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<Paper uid="C92-3144">
  <Title>THE FIRST BUC REPORT</Title>
  <Section position="2" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2. Feature Geometries
2.1. What Are Feature Geometries?
</SectionTitle>
    <Paragraph position="0"> Tile term feature geometry is taken from generative phonology, where it was introduced by Clements (1985). A feature geometry determines what feature structures are allowed by specifying what (complex or atomic) values each path in a feature structure can have. In this way, a feature geometry expresses certain kinds of feature co-occurrence restrictions (FCRs, Gazdar et al., 1985), namely, those FCRs that are local in the sense that they can be formulated in terms of path continuation restrictions. For example, we can incorporate the FCIt \[TENSE ~- PAST\] z:~ \[FINITE\] in a geometry by making TENSE a sub-feature of only FINITE (and PAST a possible value of TENSE). On the otlmr hand, we cannot encode a global FCR like</Paragraph>
  </Section>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
\[SUBJ DEF : +\] -:~ \[INDIR_OBJ NUMBER : PLURAL\].
</SectionTitle>
    <Paragraph position="0"> Also, we cannot encode a global FCR such as</Paragraph>
    <Paragraph position="2"> unless we make TENSE a sub-feature of AGREEMENT alone. This is important because allowing arbitrary or global constraints on wen-fornmd feature structures leads to undecidable systems if coupled with structure sharing (Blackburn and Spaan, 1991).</Paragraph>
    <Paragraph position="3"> Our feature geometries, just like the ones used ill phonology, specify whether or not the continuations of a given path are pairwise incmnpatible. For example, the attributes FINITE and NON-FINITE can be made incompatible continuations of the attribute VERB_FORM. As a result, in any actual feature structure at most one edge can lead from a node that a path ending in VERB_FORM leads to. What this mechanism allows us to express are also local FCRs, e.g.~</Paragraph>
  </Section>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
~(\[VERB..FORM FINITE\] A \[VERB-FORM NON-FINITE\])
</SectionTitle>
    <Paragraph position="0"> in this case.</Paragraph>
    <Paragraph position="1"> ACRES DE COLING-92, NANTES, 23-28 AO~' 1992 9 4 5 PaGe. OF COLING-92, NANTES, AUG. 23-28, 1992</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.2. How Are Feature Geometries
Used?
</SectionTitle>
      <Paragraph position="0"> The main advantage of using feature geometries is that it makes the unification operation and the unifiabi\[ity test more efficient. Traditional unification only fails if atomic values clash, whereas geometry-based unification will fail if incompatible continuations of a path are to be unified. As a matter of course, this means that an extra check is performed each time new continuations are created during unification, lfowever, if the feature geometry is reasonably structured (i.e., not flat), then the cost of this extra checking is significantly less than the gain from early unification failure. In the typical case, the growth of the comparative advantage of early unification failurc over traditional unification (i.e., the proportion of all possibilities of failure to the number of leaves) should grow faster than its comparative disadvantage, i.e., the number of checks.</Paragraph>
      <Paragraph position="1"> If feature geometries are used as intended, then the major distinctions between linguistic objects are made by attributes closer to the root of a feature structure, and minor features are in deeply subordinate positions. For example, the information that something is a verb will be superordinate to the information that it has a second person form. As a consequence, the most frequent reason for the failure of unification (which is a conflict between major class features) will be detected earliest. Typically, the opposite is true in traditional unification, i.e., only conflicts between terminal nodes of feature structures are detected. In such systems, major category clashes are found early enough only if the feature structures are very fiat, which is undesirable for other reasons.</Paragraph>
      <Paragraph position="2"> Moreover, the use of feature geometries assists the grammar-writer to develop her/his grammar in two ways. First, requiring the grammar-writer to specify a feature geometry and write rules accordingly forces her/him to take the semantics of features and feature structures more seriously than is typically the case. Second, since feature geometries define the set of possible feature structures, they also determine which paths can share values. The checking of structure sharing is not necessary during run-time unification, because it can be succeaqfufiy dealt with at compile-time, thus providing additional error checking on the grammar. These two by-products of using feature geometries should lead to better grammar-writing.</Paragraph>
