cover Mildly Context-Sensitive patterns

  • Morawietz's (2003) Two-step approach: describe syntax in two parts

▶ Constraints that restrict the syntactic derivation ▶ Functions to map the derivation to the output(s)

→ if both are Regular, then they can generate Mildly Context-Sensitive string languages For the thesis, I focus on the rst component, on restricting the syntactic derivation, and encode it using derivation trees in the Minimalist Grammars (MGs) framework.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Minimalist Grammars

  • An explicit formalization of Minimalist syntax, rst described (Stabler, 1997)
  • Two components: lexicon and operations
  • Lexicon: a nite set of Lexical Items (LIs), that consist of a phonological component,

a semantic component, and strictly ordered features

▶ Example: [which :: =n d −wh]

  • Operations: originally Merge and Move. In this thesis, I add

▶ S(emantic)-move for movement only at LF ▶ P(honological)-move for movement only at PF ▶ Cluster for movement of multiple items of the same type (e.g. multiple wh-movement),

after Sabel (2001); Grewendorf (2001), formalized for MGs in Grtner and Michaelis (2010)

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Features

Features have four attributes:

  • Name: what is the feature called?
  • Operation: what operation is the feature associated with?
  • Polarity: does the feature have negative polarity or positive polarity?
  • Representation: Does it go with an operation that takes place at PF, LF, or both?

shorthand ν ω π ρ f f Merge − [+sem,+phon] =f f Merge + [+sem,+phon] −f f Move − [+sem,+phon] +f f Move + [+sem,+phon] −sf f Move − [+sem,−phon] +sf f Move + [+sem,−phon] −pf f Move − [−sem,+phon] +pf f Move + [−sem,+phon] Example: [which :: =n d −wh]

  • d means that which has the

category feature d

  • =n means that which selects for an

LI whose category feature is n

  • −wh means that which has a wh

movement licensee feature on it that will have to be satised by Move

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Derivation trees vs. Derived phrase structure trees

  • Derivation trees show the process of the derivation, rather than the output of it
  • Instead of category labels, trees are labeled with the operation (which can be inferred

from the features of the LIs)

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Let's build a tree

(32) Mary likes the car.

TP T′ VP V′ DP car

n

the

=n d

likes

=d =d v

t

d −nom

ε

=v +nom t

Mary

d −nom

Figure 1: Phrase-structure tree

Move Merge Merge Merge Merge car

n

the

=n d

likes

=d =d v

Mary

d -nom

ε

=v +nom t

Figure 2: Derivation tree

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Let's build a tree

(33) Mary likes the car.

TP T′ VP V′ DP car

n

the

=n d

likes

=d =d v

t

d −nom

ε

=v +nom t

Mary

d −nom

Figure 1: Phrase-structure tree

Move Merge Merge Merge Merge car

n

the

=n d

likes

=d =d v

Mary

d -nom

ε

=v +nom t

Figure 2: Derivation tree

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Let's build a tree

(34) Mary likes the car.

TP T′ VP V′ DP car

n

the

=n d

likes

=d =d v

t

d −nom

ε

=v +nom t

Mary

d −nom

Figure 1: Phrase-structure tree

Move Merge Merge Merge Merge car

n

the

=n d

likes

=d =d v

Mary

d -nom

ε

=v +nom t

Figure 2: Derivation tree

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Let's build a tree

(35) Mary likes the car.

TP T′ VP V′ DP car

n

the

=n d

likes

=d =d v

t

d −nom

ε

=v +nom t

Mary

d −nom

Figure 1: Phrase-structure tree

Move Merge Merge Merge Merge car

n

the

=n d

likes

=d =d v

Mary

d -nom

ε

=v +nom t

Figure 2: Derivation tree

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Let's build a tree

(36) Mary likes the car.

