Characterizing Syllable Well-Formedness Using Inviolable Constraints - - PowerPoint PPT Presentation
Characterizing Syllable Well-Formedness Using Inviolable Constraints over Formal Word Models Kristina Strother-Garcia University of Delaware May 8, 2016 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 1 / 84 Outline Motivation 1 Toolkit:
Kristina Strother-Garcia
University of Delaware
May 8, 2016
NAPhC 2016 May 8, 2016 1 / 84
1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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in addition to strings
frameworks
principled way
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language classes of known computational power, allowing us to:
and impossible (unattested)
existing theoretical treatments
phonology (e.g., Graf, 2010a, 2010b; Heinz, 2011; Potts & Pullum, 2002; Scobbie, 1991)
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window, not globally over the entire word
at three adjacent positions at a time
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window, not globally over the entire word
at three adjacent positions at a time
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window, not globally over the entire word
at three adjacent positions at a time
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class of patterns (McNaughton, 1971; Rogers & Pullum, 2011; Rogers et al., 2013; Heinz, 2011; Heinz, Rawal, & Tanner, 2011)
to be learnable (e.g., Heinz, 2010a, 2010b; Jardine, Chandlee, Eyraud, & Heinz, 2014; Jardine & Heinz, 2016)
Majority Rules (Gainor, Lai, & Heinz, 2012; Lombardi, 1999)
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Computationally local1 constraints and functions have already been used to describe:
Heinz, Rawal, & Tanner, 2011) phonotactics
(Chandlee, 2014)
account for (Jardine, 2016)
1Works referenced here describe constraints and functions that are SL, SP, TSL, LT,
and GSL - not all SL, but local in a principled way.
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As a step towards improving the exhaustivity of our theory, we offer an account of syllable well-formedness. We have good reason to believe that much of phonology is local, so we would like to do this without referring to any non-local relations. This talk will:
1 Introduce a model-theoretic representation of syllable structure 2 Formalize some universal well-formedness constraints 3 Formalize some language-specific well-formedness constraints
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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tradition of ternary branching representations (e.g., Davis, 1985)
structures
syllabification process2, but this is not the goal of the present work
2For similar work on UR-SR mappings, see Chandlee, 2014
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
A set of node labels Σ = {C, V, ons, nuc, cod, σ}
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
A set of node positions D = {0, 1, 2, 3, 4, 5, 6}
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
(binary) δ(x, y): x immediately dominates y.
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
δ(0, 2): node 0 immediately dominates node 2.
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
(binary) (x, y): x immediately precedes y.
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σ nuc 2
1 cod 3 C 4 V 5 C 6
δ δ δ δ δ δ
(4, 5): node 4 immediately precedes node 5.
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For clarity in the remaining graphical representations of word models, we will sometimes omit:
σ nuc
cod C V C
δ δ δ δ δ δ
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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Sticking to canonical syllable types for now (e.g., no ambisyllabicity, extrasyllabicity, etc.), we can establish some universal constraints on syllable structure.
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Sticking to canonical syllable types for now (e.g., no ambisyllabicity, extrasyllabicity, etc.), we can establish some universal constraints on syllable structure.
We will formalize the first of these constraints in detail.
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This breaks down into two constraints:
1 NUCLEUS REQUIRED 2 NUCLEUS UNIQUE
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(∀x)[σ(x)] → (∃y)[nuc(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled nuc and x dominates y. σ x nuc y
δ
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(∀x)[σ(x)] → (∃y)[nuc(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled nuc and x dominates y. σ x nuc y
δ
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(∀x)[σ(x)] → (∃y)[nuc(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled nuc and x dominates y. σ x nuc y
δ
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(∀x)[σ(x)] → (∃y)[nuc(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled nuc and x dominates y. σ x nuc y
δ
Note: This constraint refers to a connected subgraph of size 2, which is analogous to a substring of size 2.
