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<Paper uid="E87-1047">
  <Title>REPRESENTATION OF FEATURE SYSTEMS IN A NON-CONNECTIONIST MOLECULAR MACHINE</Title>
  <Section position="4" start_page="0" end_page="298" type="metho">
    <SectionTitle>
UNARY FEATURE HIERARCHIES
</SectionTitle>
    <Paragraph position="0"> The feature systems under scrutiny can be termed unary feature hierarchies.</Paragraph>
    <Paragraph position="1"> 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 ....</Paragraph>
    <Paragraph position="2"> l I H tier .... H .... H ....</Paragraph>
    <Paragraph position="3">  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:</Paragraph>
    <Section position="1" start_page="298" end_page="298" type="sub_section">
      <SectionTitle>
Features Segments
</SectionTitle>
      <Paragraph position="0"/>
      <Paragraph position="2"/>
    </Section>
    <Section position="2" start_page="298" end_page="298" type="sub_section">
      <SectionTitle>
Tiers Segments
</SectionTitle>
      <Paragraph position="0"/>
      <Paragraph position="2"> English lax vowels.</Paragraph>
      <Paragraph position="3"> 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  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  i: singular noun 2: plural noun 3: sinaulare tantum 4: dual noun and duale tantum 5: plurale tantum  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.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="298" end_page="299" type="metho">
    <SectionTitle>
CONNECTIONIST MODEL OF FEATURE SYSTEMS
</SectionTitle>
    <Paragraph position="0"> 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.</Paragraph>
    <Paragraph position="1"> Finally, link prohibitions can be represented as the inhibition of particular tiers. The adjacency of tiers will correspond to super-coalitions, i.e.</Paragraph>
    <Paragraph position="2"> features on adjacent tiers are features whose activation can be synchronized at all.</Paragraph>
    <Paragraph position="3"> 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.</Paragraph>
    <Paragraph position="4"> 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.</Paragraph>
    <Paragraph position="5">  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 orderdeg Modifications correspond to the effects of the rules stored in the molecules on the path of the message.</Paragraph>
    <Paragraph position="6"> 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.</Paragraph>
  </Section>
  <Section position="6" start_page="299" end_page="299" type="metho">
    <SectionTitle>
INFORMATION PROCESSING WITH THE MOLECULAR MACHINE
</SectionTitle>
    <Paragraph position="0"> 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:  other unification will pr, vide a partial solution at best.</Paragraph>
    <Paragraph position="1"> 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.</Paragraph>
  </Section>
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