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<Paper uid="J97-4003">
  <Title>A Computational Treatment of Lexical Rules in HPSG as Covariation in Lexical Entries</Title>
  <Section position="5" start_page="559" end_page="561" type="metho">
    <SectionTitle>
5. On-the-fly Application of Lexical Rules
</SectionTitle>
    <Paragraph position="0"> We want our compiler to produce an encoding of lexical rules that allows us to execute lexical rules on-the-fly, i.e., at some time after lexical lookup. This is advantageous because postponing the execution of the interaction predicates allows more constraints on the word to be collected. When the interaction predicate is finally called, as a result of syntactic information being present, many of its possible solutions simply fail. The search tree that would have resulted from pursuing these possibilities at the beginning of processing does not have to be explored. 31 As it stands, our encoding of lexical rules and their application as covariation in lexical entries does not yet support the application of lexical rules on-the-fly. With respect to processing, the extended lexical entry of Figure 17 is problematic because before execution of the call to q_l, it is not known which information of the base lexical entry ends up in a derived lexical entry, i.e., tag ~ is completely uninstantiated. This means that there is no way of indexing the lexical entries according to what kind of 31 According to Pollard and Sag (1987) on-the-fly application of lexical rules is also well-suited to playing a role in a model of language use.</Paragraph>
    <Paragraph position="1">  Meurers and Minnen Covariation Approach to HPSG Lexical Rules derived entry one is looking for. As a result, it is necessary to execute the call to q_l immediately when the lexical entry is used during processing. Otherwise, there would be no information available to restrict the search-space of a generation or parsing process.</Paragraph>
    <Paragraph position="2"> Flickinger, Pollard, and Wasow (1985) solve this problem using additional specifications: &amp;quot;By providing with each lexical rule a generic class frame which specifies the general form and predictable properties of the rule's output, we avoid unnecessary work when the lexical rule applies&amp;quot; (p. 264). In the following, we show that the additional specifications on the extended lexical entry needed to guide processing can be deduced automatically.</Paragraph>
    <Section position="1" start_page="560" end_page="561" type="sub_section">
      <SectionTitle>
5.1 Constraint Propagation
</SectionTitle>
      <Paragraph position="0"> The intuitive idea behind this improvement of the covariation encoding is to lift into the extended lexical entry the information that is ensured after all sequences of possible lexical rule applications for a particular base lexical entry have occurred. Note that this is not an unfolding step. Unfolding the interaction predicates with respect to the lexical entries basically expands out the lexicon off-line. Instead, what we do is factor out the information common to all definitions of the called interaction predicate by computing the most specific generalization of these definitions.</Paragraph>
      <Paragraph position="1"> The most specific generalization does not necessarily provide additional constraining information. However, usually it is the case that lexical entries resulting from lexical rule application differ in very few specifications compared to the number of specifications in a base lexical entry. Most of the specifications of a lexical entry are assumed to be passed unchanged via the automatically generated frame specification. Therefore, after lifting the common information into the extended lexical entry, the out-argument in many cases contains enough information to permit a postponed execution of the interaction predicate. When C is the common information, and D1, ..., Dk are the definitions of the interaction predicate called, we use distributivity to factor out C in</Paragraph>
      <Paragraph position="3"> to contain no further common factors. Once we have computed c, we use it to make the extended lexical entry more specific. This technique closely resembles the off-line constraint propagation technique described by Marriott, Naish, and Lassez (1988). The reader is referred to Meurers and Minnen (1996) for a more detailed discussion of our use of constraint propagation. 32 We illustrate the result of constraint propagation with our example grammar. Since the running example of this paper was kept small, for expository reasons, by only including features that do get changed by one of the lexical rules (which violates the empirical observation mentioned above), the full set of lexical rules would not provide a good example. Let us therefore assume that only the lexical rules 1 and 2 of Figure 11 are given. We then only obtain seven of the clauses of Figure 22: those calling lex_rule_l or lex_rule_2, as well as the unit clauses for q_l, q_2, q3, and q_7. Applying constraint propagation to the extended lexical entry of Figure 17 yields the result shown in Figure 23. The information common to all solutions to the interaction call is lifted up into the lexical entry and becomes available upon lexical lookup.</Paragraph>
      <Paragraph position="4"> 32 In certain cases an extension of the constraint language with named disjunctions or contexted constraints (Maxwell and Kaplan 1989; Eisele and D6rre 1990; Griffith 1996) can be used to circumvent constraint propagation. Encoding the disjunctive possibilities for lexical rule application in this way, instead of with definite clause attachments, makes all relevant lexical information available at lexical lookup. For analyses proposing infinite lexica, though, a definite clause encoding of disjunctive possibilities is still necessary and constraint propagation is indispensable for efficient processing.</Paragraph>
    </Section>
    <Section position="2" start_page="561" end_page="561" type="sub_section">
      <SectionTitle>
5.2 Dynamic and Static Coroutining
</SectionTitle>
      <Paragraph position="0"> Even though we see on-the-fly application as a prerequisite of a computational treatment of lexical rules, it is important to note that a postponed evaluation of lexical rule application is not always profitable. For example, in the case of generation, underspecification of the head of a construction can lead to massive nondeterminism or even nontermination when not enough restricting information is available to generate its complements (Martinovi4 and Strzalkowski 1992; Minnen, Gerdemann, and G6tz 1995). Criteria to determine when it is most profitable to execute calls to an interaction predicate are required.</Paragraph>
