a quantifier based approach to npi licensing typology
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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

  1. 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 on 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 di�erent modules of natural language? Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 14 / 56

  2. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion How complex is natural language? Recursively-enumerable Context-sensitive Syntax Mildly context-sensitive Morphology Context-free Regular Phonology Finite Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 15 / 56

  3. 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 ( a n b m c n d m ) (31) ...mer em Hans es huus h�lfed aastriche (Shieber, 1985) ...we Hans- dat the house helped paint `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 ? Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 16 / 56

  4. 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. Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 17 / 56

  5. 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 G�rtner and Michaelis (2010) Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 18 / 56

  6. 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? Example: [which :: =n d − wh] shorthand ν ω π ρ f f − [+sem,+phon] Merge • d means that which has the =f f + [+sem,+phon] Merge category feature d − f f − [+sem,+phon] Move • =n means that which selects for an +f f + [+sem,+phon] Move LI whose category feature is n − s f f [+sem, − phon] − Move • − wh means that which has a wh + s f f + [+sem, − phon] Move movement licensee feature on it that − p f f [ − sem,+phon] − Move will have to be satis�ed by Move + p f f + [ − sem,+phon] Move Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 19 / 56

  7. 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) Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 20 / 56

  8. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Let's build a tree (32) Mary likes the car. TP Move Mary T ′ Merge d − nom ε ε VP Merge =v +nom t =v +nom t V ′ t Mary Merge d − nom d -nom Merge likes DP likes =d =d v =d =d v car car the the n n =n d =n d Figure 1: Phrase-structure tree Figure 2: Derivation tree Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 21 / 56

  9. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Let's build a tree (33) Mary likes the car. TP Move Mary T ′ Merge d − nom ε ε VP Merge =v +nom t =v +nom t V ′ t Mary Merge d − nom d -nom Merge likes DP likes =d =d v =d =d v car car the the n n =n d =n d Figure 1: Phrase-structure tree Figure 2: Derivation tree Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 21 / 56

  10. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Let's build a tree (34) Mary likes the car. TP Move Mary T ′ Merge d − nom ε ε VP Merge =v +nom t =v +nom t V ′ t Mary Merge d − nom d -nom Merge likes DP likes =d =d v =d =d v car car the the n n =n d =n d Figure 1: Phrase-structure tree Figure 2: Derivation tree Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 21 / 56

  11. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Let's build a tree (35) Mary likes the car. TP Move Mary T ′ Merge d − nom ε ε VP Merge =v +nom t =v +nom t V ′ t Mary Merge d − nom d -nom Merge likes DP likes =d =d v =d =d v car car the the n n =n d =n d Figure 1: Phrase-structure tree Figure 2: Derivation tree Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 21 / 56

  12. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Let's build a tree (36) Mary likes the car. TP Move Mary T ′ Merge d − nom ε ε VP Merge =v +nom t =v +nom t V ′ t Mary Merge d − nom d -nom Merge likes DP likes =d =d v =d =d v car car the the n n =n d =n d Figure 1: Phrase-structure tree Figure 2: Derivation tree Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 21 / 56

  13. 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 signi�cantly lower the complexity of the logical tools needed to describe the patterns Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 22 / 56

  14. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion The complexity of natural language - revised Syntactic strings Recursively-enumerable Syntactic derivation trees Context-sensitive Mildly context-sensitive Morphology Context-free Regular Phonology Finite Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 23 / 56

  15. 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 ? Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 24 / 56

  16. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion The subregular hierarchy Regular Star-Free Locally Threshold Testable Locally Testable Piecewise Testable Multi input-local TSL (MITSL) Multi-TSL (M-TSL) Input-local TSL(I-TSL) Tier-based Strictly Local (TSL) Strictly Local Strictly Piecewise Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 25 / 56

  17. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion The subregular hierarchy Regular Star-Free Locally Threshold Testable Locally Testable Piecewise Testable Multi input-local TSL (MITSL) Multi-TSL (M-TSL) Input-local TSL(I-TSL) Tier-based Strictly Local (TSL) Strictly Local Strictly Piecewise Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 25 / 56

  18. 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$, etc. • The grammar correctly rules out *$ra d$ and accepts $ra t$ Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 26 / 56

  19. 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 * Merge * Merge . . . an ε the live she the =n d = v t +nom =n d =d v d =n d Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 26 / 56

  20. 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 Tier-based Strictly Local languages Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Tier-based languages over strings Intuitive description : • Project a tier • Apply constraints over the tier Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 27 / 56

  21. 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� 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) 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 Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 27 / 56

  22. Apply SL constraints over the tier Grammar that enforces vowel harmony: *ae, *ai, *ea, *io, etc. this grammar rules out �bibobua� 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 Example (TSL over strings) • String: bibobua • Tier: T={a,e,i,o,u} • Erasing function yields: ioua Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 27 / 56

