A GameTheoretic ReInterpretation of Phonological Generalizations Yukio Takahashi

A Game-Theoretic Re-Interpretation of Phonological Generalizations Yukio Takahashi　高橋幸雄 Morioka College 盛岡大学 The research has been supported in part by the Grant-in-Aid for Scientific Research for the years 2006 -2007 (No: 18520389) by The Japan Society for the Promotion of Science and by Morioka College Academic Grant for the year 2005 1

Purposes • Description of Game-Theoretic Approach to the Theory of Phonology • Game-Theoretic Re-interpretation (Reanalysis) of Phonological Generalizations • Computationally Implementable Framework of Phonology 2

Assumptions • The theoretical model of phonology internalizes hierarchically organized phonological computational gadgets that give more than one articulatory strategy • The outputs of the system are states of equilibria among the articulatory strategies • The activity of articulating a linguistic sound is a “game” among these gadgets 3

Structure of the Presentation • Definition of the Game-Theoretic Approach to Phonology: Strategies, Society of Phonological Mind, Pay-Off Matrices… Autosegmental Spreading of Features, Underspecification • Game-Theoretic Reinterpretation of Coarticulation 4

Relevant Data • key [ ] an advanced variety of /k/ • caw [ ] a rounded and retracted variety of /k/ (Kühnert and Nolan (1999: 7) • devoicing of /l/ in [ ] Jones (19609: 220) 5

Non-Cooperative Strategies in Coarticulation • Strategic interplay of the phonological processing gadgets A better understanding of coarticulation has come from investigations … on the effects of articulatory constraints on the coarticulatory movements, i. e. on the complex interplay between influencing and influenced sounds, and on the relationship between coarticulation and articulatory antagonism [Farnetani (1990: 96)] 6

Research Scheme • Society of Phonological Mind (Cf. Takahashi 2006, to appear) The theoretical model of phonology internalizes hierarchically organized phonological computational gadgets that give more than one articulatory strategy. The outputs of the phonology are states of equilibria among the articulatory strategies. 7

Assumptions on Phonological Processing Gadgets • Linguistic articulations of sounds emerge out of the interactions of articulatory strategies of PPGs. • PPGs are composed of smaller agents (PPGs) that cannot plan articulatory strategies. • Articulatory strategies of a PPG are selected and applied so as to reach equilibria with those of other PPGs. 8

Major Elements of the Phonological Mind • Autosegmental Spreading of Features: Spreading of terminal features in featuregeometric representations (Cf. Sagey (1986)) • Structure Preservation In the lexicon, restrictions on underlying representations are applied to derived representations (Cf. Kiparsky (1982, 1985)) 9

S- and K-Societies of Phonological Mind • Overall Architecture of the Society of Phonological Mind Cognitive Effect S-Society (Spreading of Features) K-Society (Structure Preservation) 10

PPGs in [ ] and [ ] • PPG 1 for velic closure • PPG 2 for lip rounding • PPG 3 for retracting the tongue root • PPG 4 for advancing the body of the tongue • PPG 5 for feature spreading 11

Hierarchy of the PPGs • [velic closure] Feature Spreading [lip rounding] [tongue root retraction] [advanced tongue root] The higher the PPG, the larger the value of (non-) achievements. 12

Principles of Pay-Off Calculation • Pay-Off for PPGs • Anchoring on the temporal elements in featuregeometric representations in the sense of Sagey (1986) • Application of Unmarked Strategies: [1] • Non-Application of (Un-)marked Strategies: [Ø] • Application of Marked Strategies: [– 1] 13

Notation • ON and OFFS of PPGs • PPG (F) is a functional notation for the PPG that executes the articulatory process F. • PPG (a, b) stands for the linkage of PPG (a) with PPG (b) 14

Assumptions on Markedness • By default, /k/ is OFF wrt roundedness • By default, /k/ is OFF wrt retractedness • By default, /k/ is OFF wrt advancedness • Spreading of features values is an instance of the application of unmarked strategies 15

The Notion of Equilibria among Articulatory Gadgets The notion “states of equilibria among articulatory gadgets” is directly captured by the total sum of the values that these gadgets achieved. The higher the PPG in the society, the larger the value of the (non-) achievements of the PPG. 16

Symbols • ☺ (Smile Sign) the combined strategies that are felicitous, where we find the equilibria • ¶ (Paragraph Sign) the designated strategies actually executed 17

Pay-Off Matrix for [ ] lr: lip rounding PPG (Nucleus, 3 rd dim: spreading lr) ON PPG (Onset, lr) (– 1, 1, 1) ☺ ¶ ON PPG (Onset, lr) (Ø, 1, – 1)　 OFF PPG (Nucleus, lr) OFF (– 1, – 1) (Ø, – 1, Ø) 18

Pay-Off Matrix for *[ ] adv: advanced 3 rd dim: spreading PPG (nucleus, adv) ON PPG (nucleus, adv) OFF PPG (onset, adv) (– 1, 1) ON (– 1, Ø, – 1) ¶ PPG (onset, adv) (Ø, – 1) OFF (Ø, Ø, Ø) ☺ 19

S- and K-Societies (2) • (the original idea comes from Marvin Minsky) • S-Society: society of original agents • K-Society: society of agents that memorize any cognitively significant information • S-Society maps out a set of strategies of the PPGs and the set is sent to the K-Society to seek verification of the correspondence with underlying (lexical) representations. 20

High Vowel Devoicing in Japanese • Standard Japanese [ ] “low” [ ] (*[ ]) • A Variety of Tohoku Dialect in Japanese [ ] “low” [ ] “east” (*[ ]) • Devoicing of high vowels In the environment “[–voiced]___[–voiced]” (cf. Vance (1987)) 21

Payoff Matrix for *[ ] in Standard Japanese PPG for Intercons onantal Devoicin g (+1, 0, – 2) PPG for (+1, – 1, Spreadin – 2) g of Features ON /OFF (– 1, – (– 1, 0, – 2) 2) ON / OFF PPG for Cognitiv e Effect ON / OFF 22

Payoff Matrix for [ ] in Tohoku Dialect PPG for (+1, Spreadin +2) g of Features ON /OFF (– 1, +2) Intercons onantal Devoicin g (+1, 0, +2) ON / OFF (– 1, 0, +2) ON / OFF PPG for Cognitiv e Effect 23

Conclusive Remarks The framework of phonology laid out in this presentation assumes a set of phonological processing gadgets, whose operations are stipulated individually. In our framework the number of outputs from phonology is in principle specifiable: the whole set of possible outputs CAN be evaluated, and the whole theoretical system is verifiable. The possibility of computational implementation is guaranteed by the stipulation to the effect that the phonological processing gadgets (PPGs) can only be either ON or OFF. As for the possibilities of our hypothesis in other fields of inquiry, I may refer to my paper (2007), which tries to apply the reanalysis to the syntaxsemantics interface of natural language. 24

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