**Instituut voor Taal- en Kennistechnologie**

Institute for Language Technology and Artificial Intelligence

# Cognition, Chaos and Non-Deterministic Symbolic Computation: The
Chinese Room Problem Solved?

R.W. Kentridge (Click here for an Acknowledgement)
In this paper I offer an explanation of how the grounding of stimuli
in an initial analog world can effect the interpretability of symbolic
representations of the behaviour of neural networks performing
cognition. I make two assertions about the form of networks powerful
enough to perform cognition, first that they be composed of non-linear
elements and second that their architecture is recurrent. As nets of
this type are equivalent to non-linear dynamical systems I then go on
to consider how the behaviour of such systems can be represented
symbolically. The crucial feature of such representations is that
they must be non-deterministic, they therefore differ from
deterministic symbol systems such as Searle's Chinese Room. A whole
range of non-deterministic symbol systems representing a single
underlying continuous processes can be produced at different levels of
detail. Symbols in these representations are not indivisible, if the
contents of a symbol in one level of representation are known then the
subsequent behaviour of that symbol system may be interpreted in terms
of a more detailed representation in which non-determinism acts at a
finer scale. Knowing the contents of symbols therefore effects our
ability to interpret system behaviour. Symbols only have contents in
a grounded system so these multiple levels of interpretation are only
possible if stimuli are grounded in a finely detailed world.

## Introduction

What is the relationship between symbolic computation and that
performed by connectionist networks? Stevan Harnad points out a few
minor perceived differences between the capabilities of nets and
symbol systems and then goes on to concentrate on solutions to
Searle's 'Chinese Room' problem (Searle, 1980). I think he is correct
in his argument (Harnad, 1990) that symbol systems which are not
grounded in an initially analog world are indeed incomplete models of
cognition. In this paper I will point out an important difference
between deterministic symbol systems like the Chinese Room and neural
networks which may explain formally why grounded and ungrounded
systems are not equivalent.
## Power Requirements of Networks Performing Cognition

I will start by making two assertions about the power of networks
required to model cognition. First there is the well known
requirement that nets must be composed of non-linear elements if they
are to be capable of learning arbitrary classifications (Minsky and
Pappert, 1969). The second requirement is that networks which are
intended to model cognition must be capable of time-dependent
information processing (see e.g. Edelman, 1978; Kentridge, 1990). If
the units in these networks are not to have infinite memories of their
prior states and time is not sliced up arbitrarily by an all-knowing
external clock (it would have to be omniscient in order to predict the
longest window needed to detect the determining antecedents of future
events) then the architecture of these nets must be recurrent. If
these assertions are accepted then we can consider networks capable of
modelling cognition as non-linear dynamical systems from now on.
## Symbolic Representation of Non-Linear Dynamical Systems

The behaviour of non-linear dynamical systems can be reconstructed in
terms of symbolic languages defined by finite-state, stack or
nested-stack automata (Crutchfield and Young, 1990) so a basis exists
for directly comparing the symbolic computation of the Chinese Room
with that of a neural net and hence of understanding symbol-grounding.
When we consider how symbols are constructed when modelling the
behaviour of a dynamical system symbolically, following the method of
Crutchfield and Young, a fundamental difference between computation in
the Chinese Room and computation in a neural network becomes apparent.
When constructing a language from a stream of dynamical system states
we wish to produce a minimal representation which consists of sets of
states mapped onto discrete symbols together with rules specifying the
allowable transitions between sequences of those symbols. In the
process of producing a discrete symbolic description from a continuous
stream of analog system states we must make an initial discrete
partition of the data stream by dividing the state space of the
dynamical system into a number of regions and then recording which of
those regions the system is in at regular intervals. The aim of the
language reconstruction is then to reduce long sequences of these
discretely partitioned system states into individual symbols which
nevertheless still predict the subsequent behaviour of the system at
the symbolic level. If the stream of states was in fact produced by a
formal language such as that of the Chinese Room then any sufficiently
long sequence of states could be modelled by a reduced set of symbols
and deterministic transition rules between those symbols, that is, by
a deterministic grammar (see e.g. Aho, Sethi and Ullman (1986) for
methods of achieving this). This is not the case when the stream of
partitioned states is produced by a non-linear dynamical system. We
can see, just by considering the initial stream of discretely
partitioned states, that any sequence of states cannot be modelled
deterministically by an automaton simpler than the sequence itself.
The hallmark of non-linear dynamical systems is chaos. Chaos is
defined by the sensitive dependence of a system's evolution on its
initial states (Crutchfield, Farmer, Packard and Shaw, 1986). In
other words, the eventual behaviour of a chaotic system is
unpredictable unless its initial position in state space is known to
infinite precision. When we partitioned the state space of our
dynamical system into discrete regions the precision of the state
space positions used in our language reconstruction necessarily became
finite. The consequence of this is that any finite linguistic model
of a non-linear dynamical system which admits chaotic behaviour cannot
be completely deterministic - the rules governing the transitions
between symbol sequences must be probabilistic if any ordered
behaviour of the system is to be captured by a concise symbolic
description.
## Level of Non-Deterministic Representation and Grounding

