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<Paper uid="P91-1028">
  <Title>Multiple Default Inheritance in a Unification-Based</Title>
  <Section position="3" start_page="0" end_page="217" type="intro">
    <SectionTitle>
2 Classes and Inheritance
</SectionTitle>
    <Paragraph position="0"> An ELU lexicon consists of a number of 'classes', each of which is a structured collection of constraint equations and macro calls encoding information common to a set of words, together with links to other more general 'superc\]asses'. For example, if an 'intransitive' class is used to express the common syntactic properties shared by all intransitive verbs, then particular instances of intransitive verbs can be made to inherit this information by specifying the 'intransitive' class as one of their superclasses - it then becomes unnecessaw to specify the relevant properties individually for each such verb. The lexicon may be thought of as a tangled hierarchy of classes linked by inheritance paths, with, at the most specific level, lexicai classes and, at the most general, classes for which no superclasses have been defined, and which therefore inherit no information from elsewhere.</Paragraph>
    <Paragraph position="1"> S &amp;quot;Environnement Linguistique d'Unlfication&amp;quot; - see Estival (1990), and, for a description of the earlier UD system on which E~u is based, Johnson and Rosner (1989).</Paragraph>
    <Paragraph position="2">  Lexical entries are themselves classes, 4 and any information they contain is standardly specific to an individual word; lexical and non-lexical classes differ in that analysis and generation take only the former as entry points to the lexicon.</Paragraph>
    <Paragraph position="3"> Inheritance of a feature value from a superclass may be overridden by a conflicting value for that feature in a more specific class. This means, for example, that it is possible to place in the class which expresses general properties of verbs an equation such as '&lt;* aux&gt; = no' (i.e. &amp;quot;typical verbs are not auxiliaries&amp;quot;), while placing the contradictory specification '&lt;* aux&gt; = yes' in s subclass from which only anTiliaries inherit. The ability to encode exceptional properties of lexical items is extremely attractive from the linguistic point of view; the lower the position in the hierarchy at which the property appears, the more exceptional it may be considered.</Paragraph>
    <Paragraph position="4"> A class definition consists of the compiler directive '#Class' (for a non-lexicai class) or '#Word' (for a lexical class), followed by the name of that class, a possibly empty list of direct superclasses, a possible empty 'main' or default equation set, and sere or more 'variant' equation sets. The superclass declaration states from which classes the current class inherits; if more than one such superclass is specified, their order is significant, more specific classes appearing to the left of more general ones. If the current class is one of the most general in the lexicon, it inherits no information, and its superclass list is empty.</Paragraph>
    <Paragraph position="5"> Following the superclass declaration are sere or more equations representing default information, which we refer to as the 'main' equation set. These may be overridden by eontlleting information in a more specific class. Each equation in a main set functions as an independent constraint, in a msnner which will be clarified below.</Paragraph>
    <Paragraph position="6"> Variant equation sets, loosely speaking, correspend to alternatives at the same conceptual level in the hiersrchy, and in msny cases reflect the traditional ides of 'paradigm'. Equations within a variant set are absolute constraints, in contrast to those in the main set; if they conflict with informstion in a more specific class, failure of unification occurs in the normal way. Also, unlike the main set, each variant set functions as a single, possibly complex, constraint (see section 2.2). A feature 4Thus no distinction is made between classes and 'instances', as in e.g. KL-ONE (Schmolse and Lipkis, 1983) structure is created for each variant set that successfully unifies with the single structure arising from the main set. Each variant set is preceded by the vertical bar ' \['. The order of variant sets within a class is not significant, although, if a main set is employed, it must precede any variant sets.</Paragraph>
    <Paragraph position="7"> The following simplified example illustrates the form and interaction of class definitions. In equs.</Paragraph>
    <Paragraph position="8"> tions, unification variables have initial capitals, and negation of constants is indicated by ' '. 'kk' is the string concatenation operator - an equation of the form X = Y kk Z unifies X nondeterministically with the result of concatenating Y= and Z.</Paragraph>
    <Paragraph position="10"> The lexiesl class walk is declared as having two direct superclasses, Intransitive and Verb; its main set contains just one equation, which sets the value of the feature stem to be walk.</Paragraph>
    <Paragraph position="11"> Intransitive has no direct superclasses, and its main equation set assigns to the value of subcat a list with one element, a feature structure in which the value of cat is rip. Neither walk nor Intransitive has sny variant equation sets.</Paragraph>
    <Paragraph position="12"> Verb, by contrast, has three, in addition to two main set equations. The latter assign, by default, the values of cat and aux. The three variants accounted for by this example are the past tense verb, in which the value of form unifies with the result of concatenatin 8 the value of stem with the string 'ed', the third person singular form, in which the suffix string is 's', and the form representing other combinations of person and number in the present tense; in the last case, the form value is simply identical to the stem value. 5</Paragraph>
    <Section position="1" start_page="216" end_page="216" type="sub_section">
      <SectionTitle>
2.1 Class Precedence
</SectionTitle>
