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\begin{document}
\title{Simulating Language Games of the Two Word Stage using Unification and
Substitutions on a Corpus of Exemplars with a focus on Semantics \\ }
\subtitle{\em ~\\ . . . being an endeavor in cognitive simulation to
parsimoniously re-enact verbal interactions of a toddler through translation
and reckoning with pragmatic and semantic annotations of its linguistic
history. }
\author{Andreas van Cranenburgh\footnote{\texttt{acranenb@science.uva.nl}, 
0440949}} 
\maketitle
\begin{center}
%(0440949), \\ March - June 2009}
Bachelor thesis Artificial Intelligence: second draft \\
Supervisors: Remko Scha \& Jos de Bruin, \\
University of Amsterdam
\end{center}

\vspace{3em}
\begin{center}
%\begin{tabular}{|l|}
%\hrule \\
\begin{verse} {\em %\begin{verbatim}
%No less no more than a rose
%No less no more than a rose
Try to attach a meaning \\
To words that you've heard \\
\vspace{1em}

Stumbling through the dark \\
Seems I'm stumbling through the dark \\
Eveybody's stumbling through the dark \\
\vspace{1em}

The men who proceeded us here \\
Left only questions and fears

[...]

%The vanity formed by beauty lies
%You know it's a crime
} %\end{verbatim}
\end{verse}
\vspace{1em}

\hspace{3em} --- from the album {\em Rainy day music}, The Jayhawks (2003)

%\\ \hrule
%\end{tabular}
\end{center}

\newpage
\tableofcontents

\section{Introduction}

General linguistics has been dominated by Chomskian generative linguistics for
several decades. The focus is on rules and their creativity, viz.
systematicity and productivity. The central dogma is that an in-born,
Universal Grammar is necessary to adequately explain these phenomena. It holds
on to the continuity assumption, which states that language as used and
understood by children is qualitatively equal to that of adults (for
criticism, cf., \citet{tom2005}).

However, from a developmental psychology angle, several empirical findings
\citep{tom2000, tom2005} shed doubt on whether this approach is applicable to
language acquisition by children. It rather appears that language learning is
bootstrapped in a haphazard fashion, learning constructions here and there,
which can only later be synthesized to form a coherent grammar.

Rather than trying to resolve this age-old debate between rationalism and
empiricism along theoretical lines, it might be fruitful to try to model the
behavior of early language users, and demonstrate in this way that a universal
grammar is in fact not necessary to explain the phenomena observed. This
strategy echoes a suggestion made by \citet{turing1950}:

\begin{quote}
``Instead of trying to produce a programme to simulate the adult mind, why not
rather try to produce one which simulates the child's? [...] Presumably the
child-brain is something like a note-book as one buys it from the stationers.
Rather little mechanism, and lots of blank sheets.'' 
\end{quote}

\section{Theory}

\subsection{Literature review}

One of the foremost proponents of the developmental take on language
acquisition is \citet{tom2005}. He argues that linguistic abilities are
acquired gradually, in an incremental fashion. Linguistic forms are memorized
in conjunction with their communicative functions or meanings. These
constructions are then generalized so that language use becomes ever more
expressive and productive. Aspects which distinguish this approach from that
of generative linguistics is the rejection of the autonomy of syntax and the
consequential focus on semantic and pragmatic influences on learning. Aside
from that the idiomatic and figurative dimension of language presents problems
for purely formal accounts of semantics and syntax. %, so a certain informality
%should be embraced by models of language. 

The formal nature of traditional theories goes back to American (Bloomfeldian)
structuralism and the supposed arbitrariness of the sign. A counter-argument to
the arbitrariness of the sign is that derived (eg., figurative) meanings are
relatively systematically related to their canonical meanings. For example, the
verb `to come' has the canonical interpretation of spatial movement, but it
can also be applied to an event which is temporally approaching: ``Christmas is
coming'' \citep{lakoff1999}. Notice how `approaching' is also a spatial verb,
and can be analogously applied with a temporal interpretation. On top of this
analyses of semantic networks such as Wordnet indicate that semantics is scale-free,
ie.\ it exhibits the small-world phenomenon and a fractal-like self-similarity
on each scale. This entails that words are part of local clusters sparsely
interconnected by hubs with short average path lengths \cite{steyvers2005}.

