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<Paper uid="J92-2003">
  <Title>Feature Structures and Nonmonotonicity</Title>
  <Section position="3" start_page="0" end_page="187" type="relat">
    <SectionTitle>
2. Previous Work
</SectionTitle>
    <Paragraph position="0"> There are a number of phenomena that suggest that unification-based grammar formalisms might profit from the addition of some form of nonmonotonicity, and several authors have in fact suggested such extensions. In this section, we argue that these proposals suffer from a number of shortcomings. Most importantly, previous proposals have either been highly restricted in scope or have been presented in very informal  * Computational Linguistics Department, Postbus 716, 9700 AS Groningen, The Netherlands (~) 1992 Association for Computational Linguistics  Computational Linguistics Volume 18, Number 2 terms, thus leaving a number of questions concerning the exact behavior of the proposed extensions unanswered.</Paragraph>
    <Paragraph position="1"> An overview of the issues that call for the addition of non-monotonic reasoning and of some of the proposals in that direction is presented below.</Paragraph>
    <Paragraph position="2"> * Exceptional Rules. Consider a language in which the vast majority of verbs cannot precede its subject, whereas a small number of exceptional verbs can. The rule accounting for inverted structures would probably require that verbs occurring in it be marked as +INV (i.e. (INV) : +). As a consequence, all regular verbs must be marked explicitly as --INV (to prevent them from occurring in the inversion rule). Note that, in a unification-based grammar, there is no need to mark the exceptional verbs as +INV, which leads to the rather counterintuitive situation that regular verbs need to be marked extra, whereas the exceptional ones can remain underspecified. A more natural solution would be to assign all verbs the specification qNV by default (either by means of template inheritance or by means of lexical feature specification defaults as used in Generalized Phrase Structure Grammar \[GPSG; Gazdar et al. 1985\]) and to overwrite or block this specification in the exceptional cases. The possibility of incorporating an overwrite operation in a unification-based formalism is mentioned in Shieber (1986a, p. 60).</Paragraph>
    <Paragraph position="3"> * Feature Percolation Principles. Both GPSG and Head-driven Phrase Structure Grammar (HPSG; Pollard and Sag 1987) adopt the so-called Head Feature Convention (HFC). In GPSG, the HFC is a default principle: head features will normally have identical values on mother and head, but specific rules may assign incompatible values to specific head features. In unification-based formalisms, it is impossible to express this principle directly. Adding the constraint (Xo head) = (Xi head) to every rule of the form Xo --~ X1... Xn (with Xi (1 K i &lt; n) the head of the rule and assuming all head features to be collected under head) will not do, as it rules out the possibility of exceptions altogether. Shieber (1986b) therefore proposes to add this constraint conservatively, which means that, if the rule already contains conflicting information for some head feature f, the constraint is replaced by a set of constraints (Xo head f') = (Xi head f'), for all head features f' # f.</Paragraph>
    <Paragraph position="4"> * Structuring the Lexicon. Flickinger, Pollard, and Wasow (1985), Flickinger (1987), De Smedt (1990), Daelemans (1988), and others, have argued that the encoding and maintenance of the detailed lexical descriptions typical for lexicalist grammar formalisms benefits greatly from the use of (nonmonotonic) inheritance. In Flickinger, Pollard, and Wasow (1985), for instance, lexical information is organized in the form of frames, which are comparable to the templates (i.e., feature structures that may be used as part of the definition of other feature structures) of PATR-II (Shieber 1986a). A frame or specific lexical entry may inherit from more general frames. Frames can be used to encode information economically and, perhaps more importantly, as a means to express linguistic generalizations. For instance, all properties typical of verbs are defined in the VERB-frame, and properties typical of auxiliaries are defined in the AUX-frame. The AUX-frame may inherit from the VERB-frame, thus capturing the fact that an auxiliary is a kind of verb.</Paragraph>
    <Paragraph position="5">  Gosse Bourna Feature Structures and Nonmonotonicity In this approach, a mechanism that allows inheritance of information by default (i.e., a mechanism in which local information may exclude the inheritance of more general information) is of great importance. Without such a mechanism, a frame may contain only properties that hold without exception for all items that inherit from this frame. In practice, however, one often wants to define the properties that are typical for a given class in the form of a frame, without ruling out the possibility that exceptions might exist. In unification-based formalisms, templates can play the role of frames, but as unification is used to implement inheritance, nonmonotonic inheritance is impossible.</Paragraph>
    <Paragraph position="6"> * Inflectional Morphology. In PATR-II the lexicon is a list of inflected word forms associated with feature structures. The only tools available for capturing lexical generalizations are templates (see above) and lexical rules. Lexical rules may transform the feature structure of a lexical entry. An example is the rule for agentless passive (Shieber 1986a, p. 62), which transforms the feature structure for transitive past participles into a feature structure for participles occurring in agentless passive constructions.</Paragraph>
    <Paragraph position="7"> Lexical rules can only change the feature structure of a lexical entry, not its word form, and thus, the scope of these rules is rather restricted.</Paragraph>
    <Paragraph position="8"> While the examples in Flickinger, Pollard, and Wasow (1985) and Evans and Gazdar (1989a,b) suggest that the latter restriction can be easily removed, it is not so obvious how a unification-based grammar formalism can cope with the combination of rules and exceptions typical for (inflectional) morphology. For instance, it is possible to formulate a rule that describes past tense formation in English, but it is not so easy to exclude the application of this rule to irregular verbs and to describe (nonredundantly) past tense formation of these irregular verbs. Evans and Gazdar (1989a,b) present the DATR-formalism, which, among other things, contains a nonmonotonic inference system that enables an elegant account of the blocking-phenomenon just described. The examples used throughout their presentation are all drawn from inflectional morphology and illustrate once more the importance of default reasoning in this area of linguistics.</Paragraph>