TP T′ VP V′ DP car

n

the

=n d

likes

=d =d v

t

d −nom

ε

=v +nom t

Mary

d −nom

Figure 1: Phrase-structure tree

Move Merge Merge Merge Merge car

n

the

=n d

likes

=d =d v

Mary

d -nom

ε

=v +nom t

Figure 2: Derivation tree

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Back to complexity

  • Well-formed MGs derivation trees are regular (Kobele et al., 2007)
  • Ties in to the question of representation vs. logical constraints (Jardine, 2016)

▶ If the output of syntax is represented as a string-language, then we need high

complexity in the logical constraints

▶ If the output of syntax is represented as a tree-language, we can signicantly lower the

complexity of the logical tools needed to describe the patterns

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

The complexity of natural language - revised

Finite Regular Context-free Mildly context-sensitive Context-sensitive Recursively-enumerable Syntactic strings Morphology Syntactic derivation trees Phonology

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Cognitive parallelism hpyothesis

  • Recent work in phonology has found that most phonological patterns are not only

regular, they are subregular (Chandlee, 2014; Jardine, 2016)

  • Basic syntactic operations, such as Merge and Move can also be described with

subregular constraints (Graf and Heinz, 2015) → Proposal by (Graf et al., 2018):

Definition (Cognitive parallelism hypothesis)

Phonology, morphology, and syntax have the same subregular complexity over their respective structural representations. →Can other dependencies in syntax, such as NPI-licensing, also be subregular?

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

The subregular hierarchy

Regular Star-Free Locally Threshold Testable Locally Testable Multi input-local TSL (MITSL) Multi-TSL (M-TSL) Input-local TSL(I-TSL) Tier-based Strictly Local (TSL) Strictly Local Piecewise Testable Strictly Piecewise

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

The subregular hierarchy

Regular Star-Free Locally Threshold Testable Locally Testable Multi input-local TSL (MITSL) Multi-TSL (M-TSL) Input-local TSL(I-TSL) Tier-based Strictly Local (TSL) Strictly Local Piecewise Testable Strictly Piecewise

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Strictly Local languages

Intuitive description: List possible substructures of k size (or equivalently, list banned substructures of k size)

Example (SL grammar over strings)

(from Graf et al. (2018))

  • German word nal devoicing: forbid voiced segments in the end of the string
  • SL Grammar: *d$, *z$, *v$, etc.
  • The grammar correctly rules out *$rad$ and accepts $rat$

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Strictly Local languages

Intuitive description: List possible substructures of k size (or equivalently, list banned substructures of k size)

Example (SL grammar over trees)

  • Merge for nouns: one of the Merge node's LI child must have an =n selector feature,

and its other LI child must have an n category feature

  • The grammar lists banned subtrees of bound depth (in this case, 2)

* Merge live

=d v

the

=n d

* Merge she

d

an

=n d

* Merge ε

=v t +nom

the

=n d

. . .

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-based languages over strings

Intuitive description:

  • Project a tier
  • Apply constraints over the tier

Tier-based Strictly Local languages Project a tier with the help of an erasing function erase all nodes that are irrelevant for the constraint Apply SL constraints over the tier

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-based languages over strings

Intuitive description:

  • Project a tier
  • Apply constraints over the tier

Tier-based Strictly Local languages Project a tier with the help of an erasing function erase all nodes that are irrelevant for the constraint Apply SL constraints over the tier

Example (TSL over strings)

String: Tier: T={a,e,i,o,u} Erasing function yields: Grammar that enforces vowel harmony: *ae, *ai, *ea, *io, etc. this grammar rules out bibobua

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-based languages over strings

Intuitive description:

  • Project a tier
  • Apply constraints over the tier

Tier-based Strictly Local languages

  • Project a tier with the help of an erasing function erase all nodes that are irrelevant

for the constraint Apply SL constraints over the tier

Example (TSL over strings)

  • String: bibobua
  • Tier: T={a,e,i,o,u}
  • Erasing function yields: ioua

Grammar that enforces vowel harmony: *ae, *ai, *ea, *io, etc. this grammar rules out bibobua

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-based languages over strings

Intuitive description:

  • Project a tier
  • Apply constraints over the tier

Tier-based Strictly Local languages

  • Project a tier with the help of an erasing function erase all nodes that are irrelevant

for the constraint

  • Apply SL constraints over the tier

Example (TSL over strings)

  • String: bibobua
  • Tier: T={a,e,i,o,u}
  • Erasing function yields: ioua
  • Grammar that enforces vowel harmony: *ae, *ai, *ea, *io, etc.

