11

A Game-Theoretic AnalysisA Game-Theoretic Analysisof Clausal Linkage in English of Clausal Linkage in English

and Japaneseand Japanese

Yukio Takahashi, Ph.D.Yukio Takahashi, Ph.D.Morioka CollegeMorioka College

The Research has been supported in part by Grant-in-Aid for Scientific ReseThe Research has been supported in part by Grant-in-Aid for Scientific Research by The Japan Society for the Promotion of Science, Basic Research (c) farch by The Japan Society for the Promotion of Science, Basic Research (c) for the Years 2006-2007, and for the years 2008-2010, and the Morioka Colleor the Years 2006-2007, and for the years 2008-2010, and the Morioka College Academic Grant for the year 2008.ge Academic Grant for the year 2008.

The paper is a sequel to the paper to be read at The 18th International CongrThe paper is a sequel to the paper to be read at The 18th International Congress of Linguists, held in Seoul, Korea University, July the 22nd.ess of Linguists, held in Seoul, Korea University, July the 22nd.

22

Goal and the Theoretical Goal and the Theoretical Framework AssumedFramework Assumed

Adopting the insights of the work in Game Theory (cf. Dixit aAdopting the insights of the work in Game Theory (cf. Dixit and Skeath (2004)), the present paper submits a thesis that the cnd Skeath (2004)), the present paper submits a thesis that the correspondence relations assumed in the Tripartite Parallel Arcorrespondence relations assumed in the Tripartite Parallel Architecture (work by Ray Jackendoff) are “Equilibria among Grahitecture (work by Ray Jackendoff) are “Equilibria among Grammatical Processing Gadgets” in the grammars of individual lmmatical Processing Gadgets” in the grammars of individual languages. anguages.

The equilibria among grammatical processing gadgets (hencefThe equilibria among grammatical processing gadgets (henceforth, GPG) are formally definable points at which several releorth, GPG) are formally definable points at which several relevant GPGs acquires payoffs that are strategically the most higvant GPGs acquires payoffs that are strategically the most highest.hest.

The significant corollary of the thesis is that we may do away The significant corollary of the thesis is that we may do away with the set of what are called the correspondence rules. with the set of what are called the correspondence rules.

33

AssumptionsAssumptions

The grammar of a language consists of a The grammar of a language consists of a hierarchy of gadgets, which give specified hierarchy of gadgets, which give specified strategies and interact with each other to strategies and interact with each other to specify and generate the optimal outputs.specify and generate the optimal outputs.

This assumption is an interpretation of This assumption is an interpretation of Game Theory by John von Neumann, Game Theory by John von Neumann, Oskar Morgenstern and John Nash.Oskar Morgenstern and John Nash.

44

AssumptionsAssumptions

Gadgets are agents involved in a game, in a Gadgets are agents involved in a game, in a broader sense of the term where they give a set of broader sense of the term where they give a set of strategies to select an optimal output from the strategies to select an optimal output from the grammar.grammar.

Gadgets are hierarchically ordered, the subset of Gadgets are hierarchically ordered, the subset of which we call “linguistically significant gadgets.”which we call “linguistically significant gadgets.”

The sense of the linguistic significance should be The sense of the linguistic significance should be defined according to the framework of the theory defined according to the framework of the theory we assume, or the boundary conditions on which we assume, or the boundary conditions on which adjacent subfields of science of language coincide. adjacent subfields of science of language coincide.

55

AssumptionsAssumptions

Full Interpretation (FI)Full Interpretation (FI)Conceptual structures are fully anchored Conceptual structures are fully anchored onto temporal elements.onto temporal elements.

Anchored Conceptual StructuresAnchored Conceptual StructuresConceptual structures for Various Types Conceptual structures for Various Types of Events are onto specified alley of of Events are onto specified alley of temporal elementstemporal elements

66

Representation of Temporal Representation of Temporal ElementsElements P: Point in TimeP: Point in Time R: Region in Time R: Region in Time

As are assumed by Jackendoff (1987)As are assumed by Jackendoff (1987)

77

Gadgets, Ranked HigherGadgets, Ranked Higher

Gadget (Narrative: Ground-Figure)Gadget (Narrative: Ground-Figure)R → R P R, R → R P R, where the P links to the where the P links to the endpoint of the relevant eventendpoint of the relevant event

88

Gadgets for the Five Event Types Gadgets for the Five Event Types with Temporal Elementswith Temporal Elements Point EventPoint Event

The light flashed [P]The light flashed [P] AchievementAchievement

Bill arrived [RP]Bill arrived [RP] Inceptive EventInceptive Event

Bill left [PR]Bill left [PR] ProcessesProcesses

Bill ran around [R]Bill ran around [R] Progressive FormsProgressive Forms

Bill was running around [RPR]Bill was running around [RPR]

99

An Instance of Full An Instance of Full InterpretationInterpretation The passage with temporal elements The passage with temporal elements

alignedaligned Jane was patrolling the neighborhood.Jane was patrolling the neighborhood.

