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: Word Models 2 Universal Constraints 3 Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle Language-Specific Constraints 4 Discussion 5 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 2 / 84
Outline Motivation 1 Toolkit: Word Models 2 Universal Constraints 3 Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle Language-Specific Constraints 4 Discussion 5 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 3 / 84
The Present Research Program • Expresses constraints in formal logic • Represents phonological structures using word models and graphs, in addition to strings • Goals: • Formalize patterns already described in other frameworks • Formalize patterns that have been difficult to capture in other frameworks • Evaluate the relative merits of different formalizations in a principled way K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 4 / 84
Why Use These Formalizations? • Maximally explicit descriptions make clear, falsifiable predictions • Constraints expressed in logical formulae describe established language classes of known computational power , allowing us to: • Make principled distinctions between what is possible (attested) and impossible (unattested) • Evaluate under- and over-generation problems and learnability in existing theoretical treatments • Several theorists have noted the value of formal logic in theoretical phonology (e.g., Graf, 2010a, 2010b; Heinz, 2011; Potts & Pullum, 2002; Scobbie, 1991) K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 5 / 84
Computational Locality • Computationally local constraints are evaluated over a small window, not globally over the entire word • Example: [#bn] is a banned substructure in English • To check if a word contains this substructure, we only need to look at three adjacent positions at a time K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 6 / 84
Computational Locality • Computationally local constraints are evaluated over a small window, not globally over the entire word • Example: [#bn] is a banned substructure in English • To check if a word contains this substructure, we only need to look at three adjacent positions at a time # bnIk # K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 7 / 84
Computational Locality • Computationally local constraints are evaluated over a small window, not globally over the entire word • Example: [#bn] is a banned substructure in English • To check if a word contains this substructure, we only need to look at three adjacent positions at a time # bnIk # K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 8 / 84
Why Locality Matters • Shrinks the hypothesis space of phonology to a highly restricted class of patterns (McNaughton, 1971; Rogers & Pullum, 2011; Rogers et al., 2013; Heinz, 2011; Heinz, Rawal, & Tanner, 2011) • Certain types of computationally local patterns have been shown to be learnable (e.g., Heinz, 2010a, 2010b; Jardine, Chandlee, Eyraud, & Heinz, 2014; Jardine & Heinz, 2016) • Prevents counting ad infinitum, which rules out patterns like Majority Rules (Gainor, Lai, & Heinz, 2012; Lombardi, 1999) K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 9 / 84
Previous Work on Locality in Phonology Computationally local 1 constraints and functions have already been used to describe: • Local (Heinz, 2007, 2009) and long-distance (Heinz, 2010a; Heinz, Rawal, & Tanner, 2011) phonotactics • Transformations from underlying representations to surface forms (Chandlee, 2014) • Tone well-formedness patterns, including some that OT cannot account for (Jardine, 2016) 1 Works referenced here describe constraints and functions that are SL, SP, TSL, LT, and GSL - not all SL, but local in a principled way. K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 10 / 84
Case Study: Syllable Well-Formedness 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 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 11 / 84
Outline Motivation 1 Toolkit: Word Models 2 Universal Constraints 3 Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle Language-Specific Constraints 4 Discussion 5 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 12 / 84
Modeling Syllable Structure • We use formal word models to represent syllable structure in the tradition of ternary branching representations (e.g., Davis, 1985) • We focus on surface constraints on the well-formedness of these structures • This framework can, in principle, accommodate a model of the syllabification process 2 , but this is not the goal of the present work 2 For similar work on UR-SR mappings, see Chandlee, 2014 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 13 / 84
Elements of the Word Model σ 0 δ δ δ � � ons nuc cod 1 2 3 δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 14 / 84
Elements of the Word Model: Alphabet σ 0 δ δ δ Alphabet, Σ � � ons nuc cod A set of node labels 1 2 3 Σ = { C , V , ons , nuc , cod , σ } δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 15 / 84
Elements of the Word Model: Domain σ 0 δ δ δ Domain, D � � ons nuc cod A set of node positions D = { 0 , 1 , 2 , 3 , 4 , 5 , 6 } 1 2 3 δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 16 / 84
Elements of the Word Model: Labeling Relations σ 0 δ δ δ Labeling Relations (unary) � � • σ ( x ) : node x is labeled σ ons nuc cod • ons ( x ) : node x is labeled ons 1 2 3 δ δ δ • ...etc. � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 17 / 84
Elements of the Word Model: Labeling Examples σ 0 δ δ δ Examples � � ons nuc cod • σ ( 0 ) : node 0 is labeled σ 1 2 3 • C ( 4 ) : node 4 is labeled C δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 18 / 84
Elements of the Word Model: Dominance Relation σ 0 δ δ δ Immediate Dominance Relation � � ons nuc cod (binary) 1 2 3 δ ( x , y ) : x immediately dominates y . δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 19 / 84
Elements of the Word Model: Dominance Example σ 0 δ δ δ Example � � ons nuc cod δ ( 0 , 2 ) : node 0 immediately 1 2 3 dominates node 2. δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 20 / 84
Elements of the Word Model: Precedence Relation σ 0 δ δ δ Immediate Precedence Relation � � ons nuc cod (binary) 1 2 3 � ( x , y ) : x immediately precedes y . δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 21 / 84
Elements of the Word Model: Precedence Example σ 0 δ δ δ Example � � ons nuc cod � ( 4 , 5 ) : node 4 immediately 1 2 3 precedes node 5. δ δ δ � � C V C 4 5 6 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 22 / 84
Simplifying the Visual Representation For clarity in the remaining graphical representations of word models, we will sometimes omit: • Position numbers • Immediate precedence edges between ons, nuc, and cod σ δ δ δ ons nuc cod δ δ δ � � C V C K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 23 / 84
Outline Motivation 1 Toolkit: Word Models 2 Universal Constraints 3 Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle Language-Specific Constraints 4 Discussion 5 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 24 / 84
Outline Motivation 1 Toolkit: Word Models 2 Universal Constraints 3 Universal Structural Well-Formedness Constraints The Sonority Sequencing Principle Language-Specific Constraints 4 Discussion 5 K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 25 / 84
Universal Structural Well-Formedness Constraints Sticking to canonical syllable types for now (e.g., no ambisyllabicity, extrasyllabicity, etc.), we can establish some universal constraints on syllable structure. • Every syllable has exactly one nucleus • An onset must immediately precede a nucleus • A coda must immediately follow a nucleus • ...and so on K. Strother-Garcia (UD) NAPhC 2016 May 8, 2016 26 / 84
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