→ this grammar rules out bibobua

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-based languages over strings

Intuitive description:

  • Project a tier
  • Apply constraints over the tier

Tier-based Strictly Local languages

  • Project a tier with the help of an erasing function erase all nodes that are irrelevant

for the constraint

  • Apply SL constraints over the tier

Input-local tier-based Strictly Local Language (I-TSL)

  • Project a tier with a strictly local function, i.e. nodes are projected with taking local

context into consideration

  • Apply SL constraints over the tier

Multiple I-TSL (MITSL)

  • Project multiple tiers with a strictly local function
  • Apply SL constraints over each tier (they can take dierent SL constraints)

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-based languages over trees

  • Project a tree-tier from a tree

▶ Simple erasing function in the case of TSL ▶ ISL projection function in the case of I-TSL and MITSL

  • Apply substructure constraints over the tree-tier (cf. Jardine (2016)), which equals to

constraining the form of each node's daughter-string, based on that node's local context

▶ Example: If Merge does not have negation as its sibling, then it cannot have NPI as its

child.

We'll see more examples when we look at more NPI-licensing constraints.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Known results about subregular derivation trees

  • Merge constraints are SL
  • Merge with recursive adjunction is I-TSL (Graf, 2018)
  • Move is I-TSL (Graf, 2018)
  • C-command is not TSL (Vu, 2018) → ∃-NPI licensing is not TSL

→ Are NPI-licensing constraints in the quantier-based approach I-TSL?

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Outline

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∃-NPIs

  • They must be c-commanded by negation at LF
  • Two kinds of c-command relations:

▶ Base c-command: movement does not play a role, nodes c-command each other in their

base position

▶ Derived c-command: movement plays a role, it either creates or destroys c-command

relations

As it turns out, the two are dierent in terms of complexity.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Base c-command

Claim: Base c-command is I-TSL. I show this on four examples: Negation base c-commands an NPI, and licenses it Negation base c-commands multiple NPIs There is no negation to license the NPIs Negation does not c-command the NPIs

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

slide-46
SLIDE 46

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Base c-command

Claim: Base c-command is I-TSL. I show this on four examples:

  • Negation base c-commands an NPI, and

licenses it Negation base c-commands multiple NPIs There is no negation to license the NPIs Negation does not c-command the NPIs

Move Merge Merge Merge Merge Merge anybody see v we not did

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

slide-47
SLIDE 47

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Base c-command

Claim: Base c-command is I-TSL. I show this on four examples:

  • Negation base c-commands an NPI, and

licenses it

  • Negation base c-commands multiple

NPIs There is no negation to license the NPIs Negation does not c-command the NPIs

Move Merge Merge Merge Merge Merge Merge Merge anybody to anything give v we not did

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

slide-48
SLIDE 48

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Base c-command

Claim: Base c-command is I-TSL. I show this on four examples:

  • Negation base c-commands an NPI, and

licenses it

  • Negation base c-commands multiple

NPIs

  • There is no negation to license the NPIs

Negation does not c-command the NPIs

Move Merge Merge Merge Merge anybody see v we T

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

slide-49
SLIDE 49

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Base c-command

Claim: Base c-command is I-TSL. I show this on four examples:

  • Negation base c-commands an NPI, and

licenses it

  • Negation base c-commands multiple

NPIs

  • There is no negation to license the NPIs
  • Negation does not c-command the NPIs

Move Merge Merge Merge Merge anybody bothering v Merge Move Merge Merge Merge Merge Merge him trust v we not do that is

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

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SLIDE 50

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

slide-51
SLIDE 51

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

slide-52
SLIDE 52

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

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SLIDE 53

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

slide-54
SLIDE 54

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

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SLIDE 55

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

slide-56
SLIDE 56

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Projecting the tier based on local context

MergeT neg MergeT NPI NPIT Figure 3: Contexts for the tier projection for English NPI-licensing

Merge Move Merge Merge Merge Merge Merge anybody see v we not did C Merge Merge anybody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

slide-57
SLIDE 57

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Applying SL constraints over the tier

¬Merge Merge NPI Figure 4: Banned substructure for English NPI-licensing, base c-command ⊤ Merge Merge anybody Figure 5: Projected tree-tier

