A Game-Theoretic Analysis of Clausal Linkage in English and Japanese

1. A Game-Theoretic Analysisof Clausal Linkage in English and Japanese Yukio Takahashi, Ph.D. Morioka College The 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) for the Years 2006-2007, and for the years 2008-2010, and the Morioka College Academic Grant for the year 2008. The 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.

2. Goal and the Theoretical Framework Assumed • Adopting the insights of the work in Game Theory (cf. Dixit and Skeath (2004)), the present paper submits a thesis that the correspondence relations assumed in the Tripartite Parallel Architecture (work by Ray Jackendoff) are “Equilibria among Grammatical Processing Gadgets” in the grammars of individual languages. • The equilibria among grammatical processing gadgets (henceforth, GPG) are formally definable points at which several relevant GPGs acquires payoffs that are strategically the most highest. • The significant corollary of the thesis is that we may do away with the set of what are called the correspondence rules.

3. Assumptions • The grammar of a language consists of a hierarchy of gadgets, which give specified strategies and interact with each other to specify and generate the optimal outputs. • This assumption is an interpretation of Game Theory by John von Neumann, Oskar Morgenstern and John Nash.

4. Assumptions • Gadgets are agents involved in a game, in a broader sense of the term where they give a set of strategies to select an optimal output from the grammar. • Gadgets are hierarchically ordered, the subset of which we call “linguistically significant gadgets.” • The sense of the linguistic significance should be defined according to the framework of the theory we assume, or the boundary conditions on which adjacent subfields of science of language coincide.

5. Assumptions • Full Interpretation (FI)Conceptual structures are fully anchored onto temporal elements. • Anchored Conceptual StructuresConceptual structures for Various Types of Events are onto specified alley of temporal elements

6. Representation of Temporal Elements • P: Point in Time • R: Region in Time As are assumed by Jackendoff (1987)

7. Gadgets, Ranked Higher • Gadget (Narrative: Ground-Figure)R → R P R, where the P links to the endpoint of the relevant event

8. Gadgets for the Five Event Types with Temporal Elements • Point EventThe light flashed [P] • AchievementBill arrived [RP] • Inceptive EventBill left [PR] • ProcessesBill ran around [R] • Progressive FormsBill was running around [RPR]

9. An Instance of Full Interpretation • The passage with temporal elements aligned • Jane was patrolling the neighborhood. R P RJane noticed a car parked in an alley.

10. Point Event <=> Progressive Forms • Short discourses with simple past and past progressive • Jane was patrolling in the neighborhood. She noticed a car parked in an alley. • Jane noticed a car parked in an alley. She was patrolling in the neighborhood.

11. Data from English • Independent Use of Narrative When Clauses • a. I read the book. #When I was ill in hospital. • b. Jane was doing the dishes. When in came the dog.

12. Data from Japanese • Clauses before linkage • John-wa sara-wo aratteita. John-NOM dish-ACC wash-PROGRESSIVE PAST • ttosonotoki inu-ga hai-tekita when-NWC dog-NOM enter-PAST • John-wa hon-wo yon-da.John-NOM book-ACC read-PAST • ttosonotoki namida-ga afure-te kita.When-NWC tear-NOM became full of the eyes • John-wa hon-wo yon-da.John-NOM book-ACC read-PAST • ttosonotoki Ame-ga yandawhen-NWC rain-NOM stop-PAST

13. Data from Japanese • Narrative function of “ttosonotoki” • John-wa sara-wo aratteita. tosonotoki inu-ga hai-tekita (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 enter-PAST • Illicit use of “ttosonotoki” • John-wa hon-wo yon-da. #ttosonotoki 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。) • John-NOM book-ACC read-PAST when-NWC John-NOM hospital-in go-PAST • John-wa hon-wo yon-da. #ttosonotoki ame-ga yanda(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 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。【better verbalization 】ジョンは、本を読んでいた。っと、その時、雨が止んだ。【better verbalization】

14. Game-Theoretic Generalization: Payoff Matrix for Jane was doing the dishes. When in came the dog • [Event, Progressive, Narrative] • On, on, on => [1,1,2] Available < FI • On, on, off => [1,1,φ]　＞　*FI • Off, off, off => [φ,φ,φ] > *FI

15. On, on, on => [1,1,2] Available < FI • Full Interpretation and Availability R P R (Progressive)R P R (Narrative) P (Event)

16. Game-Theoretic Generalization: Payoff Matrix for I read the book. #When I was ill in hospital • [State, Progressive, Narrative] • On, on, on => [1,1,2] Unavailable *FI • On, on, off => [1,1,φ]　＞　*FI • Off, off, off => [φ,φ,φ] > *FI

17. On, on, on => [1,1,2] Unavailable *FI • Full Interpretation and Availability R P R (Progressive)R P R (Narrative) R (State)Crucially, “R” does not have any endpoint.

18. 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 • This passage is felicitous by the same reason why Jane was doing the dishes when in came the dog.

19. 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 • The clause “本を読んだ” crucially is or can be un-perfective event, so that the conceptual structure anchored on “R,” while the gadget (narrative) calls for an endpoint of the event “涙があふれてきた” (which is rather inceptive).

20. 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 • 本を読んだP R(un-perfective)R P R (narrative) P R (inceptive) • Thus, the “R” is fragrantly NOT satisfied.

21. 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 • ジョンは、本を読んでいたR P R R P R P R 涙があふれてきた

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

23. References (selected) • Declerck, Renaat (1997) When-Clauses and Temporal Structure, Routledge, London. • Dixit, Avinash and Susan Skeath (2004) Games of Strategy, 2nd edtion, W.W. Norton & Company, New York and London. • Jackendoff, Ray (1987) “The Status of Thematic Relations in Linguistic Theory,” Linguistic Inquiry 19, 369-411. • ter Meulen, Alice G.B. (2000) “Chronoscopes,” J. Higginbotham, F. Pianesi and A.C. Varzi (eds.) Speaking of Events, Oxford University Press, pp. 151-168.