R P R R P R

Jane noticed a car parked in an alley.Jane noticed a car parked in an alley.

1010

Point Event <=> Progressive Point Event <=> Progressive Forms Forms Short discourses with simple past and past Short discourses with simple past and past

progressiveprogressive

Jane was patrolling in the neighborhood. Jane was patrolling in the neighborhood. She noticed a car parked in an alley.She noticed a car parked in an alley.

Jane noticed a car parked in an alley. She Jane noticed a car parked in an alley. She was patrolling in the neighborhood.was patrolling in the neighborhood.

1111

Data from EnglishData from English

Independent Use of Narrative Independent Use of Narrative WhenWhen ClausesClauses

a. I read the book. a. I read the book. ##When I was ill in When I was ill in hospital.hospital.

b. Jane was doing the dishes. When in b. Jane was doing the dishes. When in came the dog.came the dog.

1212

Data from JapaneseData from Japanese

Clauses before linkageClauses before linkage John-wa sara-wo aratteita.John-wa sara-wo aratteita.

John-NOM dish-ACC wash-PROGRESSIVE PAST John-NOM dish-ACC wash-PROGRESSIVE PAST ttosonotoki inu-ga hai-tttosonotoki inu-ga hai-tekita ekita

when-NWC dog-NOM enter-PASTwhen-NWC dog-NOM enter-PAST John-wa hon-wo yon-da.John-wa hon-wo yon-da.

John-NOM book-ACC read-PASTJohn-NOM book-ACC read-PAST ttosonotoki namida-ga afure-te kita.ttosonotoki namida-ga afure-te kita.

When-NWC tear-NOM became full of the eyesWhen-NWC tear-NOM became full of the eyes John-wa hon-wo yon-da.John-wa hon-wo yon-da.

John-NOM book-ACC read-PASTJohn-NOM book-ACC read-PAST ttosonotoki Ame-ga yandattosonotoki Ame-ga yanda

when-NWC rain-NOM stop-PASTwhen-NWC rain-NOM stop-PAST

1313

Data from JapaneseData from Japanese Narrative function of “ttosonotoki”Narrative function of “ttosonotoki”

John-wa sara-wo aratteita. tJohn-wa sara-wo aratteita. tosonotoki inu-ga hai-tosonotoki inu-ga hai-tekitaekita ( (ジョンは皿を洗っていた。っと、その時、犬が入ってきた。ジョンは皿を洗っていた。っと、その時、犬が入ってきた。 ))

John-NOM dish-ACC wash-PROGRESSIVE PAST when-NWC dog-NOM eJohn-NOM dish-ACC wash-PROGRESSIVE PAST when-NWC dog-NOM enter-PASTnter-PAST

Illicit use of “ttosonotoki”Illicit use of “ttosonotoki” John-wa hon-wo yon-da. John-wa hon-wo yon-da. ##ttosonotoki John-wa byouin-ni ittattosonotoki John-wa byouin-ni itta

((ジョンは、本を読んだ。っと、その時、涙があふれてきた。ジョンは、本を読んだ。っと、その時、涙があふれてきた。 )) John-NOM book-ACC read-PAST when-NWC John-NOM hospital-in go-PJohn-NOM book-ACC read-PAST when-NWC John-NOM hospital-in go-P

AST AST John-wa hon-wo yon-da. John-wa hon-wo yon-da. ##ttosonotoki ame-ga yandattosonotoki ame-ga yanda

((ジョンは、本を読んだ。っとその時、雨が止んだジョンは、本を読んだ。っとその時、雨が止んだ )) John-NOM book-ACC read-PAST when-NWC it stop-PAST rainingJohn-NOM book-ACC read-PAST when-NWC it stop-PAST raining ジョンは、本を読んでいた。っと、その時、涙があふれてきた。ジョンは、本を読んでいた。っと、その時、涙があふれてきた。【【 betbet

ter verbalization ter verbalization 】】ジョンは、本を読んでいた。っと、その時、雨が止んだ。【ジョンは、本を読んでいた。っと、その時、雨が止んだ。【 better verbetter verbalizationbalization】】

1414

Game-Theoretic Generalization: Payoff Matrix for Game-Theoretic Generalization: Payoff Matrix for Jane Jane was doing the dishes. When in came the dogwas doing the dishes. When in came the dog

[Event, Progressive, Narrative][Event, Progressive, Narrative]

On, on, on => [1,1,2] Available < FIOn, on, on => [1,1,2] Available < FI On, on, off => [1,1,φ]On, on, off => [1,1,φ] 　＞　　＞　 *FI*FI Off, off, off => [φ,φ,φ] > *FIOff, off, off => [φ,φ,φ] > *FI