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(∀x, y, z)[σ(x) ∧ nuc(y) ∧ nuc(z) ∧ δ(x, y) ∧ δ(x, z)] → y = z For all nodes x, y, z, if x is labeled sigma, and y is labeled nuc, and z is labeled nuc, and x dominates y, and x dominates z, then y = z. σ x nuc y nuc z
δ δ
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(∀x, y, z)[σ(x) ∧ nuc(y) ∧ nuc(z) ∧ δ(x, y) ∧ δ(x, z)] → y = z For all nodes x, y, z, if x is labeled sigma, and y is labeled nuc, and z is labeled nuc, and x dominates y, and x dominates z, then y = z. σ x nuc y nuc z
δ δ
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(∀x, y, z)[σ(x) ∧ nuc(y) ∧ nuc(z) ∧ δ(x, y) ∧ δ(x, z)] → y = z For all nodes x, y, z, if x is labeled sigma, and y is labeled nuc, and z is labeled nuc, and x dominates y, and x dominates z, then y = z. σ x nuc y nuc z
δ δ
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(∀x, y, z)[σ(x) ∧ nuc(y) ∧ nuc(z) ∧ δ(x, y) ∧ δ(x, z)] → y = z For all nodes x, y, z, if x is labeled sigma, and y is labeled nuc, and z is labeled nuc, and x dominates y, and x dominates z, then y = z. σ x nuc y, z
δ
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(∀x, y, z)[σ(x) ∧ nuc(y) ∧ nuc(z) ∧ δ(x, y) ∧ δ(x, z)] → y = z For all nodes x, y, z, if x is labeled sigma, and y is labeled nuc, and z is labeled nuc, and x dominates y, and x dominates z, then y = z. σ x nuc y, z
δ
Note: This constraint refers to a connected subgraph of size 3.
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Other structural well-formedness constraints can be formalized in a similar way
(or less powerful logics)
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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We take the following steps to formalize the SSP:
1 Define a binary sonority relation between segment types that are
2 Extend this to a transitive relation of lesser sonority, in line with
the traditional notion of the sonority hierarchy
3 Develop a set of predicates that enforce rising sonority from onset
to nucleus and falling sonority from nucleus to coda
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IMMEDIATELY LESS SONOROUS son(x, y)
def
= [obs(x) ∧ nas(y)] ∨[nas(x) ∧ app(y)] ∨[app(x) ∧ V(y)] x is immediately less sonorous than y if:
3For brevity, we refer to only these four natural classes
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IMMEDIATELY LESS SONOROUS son(x, y)
def
= [obs(x) ∧ nas(y)] ∨[nas(x) ∧ app(y)] ∨[app(x) ∧ V(y)] x is immediately less sonorous than y if:
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IMMEDIATELY LESS SONOROUS son(x, y)
def
= [obs(x) ∧ nas(y)] ∨[nas(x) ∧ app(y)] ∨[app(x) ∧ V(y)] x is immediately less sonorous than y if:
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IMMEDIATELY LESS SONOROUS son(x, y)
def
= [obs(x) ∧ nas(y)] ∨[nas(x) ∧ app(y)] ∨[app(x) ∧ V(y)] x is immediately less sonorous than y if:
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IMMEDIATELY LESS SONOROUS son(x, y)
def
= [obs(x) ∧ nas(y)] ∨[nas(x) ∧ app(y)] ∨[app(x) ∧ V(y)] x is immediately less sonorous than y if:
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IMMEDIATELY LESS SONOROUS son(x, y)
def
= [obs(x) ∧ nas(y)] ∨[nas(x) ∧ app(y)] ∨[app(x) ∧ V(y)] Note: Obstruents are not immediately less sonorous than vowels, for example - we need a transitive relation to describe that.
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LESS SONOROUS son<(x, y) is the transitive closure of son(x, y). (∀x, y, z)[son<(x, y) ∧ son<(y, z)] → son<(x, z) For all nodes x, y, z, if x is less sonorous than y, and y is less sonorous than z, then x is less sonorous than z. Example Obstruents are less sonorous than nasals. Nasals are less sonorous than vowels. Therefore, obstruents are less sonorous than vowels.
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LESS SONOROUS son<(x, y) is the transitive closure of son(x, y). (∀x, y, z)[son<(x, y) ∧ son<(y, z)] → son<(x, z) For all nodes x, y, z, if x is less sonorous than y, and y is less sonorous than z, then x is less sonorous than z. Example Obstruents are less sonorous than nasals. Nasals are less sonorous than vowels. Therefore, obstruents are less sonorous than vowels.
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LESS SONOROUS son<(x, y) is the transitive closure of son(x, y). (∀x, y, z)[son<(x, y) ∧ son<(y, z)] → son<(x, z) For all nodes x, y, z, if x is less sonorous than y, and y is less sonorous than z, then x is less sonorous than z. Example Obstruents are less sonorous than nasals. Nasals are less sonorous than vowels. Therefore, obstruents are less sonorous than vowels.
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LESS SONOROUS son<(x, y) is the transitive closure of son(x, y). (∀x, y, z)[son<(x, y) ∧ son<(y, z)] → son<(x, z) For all nodes x, y, z, if x is less sonorous than y, and y is less sonorous than z, then x is less sonorous than z. Example Obstruents are less sonorous than nasals. Nasals are less sonorous than vowels. Therefore, obstruents are less sonorous than vowels.