%"I look upon logical proofs the way a well-bred girl looks upon a love
%letter" -- Johann Georg Hamann

The work of eg. \citet{vankampen2003} on children's' use of languages in the
two word stage indicates that their (proto-)grammar employs pragmatic operators
and content signs, instead of distinguishing all the syntactic categories
present in adult language. Verbs are not yet inflected, and determiners are
absent.

\citet{chang2004} demonstrate a computational model of Embodied Construction
Grammar that combines constructions to interpret new constructions. Their
semantic representation could serve as an inspiration. Also, the use of
Minimum Description Length learning provides a good way to prune the database of
learned constructions.

\citet{steels2004} describes his experiments with situated agents (robots fitted with cameras) that employ language games as a learning strategy. An example of a language game
is the description game: one agent describes an event that has just happened, and the
other responds by agreeing if the description matches its own experience. These
experiments simulate language genesis and grammaticalization {\em ab inito}. 

\citet{vankampen2007} discuss the modeling of early syntax acquisition using
the Data Oriented Parsing framework \citep{bod1996}. This means that all input
is stored in memory, and made available for recombination in the recognition of
novel utterances.
%cite DOP

% Future research into DOP and semantics, should definitely not take a syntactically analyzed corpus as a starting point, as was done in this project. 
% http://cf.hum.uva.nl/computerlinguistiek/bonnema/dop-sem/node48.html

\subsection{Motivation}

A previous project \citep{vancra2007} attempted to model the acquisition of
constructions in the two word stage of early child language. The model used a
corpus of utterances spoken to children, annotated with semantic
representations of the context. The aim was for this model to be able
to generalize over the sentences to discover the correct associations between
words and their semantic representations, and to be able to combine sentence
fragments into novel utterances. This model did not consider syntax and
semantics separately, in the style of construction grammar (as employed in eg.,
\citep{tom2000,tom2005}). Although indeed correct associations were found, and
novel utterances could be recognized, most of the former were incorrect, and
most of the latter non-sensical (although in part this was due to the first
issue worsening the second). Figure \ref{sit} illustrates an example of an
utterance as it was interpreted (in this case correctly) by this model.

\begin{figure}
\begin{verbatim}
1. "ball gone"  la score = 1
LINGUISTIC ABSTRACTION:
        WORDORDER: VAR:gone
        FRAME: action
                ID: action:move
                FRAME: object
                        ID: VAR
                        ABSTR: object:toy
\end{verbatim}
\caption{Example situation in a previous model}
\label{sit}
\end{figure}

In this sentence the construction "X gone" was applied to "ball", because it
matched the condition of being a toy. The construction was apparently
previously encountered when a toy was being moved. In this case the result
was satisfactory, but unfortunately most other abstractions were spurious.

The problem was that sentences were being learned as isolated fragments,
without any notion of discourse or pragmatics. Also, the semantic
representation did not fit well with all the words to be learned: it was only
good at representing actions and objects; prepositions and demonstratives
and other abstract words were not being learned. Instead of merely focusing on
semantically describing a situation, the learner should consider the total
communicative function of an utterance. The learning was implemented as making
associations between words and each part of the semantic
representation, and counting how often these associations occurred. This meant
that a lot of incorrect associations were made. Unfortunately the model did not
make use of pruning, as there was no way to know which associations had been
incorrect.

Last year another project \citep{odolphi2008} developed a formal grammar for
the two word stage, based on empirical work on child language (eg.,
\citet{vankampen2003}).  This grammar does not make use of adult-like syntactic
categories such as verb and noun, but groups expressions as topics, comments
and operators. Using this grammar it is possible to parse and produce child
utterances, because it turns out that almost all of the two word utterances
follow the pattern of this formal grammar.

These projects focussed on children's own utterances. However, it appears that
children can already comprehend more complicated sentences than they produce
themselves, as evidenced by such exchanges as:

\begin{quote}
\begin{verbatim}
*MOT:   wanna [: want to] put (th)em [= crayons] 
        back in the box ?
%act:   <4-7> MOT taps the box with her finger
%gpx:   MOT looks at CHI
*CHI:   no .
%gpx:   <bef> CHI looks up at the box . 
        CHI looks down at the chair
\end{verbatim}
 --- Childes,\footnote{\citet{childes}} New England corpus\footnote{\url{http://childes.psy.cmu.edu/data/Eng-USA/NewEngland.zip}}, Liam, November 30th, 1984
\end{quote}

\subsection{Research question}
Can an exemplar-based model of language acquisition account for the discrepancy
between language comprehension and production of children in the two word
stage? Can this model facilitate the simulation of simple language games
of parent and child?

