Deprecated: The each() function is deprecated. This message will be suppressed on further calls in /home/zhenxiangba/zhenxiangba.com/public_html/phproxy-improved-master/index.php on line 456 Robin Clark's Research Interests
Games, Numbers and Brains
My research centers around applications of classical Game Theory to the study of natural language and Neuroscience, particularly the study of the
relationship between number sense (numerosity) and the understanding of
natural language quantification.
Although work in game theoretic aspects of meaning, on the one hand, and
the neuroanatomy of number and its relationship to the understanding of
natural language quantifiers, on the other, might seem to be rather
disparate, my hope is that the two areas can be unified via Behavioral Game
Theory and by studying the neurological underpinnings of decision
making, neuroeconomics.
My work has moved away from studying linguistic meaning in terms of
(mental) representations, toward the study of language as an economic fact
or a fact about biological populations, a move that was implicit in some of
my earlier work on linguistic learning and language change in terms of genetic
algorithms.
Game Theory Game Theory provides the mathematics
for the analysis of strategic choice among rational players. Natural
language involves strategic choice at many levels, from semantics and
syntax to sociolinguistics, psycholinguistics and historical change. For
example, a speaker may want to encode a particular meaning, φ, but may
have a variety of different ways of doing so: μ, μ', μ''... and so
on, each of which encodes the meaning φ as well as other meanings. She
must, therefore, select from a range of possible ways of expressing the
intended meaning based on the costs of the communications as well as her
knowledge of the hearer's information state.
Equally, the hearer
is presented with a decision problem when confronted with an expression μ
which might have meanings φ, φ', φ'', ..., and so on. That is,
the hearer must select from a range of possible meanings that the speaker
could intend to transmit.
The decision problems faced by the
speaker and hearer can be solved by representing their choices as a game of
partial information (see Parikh, 2001). The common knowledge of the
participants can be represented as a game tree. Information flow is
enabled by solving for the Pareto-dominant Nash equilibrium (see the papers
below for details).
At present, most of my work focuses on pragmatics and semantics, but I hope
to develop models of language change, strategic choice in sociolinguistics
and so on. Since Game Theory can be used as an alternative framework for
thinking about logic and model theory, the approach promises to unify
linguistics in an unprecedented way.
Here are the slides for a talk Prashant Parikh and I gave at
Conversational Games and Strategic Inference, a workshop organized
as part of the 2007 LSA Summer Institute at Standford University. It
includes work on using some mathematical ecology, in particular a game
interpretation of the Lotka-Volterra Equation to account for the
development of defaults:
Robin Clark & Prashant Parikh. Equilibria and Equilibrium Semantics. pdf
Here's a short research note on the linguistic defaults idea,
discussing the model in more detail. It also goes into lexical games and
garden path phenomena in a bit more detail:
Robin Clark, Prashant Parikh & Neville Ryant. Evolving Linguistic
Defaults. pdf
I'm currently working with Prashant Parikh on equilibrium
semantics. The project fuses games of partial information with a
compositional semantics.
A short description of the central idea can be found in:
Prashant Parikh & Robin Clark (in press). An Introduction to Equilibrium
Semantics for Natural Language, in A-V Pietarinen (ed) Game Theory and
Linguistic Meaning (Current Research in the Semantics/Pragmatics
Interface 17). Elsevier. pdf
We've also worked up an application of games of partial information to
discourse anaphora:
Robin Clark & Prashant Parikh (2007) Game Theory and Discourse
Anaphora. Journal of Logic, Language and
Information. 16:265-282. pdf
We're also working on an application of equilibrium semantics to
definite descriptions:
Prashant Parikh & Robin Clark (in prep) The Meaning of THE: A New Account
of Definite Descriptions. pdf
We're also working on a book, Language and Equilibrium, which
describes the framework in detail as well as developing a variety of
applications.
I've also done some work trying to pull together Hintikka-style game
semantics for natural language with games of partial information. In
particular, I've worked on how quantified expressions can create discourse
entities using a semantics grounded in zero-sum games:
Robin Clark (in press) "Games, Quantifiers and Pronouns" in A-V Pietarinen (ed) Game Theory and
Linguistic Meaning (Current Research in the Semantics/Pragmatics
Interface 17). Elsevier. pdf
An earlier, and shorter, version of the preceding work was presented
at the Prague Colloquium a few years ago and appears as:
Robin Clark (in press). "Games, Quantification and Discourse Structure" in
O. Mayer, A.-V. Pietarinen & T. Tulenheimo (eds) Logic, Games and
Philosophy: Foundational Perspectives. Kluwer. pdf
I've written a paper that describes the motivation for studying
meaning from the point of view of populations as opposed to (private)
mental representations. The paper was commissioned for a book on
indeterminacy in science which I'm told is in press from MIT. The paper is
intended for a general audience.
Robin Clark (in press) "Reliable Cribs: Decipherment, Learnability and
Indeterminacy. pdf
Neuroscience I'm affiliated with the Grossman Lab at the
medical school at Penn. We've been working on the connections between
number sense (numerosity) and language, more specifically, the
interpretation of single quantifiers in sentences.
Humans distinguish themselves both in having expressive language and in
having a sense of precise number for quantities greater than 4. Other
creatures have an approximate sense of number; in particular, other animals
have a sense of "about n" where their responses, when average, have
n as a mean, the standard deviation growing as n grows, in
accord with the Weber-Fechner
Law or, perhaps more accurately, Stevens' Power
Law.
The obvious question to ask is how the capacity for precise number relates
to expressive language. It could be that precise number sense and
expressive language arose independently, their presence in humans being the
result of a series of coincidences. Equally, we might suppose that there
is a causal connection between language and precise number.
This paper summarizes our work on the relationship between numerosity
and quantifier interpretation, including work with CBD and FTD patients:
Robin Clark & Murray Grossman (2007) "Number Sense and Quantifier
Interpretation" Topoi. 26:51-62. pdf
``Neural Basis for Generalized Quantifier Comprehension'' (with Corey
Miller, Peachie Moore, Christian Devita and Murray Grossman). to appear in
Neuropsychologia.
``Verbal mediation of number knowledge: Evidence from semantic
dementia and corticobasal degeneration'' (with Casey Halpern, Peachie
Moore, Shweta Antani, Amy Colcher and Murray Grossman). Brain and
Cognition, 56, 107--115. 2004.
``Calculation impairment in neurodegenerative diseases'' (with
C. Halpern, C. McMillan, P. Moore, K. Dennis, & M. Grossman). Journal
of the Neurological Sciences. 208:31-38. 2003.
``The neural basis for generalized quantifiers.'' (with
C. McMillan, P. Moore, L. Moneta, C. DeVita, & M Grossman) Journal of
the International Neuropsychological Society; 8:318, 2002
``Calculation impairment in neurodegenerative diseases'' (with
C. Halpern, C. McMillan, P. Moore, K. Dennis & M. Grossman).
Neurology, 58:A355. 2002.