  23. 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� Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 27 / 56

  24. 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 di�erent SL constraints) Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 27 / 56

  25. 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. Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 28 / 56

  26. 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 quanti�er-based approach I-TSL? Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 29 / 56

  27. 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 30 / 56

  28. 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 di�erent in terms of complexity. Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 31 / 56

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

  30. Negation base c-commands multiple NPIs There is no negation to license the NPIs Negation does not c-command the NPIs Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Base c-command Move Merge Claim: Base c-command is I-TSL. Merge did I show this on four examples: • Negation base c-commands an NPI, and not Merge licenses it we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

  31. There is no negation to license the NPIs Negation does not c-command the NPIs Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Base c-command Move Merge Claim: Base c-command is I-TSL. did Merge not I show this on four examples: Merge • Negation base c-commands an NPI, and we Merge licenses it • Negation base c-commands multiple v Merge NPIs give Merge Merge anything to anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

  32. Negation does not c-command the NPIs Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Base c-command Move Merge Claim: Base c-command is I-TSL. Merge T I show this on four examples: • Negation base c-commands an NPI, and we Merge licenses it • Negation base c-commands multiple v Merge NPIs • There is no negation to license the NPIs see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

  33. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Base c-command Move Merge is Merge Claim: Base c-command is I-TSL. Merge Merge I show this on four examples: Move v Merge that • Negation base c-commands an NPI, and licenses it Merge bothering anybody • Negation base c-commands multiple do Merge NPIs • There is no negation to license the NPIs not Merge • Negation does not c-command the NPIs we Merge v Merge trust him Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 32 / 56

  34. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  35. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  36. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  37. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  38. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  39. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  40. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Projecting the tier based on local context Merge C Move Merge Merge Merge T Merge T NPI T Merge Merge did neg NPI not Merge anybody Figure 3: Contexts for the tier projection for English NPI-licensing we Merge v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 33 / 56

  41. This tree-tier does not violate the SL constraint in Figure 2. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Applying SL constraints over the tier ⊤ ¬ Merge Merge Merge Merge NPI anybody Figure 4: Banned substructure for English NPI-licensing, base c-command Figure 5: Projected tree-tier Technically : If Merge has a non- Merge parent, then it cannot have an NPI among its children. Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

  42. This tree-tier does not violate the SL constraint in Figure 2. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Applying SL constraints over the tier ⊤ ¬ Merge Merge Merge Merge NPI anybody Figure 4: Banned substructure for English NPI-licensing, base c-command Figure 5: Projected tree-tier Technically : If Merge has a non- Merge parent, then it cannot have an NPI among its children. Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

  43. This tree-tier does not violate the SL constraint in Figure 2. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Applying SL constraints over the tier ⊤ ¬ Merge Merge Merge Merge NPI anybody Figure 4: Banned substructure for English NPI-licensing, base c-command Figure 5: Projected tree-tier Technically : If Merge has a non- Merge parent, then it cannot have an NPI among its children. Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 34 / 56

  44. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Applying SL constraints over the tier ⊤ ¬ Merge Merge Merge Merge NPI anybody Figure 4: Banned substructure for English NPI-licensing, base c-command 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

  45. This tree-tier does not violate the SL constraint in Figure 4. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Licensing multiple NPIs Move Merge ¬ Merge did Merge not Merge Merge ⊤ we Merge Merge NPI v Merge Merge Figure 6: Banned substructure give Merge anything Merge anything Merge anybody to anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

  46. This tree-tier does not violate the SL constraint in Figure 4. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Licensing multiple NPIs ⊤ Merge ¬ Merge Merge Merge anything Merge NPI anybody Figure 6: Banned substructure Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

  47. This tree-tier does not violate the SL constraint in Figure 4. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Licensing multiple NPIs ⊤ Merge ¬ Merge Merge Merge anything Merge NPI anybody Figure 6: Banned substructure Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

  48. This tree-tier does not violate the SL constraint in Figure 4. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Licensing multiple NPIs ⊤ Merge ¬ Merge Merge Merge anything Merge NPI anybody Figure 6: Banned substructure Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 35 / 56

  49. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Licensing multiple NPIs ⊤ Merge ¬ Merge Merge Merge anything Merge NPI anybody Figure 6: Banned substructure → 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

  50. 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

  51. This tree-tier violates the SL constraint in Figure 5. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion No licensor Merge ⊤ C Move Merge ¬ Merge Merge anybody Merge T Merge NPI we Merge Figure 7: Banned substructure v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 37 / 56