These questions will be addressed by attempting to implement a model of
linguistic comprehension and production using an exmplar-based model of
language.

\subsection{Some philosophical considerations}

\subsubsection{The importance of philosophy for cognition}

Since the cognitive revolution cognition has been conceived as symbol
manipulation. This idea has kept researchers in both cognitive
psychology and artificial intelligence (AI) in business. The more or less
official ideology of `Methodological Solipsism' \citep{fodor1980} secures
research grants by asserting that other fields such as neuroscience and biology
can have no bearing on the subjects of the so-called `special
sciences.'\footnote{Upon hearing the term `special sciences,' I can't help but
think of `special' as in physically challenged and the image of `physics envy'
this evokes.}

This doctrine has come under fire from different directions. Within cognitive
science itself there is talk of a second generation \citep{lakoff1999} putting
forth embodiment as vital; as well as a revival of connectionist systems with
subsymbolic, distributed representations. But long before that there has been
vocal criticism from philosophy. \citet{dreyfus1972} correctly predicted the
failure of the bombastic ambitions of early AI, and basically claimed that this
was due to the symbol manipulation metaphor being a pipe dream:

\begin{quote}
``Philosophers have thought of man as a contemplative mind passively receiving
data about the world and then ordering the elements."
 -- \citet{dreyfus1972}
\end{quote}

In short, Dreyfus warned that artificial intelligence is rather like alchemy:
suffering from unwarranted optimism and badly in need of re-evaluating its
dogmas. The last part is exactly what I am about to do.

%naturalism, philosophy continuous with science

\subsubsection{Compositionality}

Compositionality\footnote{
``The meaning of a complex expression is a function of the meanings of its
immediate syntactic parts and the way in which they are combined.'' \\
  --- \citet{krifka1999}} 
is possible, but not necessary, in this model. In the most specific case, a
whole sentence is fully described by a single exemplar; in the most general
case, a sentence is interpreted word for word, one exemplar each.  However, it
would appear to be optimal to employ a sort of `basic-level constructions,'
(cf. basic-level categories; \citet{rosch1976}) corresponding to stable
collocations that describe a large number of sentences using a small number of
multi-word fragments from exemplars. This should be optimal because it reduces
the memory load, since not every sentence has to be stored, and because it
allows the meaning of words to be dependent on sentence context.

\subsubsection{Autonomy of syntax from semantics}

The dominant trend in linguistics is syntacto-centrism, as observed by
\citet{jack1983}. What makes syntax so interesting is rarely made explicit,
but a desire for immediate and rigorous results probably favors the systematic
nature of syntax, at the expense of the more elusive and sometimes vague nature
of semantics. Even accounts that explicitly focus on semantics and pragmatics
are often syntactic in nature; a case in point is formal semantics. But whether
these accounts actually describe semantics or merely mimic parts of it is a
difficult question. Obviously planets do not need to be able to solve
differential equations in order to orbit as we have come to expect. What we can
be reasonably sure of is that semantics is residing (or perhaps presiding) in
the human brain, but this is rather like predicting that it will rain
somewhere, tomorrow. %stop here, move on to poverty of stimulus (!?)
The useful question is whether there is some higher-order
abstraction of semantics, and whether it can be mechanized or otherwise
reproduced in certain systems. This entails that cognition is not just a
projection or construction, but a valid abstraction over neural (and possibly
other) details. This thesis makes the assumption that such an abstraction
should exist, and that an approximation can be attempted and evaluated in a
model of language use.