      <Paragraph position="0"> In an ELU lexicon, a class may inherit directly from more than one superclass, thus permitting 'multiple inheritance' (Touretsky, 1986: 7ft.), in contrast to 'simple inheritance' in which direct inheritance is allowed from only one superclass at a time. The main advantage that multiple inheritance offers over simple inheritance is the ability to inherit several (orthogonal or complementary) sets of properties from classes in more than one path through the hierarchy. In the lexical context, it has often been observed that morphological and syntactic properties are essentially disjoint; the subeategorisation class of a verb is not predictable from its conjugation class, and vice versa, for example. Multiple inheritance permits the two types of information to be separated by isolating them in distinct subhierarchies. null The question to be resolved in systems employing multiple inheritance is that of precedence: which of several superclasses with conflicting properties is to be inherited from? ELU employs the class precedence algorithm of the Common Lisp Object System (CLOS) to compute a total ordering on the superclasses of a lexicsl class, s The resulting 'class precedence list' (CPL) contains the class itself and all of its superclasses, from most specific to most general, and forms the basis for the defaulting behaviour of the lexicon. As an example, consider the following lexicon: #Word It (B D) #Class B (C) ZClass C (Y) #Class D (E) #Class E (P) #Class F () Here, the superclass declarations embody the orderin 8 constraints A &lt; B, A &lt; D, B &lt; D, B &lt; C, C &lt; F, D &lt; E, and E &lt; F; from these are derived a total order assigning to the lexical class A the CPL (A,B,C,D,E,F).</Paragraph>
    </Section>
    <Section position="2" start_page="216" end_page="217" type="sub_section">
      <SectionTitle>
2.2 Inheritance of Properties
</SectionTitle>
      <Paragraph position="0"> A lexical class such as walk in the example above corresponds to a family offeature structures. Here, as in most analyses, members of this family represent morphosyntactically distinct realizations of a single basic lexeme. Consulting the lexicon involves determining membership of the set of feature structures associated with a given lexical class; s See Steele (1990: 782ff.) for details of the aIgorithm, and Keene (1989:118ff.) for discussion. In circumstances where no such total ordering is possible, the system reports an error.</Paragraph>
      <Paragraph position="1"> the precedence relation encoded in the CPL controls the order in which defeasible information is considered, each class in the CPL adding first default and then non-default information to each FS produced by the previous class.</Paragraph>
      <Paragraph position="2"> More formally, we define default eztension, superclass eztension, and global ez~e~sion as follows: 7 (1) The default eztension of a FS ~ with respect to a set of FSs * is if U ({~b} U ~) :f: _1_, and .1_ otherwise.</Paragraph>
      <Paragraph position="3"> (2) The superclass ez~ension of a FS ~b with respect to a class c having a main equation set M and variant sets Vl,...v, is the set I ~be J.}, where M s is the smallest set of FSs such that each m E M describes some m ~ E M s, C/~s is the default extension of~b with respect to M e, and v~ is the feature structure described by vl. We refer to this set as E(~b, c).</Paragraph>
      <Paragraph position="4">  (3) The global eztensio~, of a lexlcvd class having the CPL (cl,...c,) is F~, where Fo = {T}, and</Paragraph>
      <Paragraph position="6"> With regard to (I), each of the FSs in W that can unify with ~b does so - those that cannot, because they conflict with information already present, are ignored. The condition requiring ~ to be unifiable with the result of unifying the elements of * takes account of the potential order-sensitivity of the defaulting operation - only those main sets having this property can be applied without regard to ordef. If this condition is met then the application of defaults always succeeds, producing a feature structure which, if no member of the default set is applicable, is identical to ~b. This interpretation of default unification is essentially that of Bouma (1990).</Paragraph>
      <Paragraph position="7"> The superclass extension E(~, c) is formed by applying to ~ any default equations in the main set of c, and then applying to the result each variant set in c; for variant sets Vl,... v,,, the result of this 7'A U B' here denotes the unification of A and B, 'T' denotes the most general, 'empty' FS, which unifies with all others, and '_L' denotes the inconsistent FS, equated with failure of unification.</Paragraph>
      <Paragraph position="8">  second stage is the set of FSs {@1,...@~}, where each ~ is the result of successfully unifying ~b with some different vj.</Paragraph>
      <Paragraph position="9"> To speak in procedural terms, the global extension of a lexicai class L with the CPL C is computed as follows: T is the empty FS which is input to C; each c~ in C yields as its superelass extension a set of FSs, each member of which is input to the remainder of C, (c~+l,...c,). The global extension of L is then the yield of the most general class in its CPL - expressed in a slightly different way, the global extension of L is the result of applying to T the CPL of L.</Paragraph>
      <Paragraph position="10"> It is possible to exert quite fine control over inheritance; one property may override another when assigned in a main equation set, but cause failure when assigned in a variant set. Normally, variant sets are defined so as to be mutually exclusive; a FS that unifies with more than one of the variant sets is in effect multiplied, s The inheritance systems of Calder (1989) and Flickinger (1987) make use of lexical rules - the ELU lexicon does not provide such devices, although some of their functionality may be reproduced by the variant set mechanism.</Paragraph>
      <Paragraph position="11"> The approach described here differs from some previous proposals for default inheritance in unification-based lexicons in that the process of building FSs is monotonic - classes may add information to a FS, but are unable to remove or alter it. Thus, given a CPL (ci,...c.), any FS F admitted by a class c~ subsumes every FS that can be created by applying to F the classes (c~ + I,... c,~), m n. Karttunen (1986) and Shieber (1986) describe systems in which FSs may be modified by default statements in such a way that this property does not automatically hold. These schemes permit default statements to override the effect of earlier statements, whereas default information in the ELU lexicon may itself be overridden.</Paragraph>
      <Paragraph position="12"> We now turn to some examples illustrating the r61e of defeasible inheritance in the lexicon.</Paragraph>
    </Section>
  </Section>
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