      <Paragraph position="1"> One possibility is to annotate the lexical rule encoding with such criteria by means of delay statements, as, for example, suggested by van Noord and Bouma (1994). While we consider this kind of control facility (Naish \[1986\] and references therein) to be, in general, indispensable for efficient processing, it also has disadvantages that make it desirable to search for alternative or additional mechanisms: Delay statements presuppose the procedural annotation of an otherwise declarative specification. Substantial computational expertise is required to provide restrictions on the instantiation status of a goal, which must be fulfilled before the goal can be executed. Furthermore, the computational bookkeeping necessary for the delaying mechanism is very expensive.</Paragraph>
      <Paragraph position="2"> An interesting alternative, therefore, is to automatically determine certain control problems and deal with them in an off-line fashion along the lines of Minnen, Gerdemann, and G6tz (1995) and Minnen, Gerdemann, and Hinrichs (1996). They describe the use of a dataflow analysis for an off-line improvement of grammars that determines automatically when a particular goal in a clause can best be executed.</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="561" end_page="563" type="metho">
    <SectionTitle>
6. Efficiency Evaluation
</SectionTitle>
    <Paragraph position="0"> The computational treatment of lexical rules as covariation in lexical entries was implemented in Prolog by the authors in cooperation with Dieter Martini for the ConTroll system (Gerdemann and King 1994; G6tz and Meurers 1997a). We tested the covariation approach with a complex grammar implementing an HPSG analysis covering the so-called aux-flip phenomenon, and partial-VP topicalization in the three clause types of German (Hinrichs, Meurers, and Nakazawa 1994). This test grammar includes eight lexical rules; some serve syntactic purposes, like the Partial-VP Topicalization Lexical Rule, others are of morphological nature as, for example, an inflectional lexical rule that relates nonfinite verbs to their finite form. Our compiler distinguished seven word classes. Some nouns and most verbal lexical entries fed lexical rules, and a single base lexical entry resulted in up to 12 derivations.</Paragraph>
    <Section position="1" start_page="561" end_page="562" type="sub_section">
      <SectionTitle>
6.1 Time Efficiency
</SectionTitle>
      <Paragraph position="0"> To evaluate the time efficiency of the covariation encoding, we compared the parse times for our test grammar with three different computational encodings of the lexicon:  Meurers and Minnen Covariation Approach to HPSG Lexical Rules the expanded out lexicon, the basic covariation encoding, and the covariation encoding improved by constraint propagation. 33 As discussed in Section 5.1, the parsing times with a covariation lexicon without constraint propagation suffer significantly from the lack of information directly available upon lexical lookup. For the test grammar, the resulting extended search-space of parsing with the basic covariation encoding leads to a performance that is, on average, 18 times slower than that with the expanded out lexicon.</Paragraph>
      <Paragraph position="1"> The use of constraint propagation, however, makes it possible to exploit the covariation encoding of lexical rule application such that it results in an increase in speed. Parsing with the test grammar using the constraint propagated covariation lexicon is, on average, 25 percent faster than the performance with the expanded out lexicon.</Paragraph>
      <Paragraph position="2"> The representation of lexical information in a constraint propagated covariation lexicon makes the maximum information available at lexical lookup while requiring a minimum number of nondeterministic choices to obtain this information.</Paragraph>
      <Paragraph position="3"> Summing up, the relation between parsing times with the expanded out (EXP), the covariation (COV), and the constraint propagated covariation (IMP) lexicon for the test grammar can be represented as IMP : EXP : COV = 0.75 : 1 : 18. With respect to our test grammar, the constraint propagated covariation lexicon thus is the fastest lexical encoding.</Paragraph>
    </Section>
    <Section position="2" start_page="562" end_page="563" type="sub_section">
      <SectionTitle>
6.2 Space Efficiency
</SectionTitle>
      <Paragraph position="0"> Besides the effect of requiring a minimum of nondeterministic choices and thereby reducing the number of resolution steps to increase time efficiency, the covariation encoding of lexical rules can result in an additional speedup since it reduces the space requirements of large grammars.</Paragraph>
      <Paragraph position="1"> A comparison of space efficiency between an expanded out and a covariation lexicon needs to compare two different encodings. The expanded out lexicon consists solely of lexical entries, whereas the covariation lexicon is made up of three different data structures: the extended base lexical entries, the interaction predicates, and the lexical rule predicates. We focus on a qualitative evaluation of space efficiency, rather than on providing results for the test grammar, since the space efficiency of the covariation encoding relative to the expanded out lexicon is dependent on several properties of the grammar: the number of lexical entries in the lexicon that can undergo lexical rule application, the size of the lexical entries, and the number of lexical entries belonging to a word class.</Paragraph>
      <Paragraph position="2"> Since only base lexical entries that feed lexical rules are modified by the lexical rule compiler, the covariation encoding naturally only results in space savings for those lexical entries to which lexical rules apply.</Paragraph>
      <Paragraph position="3"> The space efficiency is dependent on the size of the lexical entries since in the covariation encoding much of the lexical information that is specified in a base lexical entry is not duplicated in the lexical entries that can be derived from it, as is the case for an expanded lexicon. Thus, the more information represented in a base lexical entry, the greater the space saving achieved by the covariation encoding. In lexically oriented grammar formalisms like HPSG, the lexical entries are highly information rich. A covariation treatment of HPSG lexica therefore can be particularly profitable.</Paragraph>
      <Paragraph position="4"> The number of lexical entries belonging to a word class is relevant since the interaction predicates are identical for all lexical entries belonging to the same word class. 33 The lexicon of the test grammar can be expanded out off-line since the recursive Complement Extraction Lexical Rule applies only to full verbs, i.e, lexical entries with a complement list of finite length. As a result, the grammar does not have an infinite lexicon.</Paragraph>
      <Paragraph position="5">  Computational Linguistics Volume 23, Number 4 This means that the more lexical entries in a word class, the greater the saving in space. The covariation approach therefore is particularly attractive for grammars with a large lexicon.</Paragraph>
    </Section>
  </Section>
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