REPRESENTATION OF FEATURE SYSTEMS IN A NON-CONNECTIONIST MOLECULAR MACHINE 
L~zI6 K6im~n 
Institute of Linguistics 
Hungarian Academy of Sciences 
Budapest I., P.O.Box 19. 
H-1250 HUNGARY 
ABSTRACT 
This paper is part of an enterprise 
whose aim is to represent linguistic 
knowledge in the form of a molecular 
machine (a dynamic network). That is, the 
molecules of the network not only store, 
but also send, receive, and process 
information. It is claimed that such a 
network can be conceived of as a model of 
the coalition structure of a 
connectionist network. The paper 
describes how the class of feature 
systems called unary feature hierarchies 
(whose importance is supported by 
phonological theory but will not be 
argued for in the paper) can be 
represented in the molecular machine. 
INTRODUCTION 
Of the various branches of modern 
linguistic theory, phonology, as usual, 
was the first one to come up with really 
restrictive theories of features and 
feature systems, largely supported by 
empirical evidence coming from the study 
of a legion of linguistic phenomena. 
Phonology will most probably remain main 
source of evidence as far as the 
functioning of feature-based cognitive 
processes is concerned. 
The present paper sets out to outline 
how a particular kind of feature system, 
close to several recent theories of 
phonological features, can be represented 
in connectionist networks. However, since 
some of the mechanisms involved, 
seriality and synchronization in 
particular, fall outside the scope of the 
existing connectionist networks, a non- 
connectionist model simulating would-be 
serial connectionist networks will be 
used instead. The automaton described in 
the paper is able to unify feature 
structures as programs to be run on the 
machine itself. 
UNARY FEATURE HIERARCHIES 
The feature systems under scrutiny 
can be termed unary feature hierarchies. 
The underlying concept is close to the 
'feature geometry' approach to 
autosegmental phonology (Clements 1985) 
in that a feature specification consists 
of features appearing on tiers, and 
features on adjacent tiers can be linked 
by association ~ines. Tiers are ordered 
in a multi-dimensional space, and the set 
of features that may appear on a 
particular tier is predefined. Unarity, 
on the other hand, means that a feature 
either appears within a given 'span' (of 
time) or it does not (instead of having 
different values); the absence of a 
feature simply means lack of information 
or undersDecification. Features can only 
be linked to specified slots; on the 
other hand, tiers are adjacent to 
features rather than to tiers (hence the 
use of hierarchv instead of qeometry); 
that is, the following configuration may 
be ruled out if the H tier is adjacent to 
F but not to G: 
F/G tier .... F .... G .... 
l I H tier .... H .... H .... 
Figure I. This configuration may be ruled 
out. 
Unarity is opposed to traditional 
binary feature systems (with a marked '+' 
and an unmarked '-' value for each 
feature) and to ternary systems (with a 
marked '+', an unmarked '-', and an 
unspecified '0' value), while feature 
geometries (and hierarchies) replace the 
old-fashioned 'feature bundle' 
conception, in which each segment 
consisted of an unordered set of feature- 
-value pairs. Compare the following 
(sketchy) representations of lax vowels 
in English: 
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Features Segments 
e~i A o D u 
Low - + - - - + - 
High - - + - - - + 
Back - - - + + + + 
Round + + + 
Figure 2. English lax vowels as feature 
bundles. 
Tiers Segments 
e~ziAo9 u 
Root tier x x x x x x x 
I I I I I I 
H/L/B tier L H B B B B 
I I I 
R tier R R R 
I I 
H/L tier L H 
Figure 3. Unary feature hierarchy for 
English lax vowels. 
That is, in this approach, feature 
hierarchies not only express universal 
restrictions on feature structures (as 
feature geometries do, cf. Clements 
1985), but language specific redundancy 
rules and feature co-occurrence 
restrictions as well. In addition to the 
above, we shall assume the possibility of 
forbidding that a feature (or, rather, 
any feature of a given tier) be linked to 
another. Link prohibitions are not 
intended to be a feature value, hence the 
below representations 
a. b. 
Tier 1 .... F ........ F .... 
X 
Tier 2 
Figure 4. Configurations with and without 
link prohibition. 
specify identical elements, in spite of 
the fact that no feature can be linked to 
F in Figure 4a. (X stands for link 
prohibition.) For example, consider the 
following feature hierarchy, 
characterizing a language where plural 
and dual nouns usually behave in the same 
way (e.g. Hebrew): 
1 2 3 4 5 
Category tier ---N .... N .... N .... N .... N--- 
I x I I 
Number tier ....... NSg ....... NSg--NSg-- 
I x 
Dual tier -D 
i: singular noun 
2: plural noun 
3: sinaulare tantum 
4: dual noun and duale tantum 
5: plurale tantum 
Figure 5. Sample feature system. 
In terms of the above, the features of 
plural nouns and Dluralia tantum are 
identical, in spite of the link 
prohibition concerning the 'Non-Singular' 
feature of the latter. 