1515

On, on, on => [1,1,2] Available On, on, on => [1,1,2] Available < FI< FI Full Interpretation and AvailabilityFull Interpretation and Availability

R P R (Progressive) R P R (Progressive) R P R (Narrative)R P R (Narrative)

P (Event) P (Event)

1616

Game-Theoretic Generalization: Payoff Matrix Game-Theoretic Generalization: Payoff Matrix for for I read the book. I read the book. ##When I was ill in hospitalWhen I was ill in hospital

[State, Progressive, Narrative][State, Progressive, Narrative]

On, on, on => [1,1,2] On, on, on => [1,1,2] Unavailable Unavailable *FI*FI On, on, off => [1,1,φ]On, on, off => [1,1,φ] 　＞　　＞　 *FI*FI Off, off, off => [φ,φ,φ] > *FIOff, off, off => [φ,φ,φ] > *FI

1717

On, on, on => [1,1,2] On, on, on => [1,1,2] Unavailable Unavailable *FI*FI Full Interpretation and AvailabilityFull Interpretation and Availability

R P R (Progressive) R P R (Progressive) R P R (Narrative)R P R (Narrative)

R (State) R (State)

Crucially, “R” does not have any endpoint.Crucially, “R” does not have any endpoint.

1818

ジョンは皿を洗っていた。っジョンは皿を洗っていた。っと、その時、犬が入ってきたと、その時、犬が入ってきた This passage is felicitous by the same This passage is felicitous by the same

reason why reason why Jane was doing the dishes Jane was doing the dishes when in came the dog.when in came the dog.

1919

ジョンは、本を読んだ。っと、ジョンは、本を読んだ。っと、その時、涙があふれてきたその時、涙があふれてきた The clause “The clause “ 本を読んだ” 本を読んだ” crucially is or crucially is or

can be un-perfective event, so that the can be un-perfective event, so that the conceptual structure anchored on “R,” conceptual structure anchored on “R,” while the gadget (narrative) calls for an while the gadget (narrative) calls for an endpoint of the event “endpoint of the event “ 涙があふれてき涙があふれてきた” た” (which is rather inceptive).(which is rather inceptive).

2020

ジョンは、本を読んだ。っと、ジョンは、本を読んだ。っと、その時、涙があふれてきたその時、涙があふれてきた 本を読んだ本を読んだ

　　　　　　 P RP R 　　　　　　 (un-perfective)(un-perfective)

RR P R (narrative) P R (narrative)

P R (inceptive) P R (inceptive) Thus, the “R” is fragrantly Thus, the “R” is fragrantly NOTNOT satisfied. satisfied.

2121

ジョンは、本を読んでいた。ジョンは、本を読んでいた。っと、その時、涙があふれてっと、その時、涙があふれてきたきた ジョンは、本を読んでいたジョンは、本を読んでいた

R P RR P R R P R R P R P R P R

涙があふれてきた涙があふれてきた

2222

SummarySummary

Grammatical gadgets are hierarchically Grammatical gadgets are hierarchically organized to give varied values of payoffs. organized to give varied values of payoffs. In order for the consecutive sentences to In order for the consecutive sentences to form a passage, they (which are form a passage, they (which are themselves gadgets) should satisfy the themselves gadgets) should satisfy the condition of Full Interpretation to acquire condition of Full Interpretation to acquire higher payoffs, in which sense the gadgets higher payoffs, in which sense the gadgets are evaluated game-theoretically to select are evaluated game-theoretically to select one optimal output from the grammar.one optimal output from the grammar.

2323

References (selected)References (selected)

Declerck, Renaat (1997) When-Declerck, Renaat (1997) When-Clauses and Temporal StClauses and Temporal Structureructure, Routledge, London., Routledge, London.

Dixit, Avinash and Susan Skeath (2004) Dixit, Avinash and Susan Skeath (2004) Games of StrateGames of Strategygy, 2nd edtion, W.W. Norton & Company, New York an, 2nd edtion, W.W. Norton & Company, New York and London.d London.

Jackendoff, Ray (1987) “The Status of Thematic RelatioJackendoff, Ray (1987) “The Status of Thematic Relations in Linguistic Theory,” ns in Linguistic Theory,” Linguistic InquiryLinguistic Inquiry 19, 369-411. 19, 369-411.

ter Meulen, Alice G.B. (2000) “Chronoscopes,” J. Higgiter Meulen, Alice G.B. (2000) “Chronoscopes,” J. Higginbotham, F. Pianesi and A.C. Varzi (eds.) nbotham, F. Pianesi and A.C. Varzi (eds.) Speaking of EvSpeaking of Eventsents, Oxford University Press, pp. 151-168. , Oxford University Press, pp. 151-168.