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Using son<(x, y) as a starting point, the SSP can be formulated in two parts:
1 SON RISE RIGHT: Sonority must rise rightward from the onset 2 SON RISE LEFT: Sonority must rise leftward from the coda
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(∀x, y, z)[cod(x) ∧ δ(x, y) ∧ (z, y)] → son<(y, z) For all nodes x, y, z, if x is labeled cod, and x dominates y, and z precedes y, then y is less sonorous than z. cod x y z
δ
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(∀x, y, z)[cod(x) ∧ δ(x, y) ∧ (z, y)] → son<(y, z) For all nodes x, y, z, if x is labeled cod, and x dominates y, and z precedes y, then y is less sonorous than z. cod x y z
δ
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(∀x, y, z)[cod(x) ∧ δ(x, y) ∧ (z, y)] → son<(y, z) For all nodes x, y, z, if x is labeled cod, and x dominates y, and z precedes y, then y is less sonorous than z. cod x y z
δ
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(∀x, y, z)[cod(x) ∧ δ(x, y) ∧ (z, y)] → son<(y, z) For all nodes x, y, z, if x is labeled cod, and x dominates y, and z precedes y, then y is less sonorous than z. cod x y z
δ
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(∀x, y, z)[ons(x) ∧ δ(x, y) ∧ (y, z)] → son<(y, z) For all nodes x, y, z, if x is labeled ons, and x dominates y, and y precedes z, then y is less sonorous than z.
x y z
δ
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(∀x, y, z)[ons(x) ∧ δ(x, y) ∧ (y, z)] → son<(y, z) For all nodes x, y, z, if x is labeled ons, and x dominates y, and y precedes z, then y is less sonorous than z. nuc x y z
δ
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(∀x, y, z)[ons(x) ∧ δ(x, y) ∧ (y, z)] → son<(y, z) For all nodes x, y, z, if x is labeled ons, and x dominates y, and y precedes z, then y is less sonorous than z.
x y z
δ
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(∀x, y, z)[ons(x) ∧ δ(x, y) ∧ (y, z)] → son<(y, z) For all nodes x, y, z, if x is labeled ons, and x dominates y, and y precedes z, then y is less sonorous than z.
x y z
δ
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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Key insights from previous accounts of CV phonology (e.g., Clements, 1983; Jakobson, 1962; McCarthy, 1985):
both or neither
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In every language, one, both, or neither of these constraints holds at the surface level.
Note: These differ from OT ONSET and NOCODA in that they are inviolable constraints. Combinations of ONSET REQUIRED and CODA FORBIDDEN describe formal graph sets that may be extensionally identical to those produced from a certain ranking of violable constraints.
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(∀x)[σ(x)] → (∃y)[ons(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled ons and x dominates y. σ x
y
δ
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(∀x)[σ(x)] → (∃y)[ons(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled ons and x dominates y. σ x
y
δ
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(∀x)[σ(x)] → (∃y)[ons(y) ∧ δ(x, y)] For all nodes x labeled σ, there exists a node y labeled ons and x dominates y. σ x
y
δ
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(∀x)[σ(x)] → (¬∃y)[cod(y) ∧ δ(x, y)] For all nodes x labeled σ, there does not exist a node y labeled cod such that x dominates y. σ x cod y
δ
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(∀x)[σ(x)] → (¬∃y)[cod(y) ∧ δ(x, y)] For all nodes x labeled σ, there does not exist a node y labeled cod such that x dominates y. σ x cod y
δ
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(∀x)[σ(x)] → (¬∃y)[cod(y) ∧ δ(x, y)] For all nodes x labeled σ, there does not exist a node y labeled cod such that x dominates y. σ x cod y
δ
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The four logically possible combinations of these two constraints yield four language types (as in Blevins, 1995). ONSET REQUIRED ONSET NOT REQUIRED CODA FORBIDDEN CV (C)V CODA NOT FORBIDDEN CV(C) (C)V(C)
Table 1: Possible syllable types in basic CV typology
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1
Motivation
2
Toolkit: Word Models
3
Universal Constraints Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle
4
Language-Specific Constraints
5
Discussion
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Universal constraints (structural well-formedness & SSP) + Selection of ONSET REQUIRED and CODA FORBIDDEN = Language-specific syllable well-formedness
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The nonce word [arn.tjo] does not violate any of the given universal constraints.4 σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ δ δ
constraints - more on this later.