\subsubsection{Mentalism} %(at least when using prepared representations) 
Most accounts of cognition and language in particular are mentalistic. That is,
they posit a mental entity which manipulates explicit representations
corresponding to external states of affairs. Representations, however, are
problematic, because representations have to come from somewhere, either
learned or innate, and should, serendipitously or otherwise, faithfully
describe, ie., be isomorphic to, both distal external events and subjective
experience. The most dramatic example is the `Language of Thought' hypothesis
\citep{fodor1975}, which posits that cognition must operate on first-order
logic predicates, which are taken to be universal and in-born.  These
predicates form the so-called semantic primitives, which can be composed to
give rise to an apparent infinity of meanings -- including such artefacts as
door knobs and scissors which were certainly not part of our humble ancestors'
inventories. It is safe to say such theories are far from parsimonious or even
empirically responsible.

The other extreme is to reject mentalism and representations altogether, and
stress the tight coupling of embodied agents with their surroundings; in a
certain sense representations are made redundant by direct interactio with the
world. In this conception there should be no need for the category of mind, and
body and world are both necessary and sufficient ingredients for cognition.
\citet{rorty1979} is a proponent of this view, and accuses the
representationalist school of presuming language and mental events to be a
``mirror of nature,'' as part of the foundationalist's program in epistemology.
Instead, he argues, there is no need for a mirror, and language is merely a
part of nature. The later \citet{witt1953} rejected mentalism on the grounds
that a private (mental) language would be impossible, because language is a
social phenomenon, useful only by virtue of being shared and understood by a
speech community.  He argued that language games are the fundamental building
blocks of language, in which language use is the sole criterion of meaning. In
general anti-mentalistic accounts see language as a way of skillful coping with
the world and one's con-specifics, as opposed to the possibly conscious
manipulation of explicit symbols. Language is not a conduit which encodes
propositional and illocutionary content, but a tool by which we negotiate our
ways in the world. 

Although I highly sympathize with these views it is highly difficult to apply
such a philosophy to artificial intelligence, because it rejects
%formal models 
% tout court = without explanation. use other term. outright? utterly?
abstract mental processes and representations {\em tout court}. This excludes
the possibility of modeling aspects of language in isolation, since the
situatedness of embodied agents is what cognition revolves about. Short of
making a robot that catches up with millions of years of evolution, it would
be impossible to responsibly model the cognition of language. To break this
impasse I will make use of semantic and pragmatic representations, but without
assuming them to be canonical and actually present in the minds of children.
Instead they stand for or hint at experience and the spreading activation of
neurons, and the social conventions immanent in language use. 
% !?!?!?! quite a leap...

%\item combinatoriality 	
%How Grammar Emerges to Dampen Combinatorial Search in Parsing [My Copy]
%Symbol Grounding and Beyond (2006), pp. 76-88.
%http://www.citeulike.org/user/voiklis/article/3748122

\section{Practice}

\subsection{Exemplars and Semantics}

%[describe representation here]

The model works with a set of exemplars. Exemplars contain an utterance and its
meaning representation. The meaning representation consists of a speech act
operator and a series of clauses, ordered by salience. Clauses consist of two
predicates, where the first describes an action (ie., a fluent) or a
category\footnote{Instead of introducing an inheritance taxonomy of categories
defined using necessary and sufficient conditions, the categories are intended
to reflect basic-level categories which become intuitively and implicitly
activated in a situation.} (monotonic, atemporal), which is predicated on the
second. The first clause will often contain a topic and a comment, while the
rest might contain context, presuppositions and associated facts salient in the
relevant situation:

\begin{verbatim}
"utterance"
operator: pred1(pred2) pred3(pred4) ...
\end{verbatim}

For example:

%easier example first. this easy enough?

\begin{quote}
\begin{verbatim}
"what does a bunny do ?"
whquestion: do(X) animal(bunny)
\end{verbatim}
\end{quote}

This could be translated to logical form in the following way:

%$\exists x: [ want(x) \land juice(x) \land  food(x) ] $
\[ \exists P \; \forall x: [ P(x) \rightarrow do(x) \land bunny(x) \rightarrow animal(x) ] \]

where $P(x)$ is a variable predicate which should be instantiated upon
answering the question. Another example:

\begin{quote}
\begin{verbatim}
"want some juice ?"
ynquestion: want(juice) food(juice)
\end{verbatim}
\end{quote}

This could be translated to logical form in the following way:

%$\exists x: [ want(x) \land juice(x) \land  food(x) ] $
\[ \forall x: [ juice(x) \rightarrow \ensuremath{\mathcal{W}}ant(x) \land juice(x) \rightarrow food(x) ] \]

where $\mathcal{W}ant(x)$ is a special predicate to represent the intentional
attitude desire. But these translations do not preserve order, which is
necessary because
% \texttt{want(juice)} $\neq$ \texttt{juice(want)}, and 
the expressed \texttt{want} is more salient than the implicit categorization
\texttt{food}.  This shortcoming of logical form is recognized in construction
grammar, eg.\ `the cat bites the dog' versus `the dog is bitten by the cat'
would have the exact same logical form but are nevertheless as distinct as can
be.