      <Paragraph position="3">  3. The String Completion Limit 3.1. What Is the SCL?  The string completion limit, which is a small integer parameter of BUG's compiler, expresses a performance limitation that BUG incorporates into the automaton it produces. Imposing constraints on the complexity of derivation trees has a long tradition in linguistics. Most proposals of this sort, such as Yngve's (1961), which lirrfits the depth of possible derivation trees, or limitations on the direction of their branching (e.g., Yngve, 1960) are either too weak or too strong on their own. However, there is a suggestion that we find broad enough in its coverage, and yet conceptually simple. This is Kornai's (1984) hypothesis, in terms of which any string that can he the beginning of a grammatical string can be completed with k or less terminal symbols, where k (i.e., the SCL) is a small integer. For example, consider:</Paragraph>
      <Paragraph position="5"> In this string, each portion up to a numbered position can be completed with at most one word, as the following table illustrates (position numbers are on the left, completions in the middle, and the  minimum completion length K on the right): (1') 1,5,9, 13: ... John. K= 1 2, 6, 10, 14: ... cheese. K = 1 3, 7, 11, 15: .... K = 0 4, 8, 12, 16: ... stinks. K = 1  On the other hand, the following string, although its portions up to each number are grammatical, will be excluded if the SOL is smaller than 5: (2) The 1 cheese2 thats the4 rats that6 the7 eats thats thoo dogtt ehasedl~ ateis stolet4 The corresponding table is:  (2 t) 1: .. cheese stinks.</Paragraph>
      <Paragraph position="6"> 2: .. ro~s.</Paragraph>
      <Paragraph position="7"> 3: .. rots stinks.</Paragraph>
      <Paragraph position="8"> 4: .. rat ate rots.</Paragraph>
      <Paragraph position="9"> 5: .. ate rots.</Paragraph>
      <Paragraph position="10"> 6: .. stinks ate rots.</Paragraph>
      <Paragraph position="11"> 7: ... cat chased ate stinks.</Paragraph>
      <Paragraph position="12"> 8: ... chased ate stinks.</Paragraph>
      <Paragraph position="13"> 9: ... stinks ate stole rots.</Paragraph>
      <Paragraph position="14"> 10: ... dog chased ate stole stinks. 11: ... chased ale stole stinks.</Paragraph>
      <Paragraph position="15"> 12: ... ate stole stinks.</Paragraph>
      <Paragraph position="16"> 13: ... stole stinks.</Paragraph>
      <Paragraph position="17"> 14: ... stinks.</Paragraph>
      <Paragraph position="18">  (This seems to show that the SCL in terms must be 3 or 4.)</Paragraph>
      <Paragraph position="20"> of words ACRES DE COLING-92, NANTES, 23-28 AOt\]T 1992 9 4 6 PROC. OF COL1NG-92, NANTEs, AUG. 23-28, 1992 As (2) shows, the SCL imposes a limit on the depth of center-embedding; but, as can be seen from (1), it does not constrain the depth of fightbranching structures. Left branching, however, is limited, though the effect of this limitation is less pronounced than in the case of center-embedding.</Paragraph>
      <Paragraph position="21"> The example with the highest K that we could find in English can be accommodated if k is 3:  (3) Aflerl as verya (3') 1: ... walkiug~ sleep! K : 2 2: ... walk, sleep! K = &amp;quot;2 3: ... long walk, sleep! K : 3 Although the current implementation of BUG uses the context-free source grammar format, in which so-called cross-serial dependencies cannot be expressed, it s worth noting that the SCL also puts an upper bound on tile length of these: (4) John, t Even Carlos3 and4 Peters married respectivelys Sally, T Paul, s Susan9 andla lnez.</Paragraph>
      <Paragraph position="22"> (4') 1: ... sleeps. K = 1 2,3: ... and Peter sleep. K =3 4: ._ Peter sleep. K = 2 5: .. sleep. K : 1 6: .. Sally, Paul, Susan and Iaez. K = 5 7: .. Paul, Susan and lnez. K = 4 8: .. Susan and lnez. K = 3 9: .. and Inez. K = 2 10: .. lncz. K = 1  The SCL has two additional consequences (and maybe more). First, it excludes certain lexical categories, such as modifiers of adjective modifiers (if k &lt; 4). If, say, shlumma were a word of that category, then we would need at least 4 words to complete After a shlumma... (cf. (3) above). Second, all upper limit is placed on the uumber of obligatory daughters of non-terminal nodes.</Paragraph>