Technically: If Merge has a non-Merge parent, then it cannot have an NPI among its children. This tree-tier does not violate the SL constraint in Figure 2.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

slide-58
SLIDE 58

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Applying SL constraints over the tier

¬Merge Merge NPI Figure 4: Banned substructure for English NPI-licensing, base c-command ⊤ Merge Merge anybody Figure 5: Projected tree-tier

Technically: If Merge has a non-Merge parent, then it cannot have an NPI among its children. This tree-tier does not violate the SL constraint in Figure 2.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

slide-59
SLIDE 59

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Applying SL constraints over the tier

¬Merge Merge NPI Figure 4: Banned substructure for English NPI-licensing, base c-command ⊤ Merge Merge anybody Figure 5: Projected tree-tier

Technically: If Merge has a non-Merge parent, then it cannot have an NPI among its children. This tree-tier does not violate the SL constraint in Figure 2.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

slide-60
SLIDE 60

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Applying SL constraints over the tier

¬Merge Merge NPI Figure 4: Banned substructure for English NPI-licensing, base c-command ⊤ Merge Merge anybody Figure 5: Projected tree-tier

Technically: If Merge has a non-Merge parent, then it cannot have an NPI among its children. → This tree-tier does not violate the SL constraint in Figure 2.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

slide-61
SLIDE 61

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing multiple NPIs

¬Merge Merge NPI Figure 6: Banned substructure

Move Merge Merge Merge Merge Merge Merge Merge anybody to anything give v we not did ⊤ Merge Merge Merge anybody anything

This tree-tier does not violate the SL constraint in Figure 4.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

slide-62
SLIDE 62

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing multiple NPIs

¬Merge Merge NPI Figure 6: Banned substructure ⊤ Merge Merge Merge anybody anything

This tree-tier does not violate the SL constraint in Figure 4.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

slide-63
SLIDE 63

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing multiple NPIs

¬Merge Merge NPI Figure 6: Banned substructure ⊤ Merge Merge Merge anybody anything

This tree-tier does not violate the SL constraint in Figure 4.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

slide-64
SLIDE 64

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing multiple NPIs

¬Merge Merge NPI Figure 6: Banned substructure ⊤ Merge Merge Merge anybody anything

This tree-tier does not violate the SL constraint in Figure 4.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

slide-65
SLIDE 65

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing multiple NPIs

¬Merge Merge NPI Figure 6: Banned substructure ⊤ Merge Merge Merge anybody anything

→ This tree-tier does not violate the SL constraint in Figure 4.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

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SLIDE 66

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Ruling out unlicensed constructions

  • 1. There is no negation in the sentence:

(37) * We saw anybody.

  • 2. Negation does not c-command the NPI

(38) * That we do not trust him is bothering anyone.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 36 / 56

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SLIDE 67

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

No licensor

¬Merge Merge NPI Figure 7: Banned substructure Merge Move Merge Merge Merge Merge anybody see v we T C ⊤ Merge anybody

This tree-tier violates the SL constraint in Figure 5.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 37 / 56

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SLIDE 68

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

No licensor

¬Merge Merge NPI Figure 7: Banned substructure Merge Move Merge Merge Merge Merge anybody see v we T C ⊤ Merge anybody

This tree-tier violates the SL constraint in Figure 5.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 37 / 56

slide-69
SLIDE 69

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

No licensor

¬Merge Merge NPI Figure 7: Banned substructure Merge Move Merge Merge Merge Merge anybody see v we T C ⊤ Merge anybody

→ This tree-tier violates the SL constraint in Figure 5.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 37 / 56

slide-70
SLIDE 70

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

No c-commanding licensor

¬Merge Merge NPI Figure 8: Banned substructure

Move Merge Merge Merge Merge anybody bothering v Merge Move Merge Merge Merge Merge Merge him trust v we not do that is

⊤ Merge anybody Merge

This tree-tier violates the SL constraint in Figure 6.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 38 / 56

slide-71
SLIDE 71

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

No c-commanding licensor

¬Merge Merge NPI Figure 8: Banned substructure

Move Merge Merge Merge Merge anybody bothering v Merge Move Merge Merge Merge Merge Merge him trust v we not do that is

⊤ Merge anybody Merge

This tree-tier violates the SL constraint in Figure 6.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 38 / 56

slide-72
SLIDE 72

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

No c-commanding licensor

¬Merge Merge NPI Figure 8: Banned substructure

Move Merge Merge Merge Merge anybody bothering v Merge Move Merge Merge Merge Merge Merge him trust v we not do that is

⊤ Merge anybody Merge

→ This tree-tier violates the SL constraint in Figure 6.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 38 / 56

slide-73
SLIDE 73

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Derived c-command

Claim: Derived c-command is not I-TSL.

