A Game-Theoretic Analysis of Clausal Linkage in

A Game-Theoretic Analysis
of 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.
1
Goal and the Theoretical
Framework Assumed


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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.
2
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.
3
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.
4
Assumptions


Full Interpretation (FI)
Conceptual structures are fully anchored
onto temporal elements.
Anchored Conceptual Structures
Conceptual structures for Various Types of
Events are onto specified alley of temporal
elements
5
Representation of Temporal
Elements
P: Point in Time
 R: Region in Time
As are assumed by Jackendoff (1987)

6
Gadgets, Ranked Higher

Gadget (Narrative: Ground-Figure)
R → R P R, where the P links to the
endpoint of the relevant event
7
Gadgets for the Five Event Types
with Temporal Elements





Point Event
The light flashed [P]
Achievement
Bill arrived [RP]
Inceptive Event
Bill left [PR]
Processes
Bill ran around [R]
Progressive Forms
Bill was running around [RPR]
8
An Instance of Full
Interpretation


The passage with temporal elements
aligned
Jane was patrolling the neighborhood.
R P R
Jane noticed a car parked in an alley.
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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.

10
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.
11
Data from Japanese

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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 yanda
when-NWC rain-NOM stop-PAST
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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
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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 goPAST
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】
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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


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On, on, on => [1,1,2] Available
< FI

Full Interpretation and Availability
R
P
R (Progressive)
R
P
R (Narrative)
P
(Event)
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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


16
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.
17
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.
18
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).
19
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
PR
(un-perfective)
R P R (narrative)

P R (inceptive)
Thus, the “R” is fragrantly NOT satisfied.
20
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
RPR
R P R
P R
涙があふれてきた
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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.
22
References (selected)
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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.
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