      <Paragraph position="23"> 3,2. How Is the SCL Used? The way in which we can produce the biggest regular subset of a context-free language that respects the SCL can be sketched as follows. First we produce an RTN (recursive transition network) equivalent to the source grammar, call it A. (An RTN is like a finite-state automaton, but its input symbols may be RTNs or terminal symbols.) Then we assign a minimum completion length (K in the tables above) to each node (accepting states will bare K = 0). If B is an RTN accepted by the transition from state st to state s2 in A, then we try to replace the transition with B itself, so that initial state of B becomes st and its accepting states become s~. (This can be done with standard techniques.) Since the K-value of s2 may be bigger than 0, assigning K values to some states of B may be impossible (if those values would exceed k). We leave out those states (and whatever additional states and transitions depend on them).</Paragraph>
      <Paragraph position="24"> In those cases when the above procedure would not terminate (i.e., when s2 is an accepting state in A and B is the same RTN as some other RTN C the acceptance of which takes the machine to s~, we eliminate the transition corresponding to B, and collapse sl with the initial state of C (with the standard technique). So the procedure will terminate in all cases. In the current implementation, we use the actual finite-state network so produced, but (as our reviewer notes) we could as well use the RTN directly, and compute whether the SCL is respected as we go. We have not made experiments with this latter solution, so we cannot compare it with our current solution in terms of space and time requirements.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4. SD Versus SC
</SectionTitle>
    <Paragraph position="0"> One of tile most important aznong BUG's features is the separation of structural descriptions from structural changes in source rules. Although the unificationalists have been asserting that this old-fashioned distinction should be abandoned (arguing that pieces of information coming from different sources have the same status), many voices have been raised to show that the origins of a piece of information may matter (see Zaenen and Karttunen, 1984; Pullum and Zwicky, 1986; Ingria. 1990).</Paragraph>
    <Paragraph position="1"> The structural description in a BUG rule specifies the conditions under which the rule cml be applied in the parsing process. That is, when parsing, it refers to the right-hand side of the rewrite rule only, and it is never used to update any feature structure.</Paragraph>
    <Paragraph position="2"> The structural change, on the other hand, describes wbat action to take when the structural description is satisfied, i.e., how to build a new feature structure (when parsing, this corresponds to the left-hand side of tile context-free rule). Tbus, structural descriptions are used to check unifiability, whereas the application of structural changes actually builds structure.</Paragraph>
    <Paragraph position="3"> In usual unification-based grammars, the conditions of applying a rule are satisfied if some unification succeeds. In BUG, what determines whether a rule should apply is unifiability. Unifiability differs from unification in a crucial respect, which is illustrated by the following example: A: \[1 B: \[NUMBER = SINGULAR\] C: \[NUMBER = PLURAL\] A is unifiable with B and A is unifiable with C, even though B is not unifiable with C. Therefore, if a structural description requires unifiability of A AcrEs DE COLING-92, NANTES. 23-28 AOOT 1992 9 4 7 PROC. OF COLlNG-92, NAMES. AUQ. 23-28, 1992 with both B and C, it will be satisfied. IIowever, if we were to formulate tiffs requirement in terms of unification, as is currently done in unification-based grammars, then A, B and C will not satisfy this requirement. A similar example from 'real life' is the requirement that the auxiliary verb should agree with each subject of a co-ordination: (5) *Is/*Are Jean leaving and the others arrzving? In this example, SUMNER of is is not unifiable with that of lhe ethers, and NUMBER of arc is not unifiable with that of Jean, so traditional unification-based grammars and BUG would yield the same (correct) result. Now, consider: (6) Will Jean leave and the others arrive? This sentence is in because will's NUMBER is unifiable with both that of Jean and that of the others, although the unification of all three NUMBEII. values still leads to failure. So sou will behave correctly in this case.</Paragraph>
  </Section>
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