  • To determine if a moved node x c-commands another node, we need to project the

Move node associated with x

  • Because of the long-distance nature of Move, there is no function that can project the

right Move node based on local context

  • Even if there is a function that can, tree-tiers projected from grammatical and

ungrammatical sentences can be indistinguishable

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 39 / 56

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SLIDE 74

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Derived c-command

(39) * Anybody did not leave.

Move Merge Merge Merge Merge Merge leave v anybody not did Move Merge anybody not

(40) Nobody left anybody.

Move Merge Merge Merge Merge anybody left v nobody T Move Merge anybody nobody

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 40 / 56

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SLIDE 75

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Interim summary

  • Base c-command can be described in terms of I-TSL
  • Derived c-command cannot be described in terms of I-TSL

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 41 / 56

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SLIDE 76

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Outline

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 42 / 56

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SLIDE 77

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∀-NPIs

Recap of the licensing mechanism for ∀-NPIs:

  • NPI must scope higher than negation
  • To achieve this, NPI undergoes QR (either overt or covert) to NegP
  • Covert QR is clause-bounded, overt QR is not

How to model this? The rst part of the licensing mechanisms looks like reverse

  • NPI licensing now

NPI has to c-command negation

This would yield the same complexity results as for

  • NPIs: base c-command is I-TSL,

derived c-command is not It does not get to the other two points

If we assume that all

  • NPIs always undergo movement, we can just state the

constraints as as move and locality constraints

Both can be captured with I-TSL constraints

To keep this discussion simple, I only show licensing of a single NPI. For licensing multiple NPIs, we will need to use Cluster, but Cluster constraints are also I-TSL.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 43 / 56

slide-78
SLIDE 78

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∀-NPIs

Recap of the licensing mechanism for ∀-NPIs:

  • NPI must scope higher than negation
  • To achieve this, NPI undergoes QR (either overt or covert) to NegP
  • Covert QR is clause-bounded, overt QR is not

How to model this?

  • The rst part of the licensing mechanisms looks like reverse ∃-NPI licensing now

NPI has to c-command negation

▶ This would yield the same complexity results as for ∃-NPIs: base c-command is I-TSL,

derived c-command is not

▶ It does not get to the other two points

If we assume that all

  • NPIs always undergo movement, we can just state the

constraints as as move and locality constraints

Both can be captured with I-TSL constraints

To keep this discussion simple, I only show licensing of a single NPI. For licensing multiple NPIs, we will need to use Cluster, but Cluster constraints are also I-TSL.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 43 / 56

slide-79
SLIDE 79

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∀-NPIs

Recap of the licensing mechanism for ∀-NPIs:

  • NPI must scope higher than negation
  • To achieve this, NPI undergoes QR (either overt or covert) to NegP
  • Covert QR is clause-bounded, overt QR is not

How to model this?

  • The rst part of the licensing mechanisms looks like reverse ∃-NPI licensing now

NPI has to c-command negation

▶ This would yield the same complexity results as for ∃-NPIs: base c-command is I-TSL,

derived c-command is not

▶ It does not get to the other two points

  • If we assume that all ∀-NPIs always undergo movement, we can just state the

constraints as as move and locality constraints

▶ Both can be captured with I-TSL constraints

To keep this discussion simple, I only show licensing of a single NPI. For licensing multiple NPIs, we will need to use Cluster, but Cluster constraints are also I-TSL.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 43 / 56

slide-80
SLIDE 80

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Licensing ∀-NPIs

Recap of the licensing mechanism for ∀-NPIs:

  • NPI must scope higher than negation
  • To achieve this, NPI undergoes QR (either overt or covert) to NegP
  • Covert QR is clause-bounded, overt QR is not

How to model this?