%In a set-theoretic Venn diagram:
%\includegraphics[scale=0.75]{wantjuice}

Both predicates and their arguments can be variable by writing them as a single
uppercase letter. Variable means that the information is missing from or asked
in the utterance.

This representation makes no hard-and-fast distinction between what is
explicitly verbalized in the utterance, and that which is understood through
context, because this distinction would amount to a fully context-free,
introspectable understanding of each and every word in the utterance. Instead
of precisely describing the semantic structure of the utterance, this style
of representation views the utterance as an ellipsis glossing over parts which
can reasonably be expected to be filled in by hearers. Since this filling in of
contextual details is not necessarily a linguistic phenomenon, it is assumed
to have been completed successfully, and to be present in the initial corpus of exemplars.


\subsection{Language Use and exemplars}
%[describe operations on exemplars here, without being specific about
% implementation]

Adequate participation in a discourse context requires interpreting an
utterance, transforming this interpretation into an appropriate response, and
verbalizing this response. Interpretation consists of finding a minimal
covering set of exemplars which are compatible under unification or constrained
argument substitution. 

Response generation is finding a best fit exemplar according to an operator to
operator mapping. This mapping is a set of adjacency pairs of speech act
operators:

\begin{itemize}
\setlength{\itemsep}{0pt} %why that silly whitespace between items?! bullet points are selling points, so they should not be far between...

\item \texttt{imperative $\Rightarrow$ confirmation}
\item \texttt{ynquestion $\Rightarrow$ \{confirmation, denial\} }
\item \texttt{whquestion $\Rightarrow$ assertion }
\item \texttt{assertion $\Rightarrow$ assertion } (the child tries to mirror the parent)
\item otherwise: respond with empty utterance (eg., in case of confusion).
\end{itemize}

After picking the operator the rest of the meaning representation is concatenated to
it and the same process of unification and constrained substition against available
exemplars results in the meaning representation of a response, which is then
verbalized.

Verbalization is the mapping of instantiated clauses to lexical items inferred
from multiple exemplar occurrences. %TODO add structure to verbalization. 

Reinforcement (eg. when a parent reacts with ``that's right'') records an
identifier linking the exemplars for the previous utterance and its response to
strengthen their association.

% More? otherwise this shouldn't be a subsection.

\subsection{The model}
The first step in interpreting a novel utterance is finding the exemplar whose
utterance is most similar to it. This is implemented by iterating over the
ordered subsets of words occurring in a sentence, from long to short, and
trying to find an exemplar containing these words. The meaning of the exemplar
that is found is then used as a template to which other exemplars must conform
if they are to be used in interpreting the rest of the utterance. An exemplar
conforms to the current interpretation if it has a family resemblance with it,
ie., one of its clauses has a predicate in common with the current
interpretation.  If the matching clause has a variable argument, it is
instantiated. If it has a conflicting argument, it is substituted. In order to
curtail spurious instantiations and substitutions, only clauses describing the
words being covered are considered open to modification.

This requires some knowledge of the connections between clauses and words. This
lexical knowledge is derived from the corpus of exemplars by juxtaposing all
exemplars containing a specific word, and picking the most salient clause they
have in common as the meaning for that word, or looking for links between
clauses and words (explicitly, in the form of word indices, or implicitly,
when words and predicates or arguments coincide). This process is repeated
until no new definitions can be gleaned from the corpus of exemplars. Content
words are especially likely to receive correct definitions from this process.
This bias is acceptable because they are already acquired in the one word
stage, as opposed to function words. Function words do not necessarily carry
meaning in isolation, but rather co-ordinate and decorate sentence meaning,
which is adequately contained in exemplars.