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NUCLEUS REQUIRED NUCLEUS UNIQUE σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ
δ
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SON RISE LEFT σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ δ
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SON RISE LEFT σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ δ
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SON RISE RIGHT σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ δ
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SON RISE RIGHT σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ δ
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would not allow this form to surface
epenthesis, deletion, etc.) must be guided by additional language-specific principles
such repairs can be determined by evaluating surface forms with respect to inviolable constraints
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syllable structure
formalized in FO logic
inviolable) can formally describe syllable well-formedness
sets because they all refer to subgraphs of size 3 or smaller
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formally establish the local nature of these constraints
the SSP, extrasyllabicity, ambisyllabicity, etc.
constraints
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σ nuc cod
nuc σ a r n t j
δ δ δ δ δ δ δ δ
δ
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Clements, G. N., & Keyser, S. J. (1983). CV phonology: A generative theory of the syllable. Cambridge, MA: MIT Press. Chandlee, J. (2014). Strictly local phonological processes. (Doctoral dissertation, University of Delaware). Davis, S. (1985). Topics in syllable geometry. (Doctoral dissertation). University of Arizona. Gainor, B., Lai, R., & Heinz, J. (2012). Computational characterizations of vowel harmony patterns and pathologies. In The Proceedings of the 29th West Coast Conference on Formal Linguistics (pp. 63-71). Graf, T. (2010a). Comparing incomparable frameworks: A model theoretic approach to phonology. University of Pennsylvania Working Papers in Linguistics, 16(1), 10. Graf, T. (2010b). Logics of phonological reasoning. (Master’s thesis). University of California, Los Angeles. Heinz, J. N. (2007). Inductive learning of phonotactic patterns. (Doctoral dissertation). University of California, Los Angeles. Heinz, J. (2009). On the role of locality in learning stress patterns. Phonology, 26(02), 303-351. Heinz, J. (2010a). Learning long-distance phonotactics. Linguistic Inquiry, 41(4), 623-661. Heinz, J. (2010b). String extension learning. In Proceedings of the 48th annual meeting of the association for computational linguistics (pp. 897-906). Association for Computational Linguistics. Heinz, J. (2011). Computational Phonology–Part I: Foundations. Language and Linguistics Compass, 5(4), 140-152. Heinz, J., Rawal, C., & Tanner, H. G. (2011). Tier-based strictly local constraints for phonology. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies: short papers-Volume 2 (pp. 58-64). Association for Computational Linguistics. Jakobson, R. (1962). Selected writings 1: Phonological studies. The Hague: Mouton. Jardine, A., Chandlee, J., Eyraud, R., & Heinz, J. (2014, September). Very efficient learning of structured classes of subsequential functions from positive data. In The 12th International Conference on Grammatical Inference (Vol. 34, pp. 94-108). Jardine, A., & Heinz, J. (2016). Learning Tier-based Strictly 2-Local Languages. Transactions of the Association for Computational Linguistics, 4, 87-98. Kenstowicz, M. J. (1994). Phonology in generative grammar. Cambridge, MA: Blackwell. Lombardi, L. (1999). Positional faithfulness and voicing assimilation in Optimality Theory. Natural Language & Linguistic Theory, 17(2), 267-302. McCarthy, J. (1979). Formal problems in semitic phonology and morphology. (Doctoral dissertation). MIT, Cambridge, MA. McNaughton, R., & Papert, S. A. (1971). Counter-Free Automata (MIT research monograph no. 65). The MIT Press. Potts, C., & Pullum, G. K. (2002). Model theory and the content of OT constraints. Phonology, 19(03), 361-393. Prince, A., & Smolensky, P. (1993). Optimality theory: Constraint interaction in generative grammar. New Brunswick, NJ: Rutgers Center for Cognitive Science, Rutgers, the State University of New Jersey. Rogers, J., Heinz, J., Fero, M., Hurst, J., Lambert, D., & Wibel, S. (2013). Cognitive and sub-regular complexity. In Formal Grammar (pp. 90-108). Springer Berlin Heidelberg. Rogers, J., & Pullum, G. K. (2011). Aural pattern recognition experiments and the subregular hierarchy. Journal of Logic, Language and Information, 20(3), 329-342 Scobbie, J. M. (1991). Towards declarative phonology.
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Special thanks to Jeff Heinz, Adam Jardine, Taylor Miller, and the rest
questions, and encouragements. Thanks to Eric Bakovic, Kevin McMullin, and the entire NAPhC 2016 audience for their insightful feedback. Contact Info kmsg@udel.edu sites.udel.edu/kmsg
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