  • The rst part of the licensing mechanisms looks like reverse ∃-NPI licensing now

NPI has to c-command negation

▶ This would yield the same complexity results as for ∃-NPIs: base c-command is I-TSL,

derived c-command is not

▶ It does not get to the other two points

  • If we assume that all ∀-NPIs always undergo movement, we can just state the

constraints as as move and locality constraints

▶ Both can be captured with I-TSL constraints

To keep this discussion simple, I only show licensing of a single NPI. For licensing multiple NPIs, we will need to use Cluster, but Cluster constraints are also I-TSL.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 43 / 56

slide-81
SLIDE 81

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Assumed lexicon

  • The NPI always moves → I stipulate that movement is triggered by a −npi movement

feature

▶ −npi for overt movement ▶ −snpi for covert movement

  • The NPI moves to NegP → negation must be able to have a +npi feature to license

movement

▶ +npi for overt movement ▶ +snpi for covert movement

Move licensee Move licensor Overt Move NPI :: d −npi nem :: =t +npi t Covert Move NPI :: d −snpi nem :: =t +snpi t

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 44 / 56

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SLIDE 82

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-projections

Project two tiers:

  • Move-tier

S-move-tier

MoveT1 Merge neg

=t +npi t

NPIT1

d −npi

Figure 9: Contexts for the Move tier

(41) Sen-ki-t NPI-who-acc nem neg lt-t-am. see-pst-1sg `I did not see anyone.'

Merge Move Merge Move Merge Merge Merge Merge NPI-who

d −npi

saw

=d v

ε

=v =d v

ε

d −nom

ε

=v +nom t

not

=t +npi t

ε

=t c

Move NPI-who

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 45 / 56

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SLIDE 83

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Tier-projections

Project two tiers:

  • Move-tier
  • S-move-tier

S-moveT2 Merge neg

=t +snpi t

NPIT2

d −snpi

MergeT2 C

Figure 10: Contexts for the S-move tier

(44) Nem neg lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc `I did not see anyone.'

Merge S-Move Merge Move Merge Merge Merge Merge NPI-who

d −snpi

saw

=d v

ε

=v =d v

ε

d −nom

ε

=v +nom t

not

=t +snpi t

ε

=t c

Merge S-Move NPI-who

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 45 / 56

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SLIDE 84

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 85

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (47) Sen-ki-t NPI-who-acc nem neg lt-t-am. see-pst-1sg `I did not see anyone.'

Merge Move Merge Move Merge Merge Merge Merge NPI-who

d −npi

saw

=d v

ε

=v =d v

ε

d −nom

ε

=v +nom t

not

=t +npi t

ε

=t c

Move NPI-who

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

slide-86
SLIDE 86

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (49) Sen-ki-t NPI-who-acc nem neg lt-t-am. see-pst-1sg `I did not see anyone.'

Move NPI-who

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 87

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (51) Sen-ki-t NPI-who-acc nem neg lt-t-am. see-pst-1sg `I did not see anyone.'

Move NPI-who

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 88

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (53) Sen-ki-t NPI-who-acc nem neg lt-t-am. see-pst-1sg `I did not see anyone.'

Move NPI-who

→ The tier-tree does not violate any of the constraints in Figure 11.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 89

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (56) * Lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc

Merge Move Merge Merge Merge Merge NPI-who

d −npi

saw

=d v

ε

=v =d v

ε

d −nom

ε

=v +nom t

ε

=t c

⊤ NPI-who

d −npi

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 90

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (58) * Lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc

⊤ NPI-who

d −npi

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 91

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Constraints on the Move-tier

Move ⊥ Move NPI NPI ⊤ NPI Figure 11: Banned substructures for the Move tier

Technically: Move must have exactly one NPI-child. (60) * Lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc

⊤ NPI-who

d −npi

→ The tier-tree violates one of the constraints in Figure 11.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

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SLIDE 92

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Move constraints on the S-move-tier

(61) Nem neg lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc `I did not see anyone.'

Merge S-Move Merge Move Merge Merge Merge Merge NPI-who

d −snpi

saw

=d v

ε

=v =d v

ε

d −nom

ε

=v +nom t

not

=t +snpi t

ε

=t c

Merge S-Move NPI-who

None of the constraints are violated in the tier-tree.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

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SLIDE 93

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Move constraints on the S-move-tier

S-move $ S-move NPI NPI ¬S-move NPI Figure 12: Banned substructures for the S-move tier

(64) Nem neg lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc `I did not see anyone.'

