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<Paper uid="E91-1050">
  <Title>A Language for the Statement of Binary Relations over Feature Structures</Title>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 The rule name plays no part in the interpretation of
</SectionTitle>
    <Paragraph position="0"> roles, but provides a convenient reference for tracing their ordering and application.</Paragraph>
  </Section>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 The equations in each of (ii) and (iii) must he
</SectionTitle>
    <Paragraph position="0"> uniquely rooted. The current implementation disallows disjunction in the equation sets for this reason.</Paragraph>
    <Paragraph position="1"> - 287 (iv) a (possibly empty) set of 'transfer correspondence statements' - equations describing transfer correspondences that must hold between variable bindings established in (ii) and (iii).</Paragraph>
    <Paragraph position="2"> A transfer rule relates the two FSs it describes either directly or indirectly, via the rule's transfer correspondence statements; in order for the relation to hold between the source and destination FS, it must hold between the FSs to which any transfer-variables are bound. An example of a transfer rule is given below: :T: exampled :LI: &lt;* a b&gt; = XI</Paragraph>
    <Paragraph position="4"> This rule establishes a correspondence between the two feature structures shown below, (1) being the FS described by the equations under 'Ll' and (2) by those under 'L2': The correspondence is licensed provisionally for this FS pair by &amp;quot;example-l&amp;quot;; it is licensed absolutely for a pair of FSs (1') and (2') having the same root as (1) and (2) respectively only  if: (i) (1') contains sub-FSs (z unified with X1 and \[3 unified with Y1 in (1), (ii) (2') contains sub-FSs y unified with X2 and 8 unified with 3(2 in (2), and (iii) the same type of correspondence is licensed, possibly by some other rule, between (x and y and between \[~ and 8.</Paragraph>
    <Paragraph position="5">  Complex FSs are analysed and constructed recursively as a result of the passage of control through transfer variables. / In the abstract, transfer rules have no inherent directionality; the two FSs above may be visualized interchangeably as input and output, or 'source' and 'destination'. When compiled for a particular application, however, they are interpreted directionally, the domain of the transfer relation being collectively characterized by the equation sets labelled 'LI' and the range by those labelled 'L2', or vice versa. One may then think of compiled transfer rules as having a 'left-hand' or 'input' and a 'right-hand' or 'output' side, the former describing a source FS and the latter a destination FS. We shall use these terms freely in contexts where directionality is at issue, and assume that the rules have been compiled accordingly.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.2. Interpretation
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      <Paragraph position="0"> The relation of transfer between a source FS X and a destination FS A is defined recursively in terms of the quintuple (R, C/bx(R), ~p(R), T(R), O(Z)), where R is a rule, ~(R) and * p(R) are, respectively, the FSs induced by the left-hand and right-hand equation sets in R, T(R) is the set of transfer correspondence statements in R, and O(Y~) is the result of con- null vertin\[\[ any path-final variables in Z to constants:-' null Z stands in the transfer relation to A with respect to Riff: (i) (b~.(R) subsumes (~(Y-), and (ii) ~p(R) unifies with A, and (iii) for each % e T(R), the sub-FSs of 5&amp;quot;- and A  unifying with the transfer variables mentioned in 'c stand in the transfer relation with respect to some rule in the currently accessible rule set.</Paragraph>
      <Paragraph position="1"> The first clause of this definition states the condition under which a rule is a candidate for application to a given input FS. The second states the condition under which a rule is a candidate for application to a given output FS. Note that the operations differ; whereas the matching in (i) is based on subsumption, the action in (ii) employs unification. As a consequence, the FS q)p(R) is added to the output FS A. The third clause imposes the further condition that, in order for \]: and A to be related by R, any FSs they contain which are explicitly connected via variable binding and a transfer correspondenc e statement in T(R) are also related.</Paragraph>
      <Paragraph position="2"> As will be~ seen from clause (iii) of the definition, a complex FS is traversed from root to terminals, control being passed via variables in tran~er equations, and the extent of each sub-transfer (i.e. how much of the input FS is consumed at each stage) being determined by 5 It may well be the case that, in certain applications or envixonments, source FSs will not contain such variables; the possibility must be acknowledged nevertheless, since non-declarative rule interactions may otherwise ocCUlt'. null - 288 the path specifications in the left-hand side equation set of the currently active rule. Possible paths through the FS from a given point are determined collectively by the left-hand side equations of all rules, together with their transfer correspondence statements.</Paragraph>