After finding the first exemplar further exemplars are sought in order to cover
the remaining words in the utterance. The words are covered in a greedy
fashion, the longest matching construction is used first. This process
currently does not perform backtracking, but this could be added for cases
where first matching a shorter construction enables a longer construction to be
used later.  See figure \ref{step} and \ref{res} for depictions of the steps
involved with interpreting an utterance.

%in dia, export to eps, then
%epstopdf playwith.eps
%epstopdf playwithres.eps
\begin{figure}
\includegraphics[scale=0.4]{playwith.pdf}
\caption{Interpretation process in a step-wise fashion}
\label{step}
\end{figure}
%do you want to play with that [= ball] ?

\begin{figure}
\includegraphics[scale=0.4]{playwithres.pdf}
\caption{Interpretation depicted as resolution process}
\label{res}
\end{figure}

It is possible to use demonstratives in sentences, as long as the referent is
supplied on input:

\begin{verbatim}
utterance: what is this [=ball] ?
meaning: whquestion: point(X) Y(X)
interpretation: whquestion: point(ball) toy(ball)
\end{verbatim}

Interpreting this exemplar will cause the meaning of ``ball" to be inserted, in
this case by substituting the variable predicate Y with the meaning of ``ball''
(without a variable predicate it will be concatenated).

%pseudo code?

One of the advantages of the algorithm just described is its graceful
degradation. Given sufficient redundancy, words can be misperceived or left
out, and the remaining words might still enable correct interpretation. This
feature enables natural interpretation of ellipses without specialized
mechanisms:

\begin{verbatim}
Parent: kitty do ?
	interpretation: whquestion: do(X) animal(cat)
	reaction: assertion: do(meow) animal(cat)
Child:  meow@o
\end{verbatim}

% definition of subfloat command:
\newbox\subfigbox
\makeatletter
\newenvironment{subfloat}
{\def\caption##1{\gdef\subcapsave{\relax##1}}%
\let\subcapsave\@empty
\setbox\subfigbox\hbox
\bgroup}
{\egroup
\subfigure[\subcapsave]{\box\subfigbox}}
\makeatother

%\newpage % ?

\subsection{Results}

After testing the model interactively during development, a more systematic
form of evaluation was introduced. By re-enacting fragments of dialogues from Childes
data, it becomes possible to juxtapose the responses of a real child to those
of the model developed in this thesis. See figure \ref{cookie} and \ref{cow}
for two such comparisons.

\begin{figure}
\begin{center}%
\begin{subfloat}%
\begin{minipage}{2.5in}
\begin{verbatim}
*MOT:   what shall we do ?
*CHI:   eat.
*MOT:   shall we eat cookies ?
*CHI:   ah
*MOT:   shall we ?
*CHI:   mmhmm.
*MOT:   where are the cookies ?
*CHI:   in bag.
*MOT:   cookie in the bag ?
*CHI:   baby eat.
*MOT:   ..
*CHI:   baby eat.
*MOT:   ..
*CHI:   cookies.
*MOT:   baby eat cookies ?
*CHI:   eat cookies.

\end{verbatim}
\end{minipage}
\caption{Childes fragment, as used in \citet{turnhout2007}}
\end{subfloat}%
%\goodgap
\begin{subfloat}%
\begin{minipage}{2.5in}
\begin{verbatim}
*MOT:   what shall we do ?
*CHI:   eat
*MOT:   shall we eat cookies ?
*CHI:   0
*MOT:   shall we ?
*CHI:   0
*MOT:   where are the cookies ?
*CHI:   cookie bag
*MOT:   cookie in the bag ?
*CHI:   cookie bag
*MOT:   ..
*CHI:
*MOT:   ..
*CHI:
*MOT:   baby eat cookies ?
*CHI:   eat

\end{verbatim}
\end{minipage}
\caption{Model output}
\end{subfloat}
\end{center}
\label{cookie}
\caption{Comparison of Childes data and the responses generated by the model
under discussion}
\end{figure}

\begin{figure}
\begin{center}%
\begin{subfloat}%
\begin{minipage}{2.5in}
\begin{verbatim}
*MOT:   that's the cow .
*MOT:   what's this ?
*CHI:   yyy .
*MOT:   is that a donkey ?
*CHI:   donkey .
*MOT:   right .
*MOT:   that's a donkey .
*CHI:   0 .
*MOT:   what's this ?
*CHI:   duck .
*MOT:   what does a duckie say ?
*CHI:   0 [<] .
*CHI:   quack@o .