Merge S-Move NPI-who

None of the constraints are violated in the tier-tree.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

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SLIDE 94

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Move constraints on the S-move-tier

S-move $ S-move NPI NPI ¬S-move NPI Figure 12: Banned substructures for the S-move tier

(66) Nem neg lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc `I did not see anyone.'

Merge S-Move NPI-who

None of the constraints are violated in the tier-tree.

Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

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SLIDE 95

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Move constraints on the S-move-tier

S-move $ S-move NPI NPI ¬S-move NPI Figure 12: Banned substructures for the S-move tier

(68) Nem neg lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc `I did not see anyone.'

Merge S-Move NPI-who

None of the constraints are violated in the tier-tree.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Move constraints on the S-move-tier

S-move $ S-move NPI NPI ¬S-move NPI Figure 12: Banned substructures for the S-move tier

(70) Nem neg lt-t-am see-pst-1sg sen-ki-t. NPI-who-acc `I did not see anyone.'

Merge S-Move NPI-who

→ None of the constraints are violated in the tier-tree.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Locality constraints on the S-move tier

Merge S-Move Merge Move Merge Merge Merge Merge Merge Move Merge Merge Merge Merge NPI-who-com d −s npi meet =d v ε =v =d v Peter d -nom ε =v +nom t that =t c thought =c v ε =v =d v ε d -nom ε =v +nom t not =t +snpi t ε =t c

Merge S-move Merge NPI-who-com

(71) * Nem neg gondol-t-am, think-pst-1sg hogy that Pter Peter tallkoz-na meet-cond.3sg sen-ki-vel. `I did not think that Peter would meet with anyone.' This tier-tree violates both of the locality constraints.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Locality constraints on the S-move tier

S-move Merge Merge NPI Figure 13: Banned substructures for the S-move tier

(74) * Nem neg gondol-t-am, think-pst-1sg hogy that Pter Peter tallkoz-na meet-cond.3sg sen-ki-vel. `I did not think that Peter would meet with anyone.'

Merge S-move Merge NPI-who-com

This tier-tree violates both of the locality constraints.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Locality constraints on the S-move tier

S-move Merge Merge NPI Figure 13: Banned substructures for the S-move tier

(76) * Nem neg gondol-t-am, think-pst-1sg hogy that Pter Peter tallkoz-na meet-cond.3sg sen-ki-vel. `I did not think that Peter would meet with anyone.'

Merge S-move Merge NPI-who-com

This tier-tree violates both of the locality constraints.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Locality constraints on the S-move tier

S-move Merge Merge NPI Figure 13: Banned substructures for the S-move tier

(78) * Nem neg gondol-t-am, think-pst-1sg hogy that Pter Peter tallkoz-na meet-cond.3sg sen-ki-vel. `I did not think that Peter would meet with anyone.'

Merge S-move Merge NPI-who-com

This tier-tree violates both of the locality constraints.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Locality constraints on the S-move tier

S-move Merge Merge NPI Figure 13: Banned substructures for the S-move tier

(80) * Nem neg gondol-t-am, think-pst-1sg hogy that Pter Peter tallkoz-na meet-cond.3sg sen-ki-vel. `I did not think that Peter would meet with anyone.'

Merge S-move Merge NPI-who-com

→ This tier-tree violates both of the locality constraints.

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Outline

Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Summary

  • ∃-NPIs: licensor must c-command the NPI at LF

▶ Base c-command is an Input Local-TSL constraint (I-TSL) ▶ Derived c-command is not I-TSL

  • ∀-NPIs: NPI must c-command the licensor at LF (achieved through

Quantier-raising (QR))

▶ If we stipulate all the necessary features to ensure that NPIs always move to NegP at

LF, then we only need constraints to regulate Move and S-move (which are needed for well-formed derivation trees also)

▶ We had to project two separate tiers, making the overall NPI-licensing constraint

Multiple Input-local Tier-based Strictly Local (MITSL)

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Take-away

Theoretical analysis can help lower the computational complexity of syntactic constraints.