      <Paragraph position="3"> Because FSs are finite and acyclic, termination is guaranteed as long as there is no rule of the form shown below. This is able to apply (in the 'L1--&gt;L2' direction - we ignore the converse) without consuming part of the source FS: :T: infinite-recursion :LI: &lt;*&gt;-- X :L2&amp;quot; ... :X: X &lt;--&gt; Y Coherence of a destination FS with respect to a source FS and a set of transfer rules is ensured by the formalism; material can only be introduced into a destination FS by the right-hand side of transfer rules which have successfully applied. Completeness, on the other hand, must be verified explicitly; every part of the source FS must be subsumed by a subpart of the FS obtained by unifying the FSs induced by the left-hand side patterns of every rules that has successfully applied. In the current implementation, it is possible to declare that certain subparts of a source FS are not to be transferred; in this case, it is the remainder of  that FS which must be covered by the rules.</Paragraph>
      <Paragraph position="4"> 3. Applications of the Formalism  We now illustrate how the transfer rule formalism may be exploited, and indicate briefly how the rule invocation regime may vary. The machine translation example in the following section assumes parallel invocation of the rule set, while that involving reductions to canonical form seems most amenable to the serial invocation of individual rules or subsets of rules.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.1. Machine Translation
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      <Paragraph position="0"> Perhaps the most obvious application for the formalism presented here lies in the domain of machine translation. The transfer model of MT may be thought of as involving three distinct mappings; from the source language expression to a source linguistic representation, from the source representation to a target representation, and from this to an expression in the target language. The first and last of these are to be performed by parsing and generation with natural language grammars, but, while proposals have been made to combine some of the three stages (e.g. Kaplan et at., 1989), there are advantages in treating the intermediate, transfer, stage independently.</Paragraph>
      <Paragraph position="1"> As an example, consider the FSs shown below: 6  (3) \[sem Ipred schwimmen \]\] args (&lt;1&gt; sem pred Maria) Lmod sem pred gem (4) Isem \[pred aimer \[ )1 args (&lt;I&gt; sem pred Maria, &lt;2&gt; sem pred nager\] args (#I)\] (3) and (4) are possible representations for the  German sentence Maria schwimmt gem, and the French sentence Maria aime nager, both of which might translate into English as 'Maria likes swimming'. Note that, whereas (3) has the predicate which translates 'swim' at the top level, and contains a modifier gem which might be glossed as 'gladly', (4) embeds the 'swim' predicate within an argument to the main predicate aimer 'like', and links the first argument of aimer to the first argument of nager by means of a re-entrancy. 7 The set of rules given below together establish a transfer relation between (3) and (4): s Note the use of a list, indicated by '(... )', to encode arguments in these FSs, the identification of elements on such a llst by e. 8. '&lt;1&gt;', and re-entrancy flagged by '#'. 7 Clearly, one could employ a similar analysis for the German sentence by making gem an 'equl' predicate like aimer - this would amount to simplifying transfer by shifting complexity from the transfer rules into the Gearman grammar.</Paragraph>
      <Paragraph position="2"> 8 This is not quite true; the variables 'Tf and 'Tg' in the rule &amp;quot;gem-aimer&amp;quot; will bind to lists (the empty list in this case), and we therefore require additional generic list-transfer rules that will have the effect of passing through a list, recursively transferring heads and tails. Implementations for systems that lack the list data type will naturally be able to dispense with this. In addition, the lexical transfer rules assume the presence in the current set of a rule consuming the '&lt;* sere pred&gt;' paths terminating in Paul and Maria.</Paragraph>
      <Paragraph position="3">  The pair of rules ':TA:PaulPaul' and ':TA: Maria Maria' are 'lexical transfer rules'; they state a transfer relation between atomic FSs (i.e. words, in the context of MT), rather than complex ones, and, further, do so without reference to the context of these FSs. They are equivalent to e.g.</Paragraph>