\end{verbatim}
\end{minipage}
\caption{Childes fragment, New England corpus, Cristopher, July 19th, 1984}
\end{subfloat}%
%\goodgap
\begin{subfloat}%
\begin{minipage}{2.5in}
\begin{verbatim}
*MOT:   that's the cow .
*CHI:   cow
*MOT:   what's this ?
*CHI:   
*MOT:   is that a donkey ?
*CHI:   donkey
*MOT:   right .
*CHI:   
*MOT:   that's a donkey .
*CHI:   donkey
*MOT:   what's this [=duckie] ?
*CHI:   duckie
*MOT:   what does a duckie say ?
*CHI:   quack@o

\end{verbatim}
\end{minipage}
\caption{Model output}
\end{subfloat}
\end{center}
\label{cow}
\caption{Further comparison of Childes data and the responses generated by the
model under discussion}
\end{figure}

However, this method of evaluation only concerns the re-enactment of dialogues using
exemplars of that same dialogue, which is to say it does not need to generalize or
otherwise combine exemplars (it may still do so, however).

Another method of evaluation is to take a sentence from the corpus of another
child, and see if it is correctly interpreted by the current set of exemplars,
demonstrating the generalization capabilities central to this model:

\begin{verbatim}
Parent:  what does a duck say
        'what does a' in '+^ what does a bunny do ?'
meaning initialized as: whquestion: do(X) animal(bunny)
substituted (bunny) with (duck)
        'duck' in 'duck .'
        and 'assertion: animal(duck)' 
	matches 'whquestion: do(X) animal(bunny)'
        'say' in 'what does a lion say ?'
        and 'whquestion: do(X) animal(lion)' 
	matches 'whquestion: do(X) animal(duck)'
        interpretation: whquestion: do(X) animal(duck)
possible reactions: ['assertion: do(quack) animal(duck)']
instantiated (X) with (quack)
['assertion: do(quack) animal(duck)']
        reaction: assertion: do(quack) animal(duck)
reduced: quack@o .
Child:  quack@o
\end{verbatim}

It is also possible to let the model talk to itself, perhaps as an internal form of
practice. It has been suggested that dreams and imagination function in this
way, while it is also related to the Vygotskyan notion of self-talk and
egocentric speech (which differs from Piaget's usage of the term in that it
develops from social speech, according to Vygotsky). %Maybe cite Thought & Language
% THOUGHT develops from SOCIAL to INDIVIDUAL, not other way around as Piaget,
% Chomsky, et al would have it!

The model successively plays the role of mother and child. The `dialogue' begins
with a random utterance by the mother, to which the model replies. When the
reply of the mother to the child would be the same a new random utterance is
taken from the set of exemplars which have not already been used (simulating
initiative on the part of the parent). A fragment of an example dialogue looks
like this:

\begin{verbatim}
*MOT: this is a gate .
*CHI: gate
*MOT: okay well Mommy will color too .
*CHI: Mommy color
*MOT: what does a cow say ?
*CHI: moo@o
*MOT: oh isn't that [= CHI's paper] nice .
*CHI: nice
\end{verbatim}

%\begin{itemize}
%\item show some example output (generalizations, ellipses)
%\item comparisons with childes data: see figure \ref{cookie} and \ref{cow}
%\item TODO: human judgments of output (double blind)
%\end{itemize}

\section{Discussion}

TBD.


\begin{itemize}
\item Formulate the possible contribution of this work to the field of language
acquisition.

\item Answer research question (answer probably affirmative, though not
definitively). Return to points made in introduction (eg., Turing's quote)

\item Still missing: language games with more than two moves, concrete
situation model, learning new representations (which requires a notion of relevance).

\item Future directions: suggest multi-resolution exemplars augmented with
video data using restricted boltzmann machines as possible alternative to
explicit, symbolic representations. 
%But: questionable whether the mechanisms of the current model can be
%internalized by a neural net.

\end{itemize}

\newpage
\addcontentsline{toc}{section}{\numberline{5}References}
\bibliographystyle{plainnat}
\bibliography{thesis}

\end{document}

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