  • Assuming a hierarchical structure rather than a string as the relevant data structure

lowers the power of the necessary logic to describe syntactic dependencies

  • Assuming covert movement as a core mechanism in the licensing of universally

quantied NPIs lowers the computational complexity of their constraints

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Introduction Quantifier-based approach Computational background ∃-NPIs ∀-NPIs Discussion

Implications

If all syntactic dependencies are subregular, then

  • We have a better grasp on possible and impossible typological patterns
  • We can develop more eective learning algorithms
  • We can develop more eective processing algorithms

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What's next?

We are still in the beginning of studying subregular syntax. There is a lot to do!

  • Give a similar analysis of other NPI-licensing aproaches, e.g. Collins and Postal's

(2015) NEG-raising account which assumes movement for ∃-NPIs as well

  • Pin-down the complexity of derived c-command dependencies
  • Develop learning algorithms for subregular tree-languages
  • Map out other syntactic dependencies
  • Study the nature of the mapping functions from derivation trees to outputs
  • Study dierent representations of syntactic derivation, e.g. dependency trees (Graf

and De Santo, 2019)

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Thank you for coming!

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References

References I

Chandlee, J. (2014). Strictly local phonological processes. Ph. D. thesis, University of Delaware. Collins, C. and P. M. Postal (2015). A Typology of Negative Polarity Items. Grtner, H.-m. and J. Michaelis (2010). On the Treatment of Multiple-Wh-Interrogatives in Minimalist

  • Grammars. In T. Hanneforth and G. Fanselow (Eds.), Language and Logos, pp. 339366. Berlin:

Akademie Verlag. Giannakidou, A. (2000). Negative... Concord? Natural Language & Linguistic Theory& Linguistic Theory 18(3), 457523. Graf, T. (2018). Why movement comes for free once you have adjunction. Proceedings of CLS 53, 117137. Graf, T. and A. De Santo (2019). Sensing Tree Automata as a Model of Syntactic Dependencies. Proceedings of the 16th Meeting on the Mathematics of Language (MOL 2019). Graf, T., A. De Santo, J. Rawski, A. Aksenova, H. Dolatian, S. Moradi, H. Baek, S. Yang, and J. Heinz (2018). Tiers and Relativized Locality Across Language Modules. Graf, T. and J. Heinz (2015). Commonality in Disparity : The Computational View of Syntax and Phonology A New View of the Power of Syntax and Phonology. Grewendorf, G. (2001). Multiple Wh-Fronting. Linguistic Inquiry 32(1), 87122. Jardine, A. (2016). Locality and non-linear representations in tonal phonology. Ph. D. thesis, University of Delaware.

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References

References II

Joshi, A. K. (1985). Tree adjoining grammars: How much context-sensitivity is required to provide reasonable structural descriptions? In D. Dowty, Karttuhen, and A. Zwicky (Eds.), Natural Language Parsing: Psychological, Computational, and Theoretical Perspectives, pp. 206250. Cambridge University Press. Kobele, G. M., C. Retor, and S. Salvati (2007). An automata-theoretic approach to minimalism. Model theoretic syntax at 10, 7180. Morawietz, F. (2003). Two-Step Approaches to Natural Language Formalism, Volume 64. New York: Mouton de Gruyter. Reinhart, T. (1976). The syntactic domain of anaphora. Ph. D. thesis, Massachussetts Institute of Technology. Sabel, J. (2001). Deriving Multiple Head and Phrasal Movement: The Cluster Hypothesis. Linguistic Inquiry 32(3), 532547. Shieber, S. M. (1985). Evidence against the context-freeness of natural language. Linguistics and Philosophy 8, 333343. Stabler, E. (1997). Derivational minimalism. In Logical aspects of computational linguistics, pp. 6895. Thatcher, J. W. (1967). Characterizing derivation trees of context-free grammars through a generalization

  • f nite automata theory. Journal of Computer and System Sciences 1(4), 317322.

Vu, M. H. (2018). Towards a formal description of NPI-licensing patterns. Poster presentation at the Society of Computation in Language, Salt Lake City, UT. Wurmbrand, S. (2018). The cost of raising quantiers. Glossa: a journal of general linguistics 3(1), 140.

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