  52. This tree-tier violates the SL constraint in Figure 5. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion No licensor Merge ⊤ Move Merge C ¬ Merge Merge anybody Merge T Merge NPI we Merge Figure 7: Banned substructure v Merge see anybody Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 37 / 56

  53. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion No licensor Merge ⊤ Move Merge C ¬ Merge Merge anybody Merge T Merge NPI we Merge Figure 7: Banned substructure v Merge see 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

  54. This tree-tier violates the SL constraint in Figure 6. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion No c-commanding licensor Move ⊤ Merge Merge Merge is Merge ¬ Merge Merge Merge anybody v that Move Merge Merge Merge bothering anybody NPI Merge do not Merge Figure 8: Banned substructure we Merge v Merge trust him Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 38 / 56

  55. This tree-tier violates the SL constraint in Figure 6. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion No c-commanding licensor Move ⊤ Merge Merge Merge is Merge ¬ Merge Merge Merge anybody v that Move Merge Merge Merge bothering anybody NPI do Merge not Merge Figure 8: Banned substructure we Merge v Merge trust him Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 38 / 56

  56. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion No c-commanding licensor Move ⊤ Merge Merge Merge is Merge ¬ Merge Merge Merge anybody v that Move Merge Merge Merge bothering anybody NPI do Merge not Merge Figure 8: Banned substructure we Merge v Merge trust him → 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

  57. 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

  58. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Derived c-command (39) * Anybody did not leave. (40) Nobody left anybody. Move Move Move Move Merge Merge Merge Merge not did Merge anybody T Merge nobody anybody not Merge nobody Merge v anybody Merge Merge v Merge left anybody leave Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 40 / 56

  59. 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

  60. 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

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

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

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

  64. 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

  65. 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 ▶ − s npi for covert movement • The NPI moves to NegP → negation must be able to have a + npi feature to license movement ▶ + npi for overt movement ▶ + s npi for covert movement Move licensee Move licensor Overt Move NPI :: d − npi nem :: =t +npi t nem :: =t + s npi t Covert Move NPI :: d − s npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 44 / 56

  66. S-move -tier Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Tier-projections Project two tiers: • Move -tier Merge Move ε Move NPI-who =t c Move T 1 NPI T 1 Merge d − npi Merge not Move =t +npi t Merge neg =t +npi t ε Merge = v +nom t Figure 9: Contexts for the Move tier ε Merge d − nom ε (41) Sen-ki-t nem l�t-t-am. Merge =v =d v NPI-who- acc see- pst - 1sg neg saw NPI-who `I did not see anyone.' =d v d − npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 45 / 56

  67. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Tier-projections Project two tiers: • Move -tier Merge Merge • S-move -tier ε S-Move S-Move =t c S-move T 2 NPI T 2 Merge T 2 d − s npi Merge NPI-who Merge C not Move =t + s npi t neg Merge =t + s npi t ε Merge = v +nom t Figure 10: Contexts for the S-move tier ε Merge d − nom (44) Nem l�t-t-am sen-ki-t. ε Merge see- pst - 1sg NPI-who- acc neg =v =d v `I did not see anyone.' saw NPI-who =d v d − s npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 45 / 56

  68. 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

  69. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Move Move ⊤ Merge Move ε Move ⊥ NPI NPI NPI NPI-who =t c Merge Figure 11: Banned substructures for the Move tier not Move =t +npi t Technically : Move must have exactly one NPI-child. Merge ε Merge (47) Sen-ki-t nem l�t-t-am. = v +nom t NPI-who- acc neg see- pst - 1sg ε Merge `I did not see anyone.' d − nom ε Merge =v =d v saw NPI-who =d v d − npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

  70. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Move Move Move ⊤ ⊥ NPI NPI NPI NPI-who Figure 11: Banned substructures for the Move tier Technically : Move must have exactly one NPI-child. (49) Sen-ki-t nem l�t-t-am. NPI-who- acc neg see- pst - 1sg `I did not see anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

  71. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Move Move Move ⊤ ⊥ NPI NPI NPI NPI-who Figure 11: Banned substructures for the Move tier Technically : Move must have exactly one NPI-child. (51) Sen-ki-t nem l�t-t-am. NPI-who- acc neg see- pst - 1sg `I did not see anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

  72. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Move Move Move ⊤ ⊥ NPI NPI NPI NPI-who Figure 11: Banned substructures for the Move tier Technically : Move must have exactly one NPI-child. (53) Sen-ki-t nem l�t-t-am. NPI-who- acc neg see- pst - 1sg `I did not see anyone.' → 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

  73. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Merge Move Move ⊤ ⊤ ε Move NPI-who ⊥ NPI NPI NPI =t c d − npi Merge Figure 11: Banned substructures for the Move tier ε Merge = v +nom t Technically : Move must have exactly one NPI-child. ε Merge d − nom (56) * L�t-t-am sen-ki-t. ε Merge see- pst - 1sg NPI-who- acc =v =d v saw NPI-who =d v d − npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