      <Paragraph position="4">  The re-entrancy in FS (4), in which the first argument associated with the predicate aimer is also the argument associated with the embedded predicate nager, is of some interest in connection with transfer. Taking (4) as the source, application of &amp;quot;gern-aimer&amp;quot; results in the binding of both instances of the variable 'Af' to the sub-FS indexed as '&lt;1&gt;' which is subject to the relevant transfer correspondence statement and whose corresponding destination sub-FS (in this case identical) will be present in the overall destination FS as the first element on the argument list of schwimmen. Reversing the direction, with (3) as the source, the variable 'Ag' is bound to the sub-FS indexed as '&lt;1&gt;', whose corresponding destination sub-FS is similarly present in the overall destination FS, this time as the first element in both argument lists, and, moreover, owing to the identity of variables in &amp;quot;gern-aimer&amp;quot;, unified rather than duplicated. Re-entrancy may thus be detected in the source FS and created in the destination; naturally, responsibility for correctly analysing structures confining reentrancies, and enforcing them where desired in output structures, lies with the writer of transfer rules.</Paragraph>
    </Section>
    <Section position="3" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.2. Reduction to Canonical Form
</SectionTitle>
      <Paragraph position="0"> It is often the case that a grammar assigns just one of a range of logically equivalent representations to a sentence; designers of grammars for use in analysis generally take care to ensure that the result of parsing a non-ambiguous sentence is a unique semantic representation, and multiple representations are seen as the hallmark of (pre-theoretical) ambiguity. In generation, as Shieber (1988) and Appelt (1989) observe, a situation may arise in which the representation supplied as input to the process (perhaps by another program) is not itself directly suitable, but is logically equivalent to one that is. The use of distinct grammars for parsing and generation could provide a solution to this problem, but it raises others connected with management of the resulting system. An alternative is to define equivalence classes of representations, and reduce all members of a class to the single canonical form which the grammar can map into a senfence. Exactly how the classes and reductions are defined will doubtless depend on many factors; we consider here some of the standard logical equivalences exploited in reducing arbitrary expressions of the propositional calcuius to disjunctive normal form.</Paragraph>
      <Paragraph position="1">  The two rules shown above express equivalences which are more familiar as: --,(-,p) ~ p and -,(p v q) ~-~ (-,p ^ -,q).</Paragraph>
      <Paragraph position="2"> the - 290 The mode of application required here is rather different from that described in the preceding section, for a context in which &amp;quot;not-not&amp;quot; applies may not exist prior to the application of &amp;quot;not-or&amp;quot;. Consider the three FSs below:  Given (5), the desired result is (7), by way of (6). A suitable context for the role &amp;quot;not-not&amp;quot; is created by &amp;quot;not-or&amp;quot;; note, however, that this context exists only in the destination FS, and not in the source. What is required is a serial mode of invocation, as opposed to the parallel mode assumed for the MT application, with the 'output' of one rule serving as the 'input' to another. An alternative would be to formulate transfer rules that encompass a wider context; drawbacks of such an approach would be that it is not possible to cater for all contexts, and that, in attempting to do so, one would dimini.~h the locality and thus the transparency of the rules. There are several possibilities for implementing serial rule invocation; the most straightforward involves taking an output FS as the input to another pass through the rule set. In this case, vacuous application of the rule set must be detected in order to ensure termination. null It will not normally be desirable to apply canonicalization rules 'in reverse': the effect will be to derive all forms that are logically equivalent to the input, and, if the relevant equivalence classes are not finite, the process will not terminate. Consider the rule &amp;quot;notnot&amp;quot;; its presence in a rule set compiled with 'L2' as the left-hand side will result in the derivation of forms involving, at each point, an embedding of the source FS under a progressively higher even number of nots. This is as it should be, however, given the semantics of transfer rules outlined in section 2, since, in this direction, the rule characterizes a relation whose range is not finite. Individual applications of the rule terminate, nevertheless.</Paragraph>
    </Section>
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