I have described a deep difference between the deterministic symbolic
computation of the Chinese Room and non-deterministic symbolic
descriptions of neural networks' behaviour. How does this difference
relate to the symbol-grounding problem? Consider what happens as we
change the size of partitions in our initial discretization of the
continuous analog stream of system states. We can produce a whole
series of non-deterministic symbolic models at different scales of
partition all of which describe the behaviour of the underlying
dynamical system. As we decrease the size of our partition the
predictability of subsequent system behaviour increases and hence the
symbols and transition probabilities produced in our reconstruction
change. Sequences of fine-grain states which correspond to symbols
are collapsed or broken up in coarsely partitioned models. The
transitions between symbols in a coarsely partitioned model are more
precisely described in a finely partitioned model. If we know
something about the set of system states from which an individual
symbol is derived in the coarse model then our predictions of the
subsequent symbolic behaviour of the system change. The internal
structure of the symbol clearly contributes to system behaviour even
at the symbolic level. The behaviour of a system in which the
starting state (the sensory input) is analog (grounded) is, in theory,
deterministic and in practical symbolic representations is better
predicted if we know something of the contents of symbols. These
multiple levels of symbolic interpretation are not possible in an
ungrounded system in which symbols are indivisible.
## Is Cognition Chaotic?

One question still needs to be addressed: 'Are neural-networks which
perform cognition likely to exhibit chaotic behaviour?' If the answer
to this question was 'no' then the preceding argument about
non-determinism and chaos would be irrelevant. Crutchfield and Young
(1990) show, however, that before the onset of chaos the behaviour of
non-linear dynamical systems can be modelled symbolically by
finite-state automata, whereas their behaviour during the transition
to chaos is only adequately modelled by nested-stack automata. In
linguistic terms finite-state automata are equivalent to regular
grammars (Chomsky, 1963) while nested-stack automata are equivalent to
indexed grammars which include all context-free grammars and some
context-sensitive ones (Aho, 1969). Regular grammars are inadequate
to describe natural language descriptions of the world, some form of
recursive grammar (context-free at the least) is required (Chomsky,
1963). We can conclude that a neural network powerful enough to
perform the cognitive tasks required by the Chinese Room problem must
therefore exhibit chaotic behaviour.
It is interesting to note finally that Crutchfield and Young
also show that non-deterministic symbol systems achieve a
maximum amount of computation in terms of complexity at the
phase-transition between predictable and chaotic behaviour. I have
recently (Kentridge, forthcoming) provided evidence suggesting that
physiologically realistic neural network models are easily maintained
at this phase-transition by diffuse background activity through a
mechanism of self-organizing criticality (Bak, Tang and Wiesenfeld,
1988). It is therefore not implausible that cognition is achieved by
the brain performing efficient non-deterministic symbolic computation
at a phase-transition.

## Conclusion

To return to the Chinese Room Problem, I propose the following
explanation: A Chinese speaker in the real world can understand
Chinese because he or she has access to a hierarchy of probabilistic
symbolic interpretations of the world; Searle in the Chinese Room
cannot because he only has access to a single level of symbols and an
inadequate set of deterministic rules connecting them.
**Acknowledgement**: This research was supported
by DRA Fort Halstead, Contract 2051/047/RARDE. I would like to thank
Rosemary Stevenson for helpful comments on an earlier draft of this
paper.

Harnad's response
Harnad's target article

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