    <Paragraph position="9"> * Gapping. In Kaplan (1987) it is observed that gapping constructions and other forms of nonconstituent conjunction can be analyzed in Lexical Functional Grammar (Bresnan and Kaplan, 1982) as the conjunction of two functional-structures (f-structures), one of which may be incomplete.</Paragraph>
    <Paragraph position="10"> The missing information in the incomplete f-structure can be filled in if it is merged with the complete f-structure, using an operation called priority union. Priority union of two f-structures A and B is defined as an operation that extends A with information from B that is not included (or filled in) in A. As not all information in B is present in the priority union of A and B, this operation introduces nonmonotonicity.</Paragraph>
    <Paragraph position="11"> The proposals for incorporating the kind of default reasoning that is required for each of the phenomena above are both rather diverse and idiosyncratic and, furthermore, suffer from a number of shortcomings.</Paragraph>
    <Paragraph position="12"> The Head Feature Convention and Feature Specification Defaults of GPSG, for instance, appear to be motivated with a very particular set of linguistic phenomena in mind and also are rather intimately connected to peculiarities of the GPSG-formalism. What  Computational Linguistics Volume 18, Number 2 is particularly striking is the fact that two different conceptions of default appear to play a role: a head feature is exempt from the HFC only if this would otherwise lead to an inconsistency, whereas a feature is exempt from having the value specified in some feature specification default (among others) if this feature covaries with another feature.</Paragraph>
    <Paragraph position="13"> Overwrite and add conservatively are also highly restricted operations. From the examples given in Shieber (1986a) it seems as if overwriting can only be used to add or substitute (nonmonotonically) one atomic feature value in a given (possibly complex) feature structure (which acts as default). Add conservatively, on the other hand, is only used to add one reentrancy (as far as possible) to a given feature structure (which acts as nondefault). An additional restriction is that add conservatively is well behaved only for the kind of feature structures used in GPSG (that is, feature structures in which limited use is made of covariation or reentrancy). Consider for instance the example in (1). 1 Adding the constraint (Xo head) = (X1 head) to (1) conservatively could result in either la or lb.</Paragraph>
    <Paragraph position="15"> As add conservatively and overwriting are, in a sense, mirror images of each other, it is tempting to generalize the definitions of these operations and to think of them as operations on arbitrary feature structures, whose effect is equivalent to that of priority union. Thus, given two feature structures FSD (the default) and FSND (the nondefault), adding FSp to FSND conservatively would be equivalent to overwriting FSD with FSND, and to the priority union of FSND and FSD (i.e. FSND/FSD in the notation of Kaplan \[1987\]). However, in light of the example above, it should be clear that such a generalization is highly problematic. Other examples worth considering are 2 and 3.</Paragraph>
    <Paragraph position="16"> 1 Whether this kind of situation can occur in GPSG probably depends on whether one is willing to conclude from examples such as: S\[COMPo~\] ---* {\[SUBCATa\]}, H\[COMP NIL\] (Gazdar et al. 1985, p. 248) that covariation of arbitrary categories is in principle not excluded in this formalism.  Again, if we try to combine the two feature structures along the lines of any one of the operations mentioned above, there are at least two possible results (note that in Example 3, we could either preserve the information that features f and g are reentrant, or preserve the information that f : a), and there is no telling which one is correct. Two conclusions can be drawn at this point. First of all, on the basis of the examples just given, it can be concluded that a nonmonotonic operation on feature structures that relies (only) on the fact that the result should be consistent must be very restricted indeed, as more generic versions will always run into the problem that there can be several mutually exclusive solutions to solving a given unification conflict. Second, claims that the operations add conservatively, overwriting, and priority union are equivalent are unwarranted, as no definitions of these operations are available that are sufficiently explicit to determine what their result would be in moderately complex examples such as 1-3.</Paragraph>
    <Paragraph position="17"> The approach exemplified by Flickinger (1987) and others is to use a general-purpose knowledge representation formalism to represent linguistic information and model default inheritance. Feature structures are defined as classes of some sort, which may inherit from other, more generic, classes. The inheritance strategy used says that information in the generic class is to be included in the specific class as well, as long as the specific class does not contain local information that is in conflict with the information to be inherited. Such an inheritance strategy will run into problems, however, if reentrancies are generally allowed. For instance, think of the examples presented above as involving a generic class FSD from which a specific class FSND inherits. The inheritance procedure in, for instance, Flickinger (1987, p. 59ff) does not say anything about which one of the possible results will be chosen.</Paragraph>
    <Paragraph position="18"> The work of Evans and Gazdar (1989a,b), finally, is not easily incorporated in a unification-based formalism, as they use semantic nets instead of feature structures to represent linguistic information. That is, although the syntax of DATR is suggestively similar to that of, for instance, PATR-II, DATR descriptions do in fact denote graphs that differ rather substantially from the graphs used to represent feature structures (see Evans and Gazdar 1989b). The nonmonotonic reasoning facilities of DATR therefore are not directly applicable in a unification-based formalism either.</Paragraph>
    <Paragraph position="19"> We conclude that a formally explicit definition of a nonmonotonic operation on feature structures is still missing. In particular, the interaction of reentrancy and non-monotonicity is a subtle issue, which has not been given the attention it deserves. That there is a need for nonmonotonic devices is obvious from the fact that several authors have found it necessary to introduce partial solutions for dealing with nonmonotonicity in a unification-based setting. The intuitions underlying these proposals appear to be compatible, if not identical, and thus it seems attractive to consider an operation that subsumes the effects of the proposals so far. Default Unification, as defined below, is an attempt to provide such an operation.</Paragraph>
    <Paragraph position="20">  Computational Linguistics Volume 18, Number 2</Paragraph>
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