CONNECTIONIST MODEL OF FEATURE SYSTEMS 
Obviously, the presence of a feature 
in a segment corresponds to a relatively 
high activation level of a node or a 
coalition of nodes in a connectionist 
network. The vertical geometry of tiers 
determines the possibilities of linking; 
the essential function of links is to 
synchronize the activation of features, 
but they also express their dependency 
relations. Thus association lines 
corespond to the fact that the activation 
of a node or coalition controls the 
activation of another node or coalition. 
Finally, link prohibitions can be 
represented as the inhibition of 
particular tiers. The adjacency of tiers 
will correspond to super-coalitions, i.e. 
features on adjacent tiers are features 
whose activation can be synchronized at 
all. 
In our present knowledge, none of the 
existing connectionist networks can learn 
and encode the sequential activation of 
nodes or coalitions of nodes, albeit the 
organization of human memory is most 
probably highly serialized. To overcome 
this deficiency (and for other reasons as 
well) we designed a molecular machine 
(cf. Kalm~n and Kornai 1985) to model the 
functioning of a sequential connectionist 
network. 
In this machine, each molecule 
contains a more or less stable piece of 
knowledge encoding the coalition 
structure it participates in, in the form 
of a layout of the surrounding network. 
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Molecules are able to send messages 
to each other; a message has the same 
form as the pieces of information stored 
in the molecules, i.e. it is a directed 
graph representing a substructure of 
molecules with their dependencies. When a 
molecule receives a message, it unifies 
the message with its own map, and it 
forwards the resulting information. The 
ultimate addressees are the 'output 
molecules', which can perform extra 
actions when receiving a properly 
addressed message. That is, the message 
acts as a program that will, after some 
modifications it undergoes, activate a 
set of output molecules in a well-defined 
order° Modifications correspond to the 
effects of the rules stored in the 
molecules on the path of the message. 
One of the most important 
characteristics of the messages sent (and 
other maps) is that they may contain 
missing steps, i.e. distinguished nodes 
encoding lack of information concerning 
the way between two nodes. Missing steps 
can be eliminated by unification, 
provided that the required path is 
specified in the map of a processing 
molecule. This mechanism corresponds to 
the function of 'super-coalitions', i.e. 
the synchronization and sequencing of the 
activation of otherwise distinct 
coalitions. 
INFORMATION PROCESSING WITH THE MOLECULAR MACHINE 
The basic operation performed by the 
molecular machine is a kind of 
unification, differing from the 
corresponding operation used in 
unification-based grammars by virtue of 
the differences in the feature structures 
and their representations. Since the map 
graphs of the molecular machine contain 
no node variables, unification 
essentially means the elimination of 
missing steps. Missing steps encode both 
alternative and conjunctive relations: 
A B 
V 
C D 
Figure 6. Sample directed graph with 
missing step. 
The missing step (the asterisk) in Figure 
6 can only be eliminated by supplying a 
path from A and B to either C or D, e.g. 
by unifying the graph in Figure 6 with 
the following: 
A B 
C 
Figure 7. Sample directed graph without 
missing step. 
Figure 7 is also the resulting graph. Any 
other unification will pr, vide a partial 
solution at best. 
The control function of the directed 
graphs in question is due to the fact 
that the addressed molecules are able to 
reduce the messages they receive. For 
example, in the case of the graph on 
Figure 7, both molecules A and B will 
remove their addresses from the top level 
before forwarding the graph. The graph on 
Figure 6, on the other hand, will be 
unable to activate any of the addressees 
because of the missing step it contains. 
The unification and control functions 
of the molecular machine together define 
a particular conception of phonological 
rule systems, which can be argued for on 
independent grounds as well. Under this 
approach, the function of a phonological 
rule system is essentially to resolve 
problems arising from morphological 
processes, i.e. to fix ill-formed 
representations resulting from affixation 
by supplying missing features (e.g. in 
vowel harmony), linking or delinking 
features according to the derived context 
(e.g. in voice assimilation). Note that 
delinking in the present form of the 
machine consists of adding an inhibitory 
link leading to the feature to be 
delinked. 
FURTHER PLANS, IMPLEMENTATION 
It is far from evident that syntactic 
and semantic rule systems should carry 
out operations similar to those in 
phonological rules. On the other hand, 
the operation of the molecular machine 
are general enough to eventually 
encompass syntactic and semantic 
processes such as recognition and 
completion of syntactic patterns, 
inference making through unification, 
etc. Some of these operations are 
outlined in Kalman and Kornai (1985) and 
Kalman (1986). 
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A small molecular machine is 
implemented in Zoltan Schreter's (FPSE, 
Geneva University) CNS connectionist 
simulation system running on Olivetti 
M24/M28 PCs. However, owing to the 
capacity of the machines (and of TLC 
Lisp, in which the system has been 
written) the number of molecules is 
extremely limited, and the performance 
obtained is rather poor. 
REFERENCES 
Clements, George N. 1985. The 
geometry of phonological features. 
Phonology yearbook 2, 225-252. 
Kalman, Laszl6 and Andras Kornai. 
1985. A finite-state approach to 
generation and parsing. Paper presented 
at the Generative Grammar Fiesta, 
Salzburg. 
K~im~n, I~szl6. 1986. Semantic 
interpretation in a dynamic knowledge 
representation. Mfihelymunk~k (Working 
Papers of the Institute of Linguistics) 
1, No. 2, pp. 31-51. 
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