  74. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Move Move ⊤ ⊤ NPI NPI NPI NPI-who ⊥ d − npi Figure 11: Banned substructures for the Move tier Technically : Move must have exactly one NPI-child. (58) * L�t-t-am sen-ki-t. see- pst - 1sg NPI-who- acc Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 46 / 56

  75. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Constraints on the Move-tier Move Move ⊤ ⊤ NPI NPI NPI NPI-who ⊥ d − npi Figure 11: Banned substructures for the Move tier Technically : Move must have exactly one NPI-child. (60) * L�t-t-am sen-ki-t. see- pst - 1sg NPI-who- acc → 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

  76. None of the constraints are violated in the tier-tree. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Move constraints on the S-move-tier Merge Merge ε (61) Nem l�t-t-am S-Move S-Move =t c see- pst - 1sg neg Merge NPI-who sen-ki-t. not Move NPI-who- acc =t + s npi t `I did not see anyone.' Merge ε Merge = v +nom t ε Merge d − nom ε Merge =v =d v saw NPI-who =d v d − s npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

  77. None of the constraints are violated in the tier-tree. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Move constraints on the S-move-tier S-move S-move ¬ S-move Merge NPI NPI NPI $ Figure 12: Banned substructures for the S-Move S-move tier NPI-who (64) Nem l�t-t-am sen-ki-t. neg see- pst - 1sg NPI-who- acc `I did not see anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

  78. None of the constraints are violated in the tier-tree. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Move constraints on the S-move-tier S-move S-move ¬ S-move Merge NPI NPI NPI $ Figure 12: Banned substructures for the S-Move S-move tier NPI-who (66) Nem l�t-t-am sen-ki-t. neg see- pst - 1sg NPI-who- acc `I did not see anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

  79. None of the constraints are violated in the tier-tree. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Move constraints on the S-move-tier S-move S-move ¬ S-move Merge NPI NPI NPI $ Figure 12: Banned substructures for the S-Move S-move tier NPI-who (68) Nem l�t-t-am sen-ki-t. neg see- pst - 1sg NPI-who- acc `I did not see anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 47 / 56

  80. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Move constraints on the S-move-tier S-move S-move ¬ S-move Merge NPI NPI NPI $ Figure 12: Banned substructures for the S-Move S-move tier NPI-who (70) Nem l�t-t-am sen-ki-t. neg see- pst - 1sg NPI-who- acc `I did not see anyone.' → 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

  81. This tier-tree violates both of the locality constraints. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Locality constraints on the S-move tier Merge ε S-Move =t c Merge not Move =t + s npi t (71) * Nem gondol-t-am, hogy Merge neg think- pst - 1sg that ε Merge = v +nom t Merge P�ter tal�lkoz-na ε Merge d -nom Peter meet- cond.3sg S-move ε Merge =v =d v sen-ki-vel. thought Merge Merge =c v that Move `I did not think that Peter =t c NPI-who- com Merge would meet with anyone.' ε Merge = v +nom t Peter Merge d -nom ε Merge =v =d v meet NPI-who- com =d v d − s npi Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 48 / 56

  82. This tier-tree violates both of the locality constraints. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Locality constraints on the S-move tier S-move Merge Merge NPI Merge Figure 13: Banned substructures for the S-move S-move tier Merge (74) * Nem gondol-t-am, hogy P�ter think- pst - 1sg that Peter neg tal�lkoz-na sen-ki-vel. NPI-who- com meet- cond.3sg `I did not think that Peter would meet with anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 48 / 56

  83. This tier-tree violates both of the locality constraints. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Locality constraints on the S-move tier S-move Merge Merge NPI Merge Figure 13: Banned substructures for the S-move S-move tier Merge (76) * Nem gondol-t-am, hogy P�ter neg think- pst - 1sg that Peter tal�lkoz-na sen-ki-vel. NPI-who- com meet- cond.3sg `I did not think that Peter would meet with anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 48 / 56

  84. This tier-tree violates both of the locality constraints. Introduction Quantifier-based approach Computational background ∃ -NPIs ∀ -NPIs Discussion Locality constraints on the S-move tier S-move Merge Merge NPI Merge Figure 13: Banned substructures for the S-move S-move tier Merge (78) * Nem gondol-t-am, hogy P�ter neg think- pst - 1sg that Peter NPI-who- com tal�lkoz-na sen-ki-vel. meet- cond.3sg `I did not think that Peter would meet with anyone.' Mai Ha Vu A quantifier-based approach to NPI-licensing typology October 4, 2019 48 / 56

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