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<Paper uid="J99-4002">
  <Title>Lexical Rules in Constraint-based Grammars</Title>
  <Section position="2" start_page="0" end_page="488" type="abstr">
    <SectionTitle>
1. Introduction
</SectionTitle>
    <Paragraph position="0"> In lexicalist approaches to grammar, lexical rules are a crucial component of the overall theory and more and more generalizations have come to be stated within them. For example, in the development of HPSG (Pollard and Sag 1987, 1994) from GPSG (Gazdar et al. 1985) several syntactic metarules concerning the location of empty categories in unbounded dependency constructions are restated as lexical rules. One example is the Subject Extraction rule, which licenses subject extractions from sentential complements. Inflectional morphological rules, such as Plural Formation, and rules of verb alternation, such as Passive, are also stated as lexical rules by Pollard and Sag. Recently, Bouma and van Noord (1994) have proposed a lexical rule of Adjunct Introduction, which can recursively add adverbial categories to the SUBCAT list of a verbal category.</Paragraph>
    <Paragraph position="1"> There are three main problems with the treatment of lexical, or what might be better termed unary, rules as a homogeneous class.</Paragraph>
    <Paragraph position="2">  * Computer Laboratory, University of Cambridge, Pembroke Street, Cambridge CB2 3QG, UK. E-maih ejb@cl.cam.ac.uk t Center for the Study of Language and Information, Stanford University, Ventura Hall, Stanford, CA 94305. E-mail: aac@csli.stanford.edu (~) 1999 Association for Computational Linguistics  Computational Linguistics Volume 25, Number 4 Firstly, Carpenter (1991) demonstrates that if lexical rules are able to perform arbitrary manipulations (deletion, addition, and permutation) of potentially unbounded lists, any recursively enumerable language can be generated, even if the nonderived lexicon and grammar only generate context-free languages. However, once we are committed to treating rules such as Passive and Adjunct Introduction in a homogeneous way, restrictions that prevent lexical rules from increasing generative capacity, such as constraining the use of category variables, bounding the length of the suB-CAT list, or limiting recursive application, cannot be imposed. Subdividing lexical and unary syntactic rules allows such restrictions to be naturally maintained in the lexicon. Secondly, within theories like HPSG, which utilize constraint logics over (typed) feature structures ((T)FSs) as the lexical and grammatical representation language, the formal status of lexical rules is unclear. They do not have a straightforward interpretation as logical constraints and are normally treated as metalevel conditional generalizations concerning the set of admissible lexical entries. This leads to immediate disadvantages, such as nondeclarativity, potential nontermination in application, and the need for the grammar writer to specify what stays unchanged as well as what changes in a derived entry. Our approach to lexical rules improves this situation by formalizing them in terms of default unification utilizing existing operations in the typed default feature structure (TDFS) representation language (Lascarides et al. 1995; Lascarides and Copestake 1999).</Paragraph>
    <Paragraph position="3"> Thirdly, most lexical, though not unary, rules are semiproductive. In HPSG, lexical rules are interpreted as generative rules encoding putatively exceptionless conditional generalizations concerning the existence of derived lexical entries. Exceptions and irregularities must be marked explicitly in lexical entries. While this approach is defensible for rules of inflectional morphology, generalizations about unbounded dependency constructions and adjunct introduction, it is less plausible when we come to consider morphological rules of derivation or most verb diathesis alternations. These latter are semiproductive; that is, subject to blocking (preemption by synonymy or by lexical form), to arbitrary lexical gaps, and to varying degrees of conventionalization (see Jackendoff \[1997a\] for a recent discussion). It is technically possible to reinterpret (some) lexical rules as (lexical) redundancy rules using constraint-based techniques (e.g., Sanfilippo 1993). However, this approach reduces lexical rules to a purely abbreviatory device even more thoroughly than Jackendoff's (1975) original proposal. We will argue in Section 7 that the pure redundancy rule interpretation is not optimal, even for semiproductive lexical rules, as such rules are utilized in the production and interpretation of nonce usages and neologisms.</Paragraph>
    <Paragraph position="4"> Throughout the paper, we assume a linguistic framework based on typed feature structures like HPSG, but allowing for defeasible specification in typed default feature structures (e.g., Lascarides et al. 1995). We distinguish between lexical rules and other unary rules and present an account of lexical rules compatible with this framework and, potentially, with other constraint-based (T)FS frameworks. We argue that this account satisfactorily addresses the issues of generative power, formal interpretation, and semiproductivity. In Section 2 we discuss the use and interpretation of HPSG-style lexical rules in more detail. In Section 3 we present the TDFS framework for lexical and grammatical representation, which extends monotonic theories of lexical organization with default inheritance and defeasible specification. In Section 4, we formalize lexical rules in terms of default unification and demonstrate that this leads to a more restricted operation fully defined in terms of the nonmonotonic conditional logic of TDFSs. In Section 5 we show that, despite this restricted capacity, a linguistically insightful account of English dative constructions can be formulated, which treats them as (mostly) deri, ed by lexical rule. This draws on insights from Dowty's (1989) theory  Abbreviated form of the Third Singular Verb Formation lexical rule.</Paragraph>
    <Paragraph position="5"> of proto-roles, Sanfilippo's (1990, 1992, 1993) treatment of verb alternations in UCG (Zeevat, Klein, and Calder 1987) and Goldberg's (1995) analysis in Construction Grammar. In Section 6 we argue that the dative alternation is a semiproductive process in English not fully reducible to an abbreviatory convention, and provide an account of lexical rule application within a probabilistic version of the TDFS framework that captures the variable acceptability of different verbs in the dative construction. Thus, we modify and extend the analysis of dative in Lascarides et al. (1995) by providing a more adequate and restrictive formalization of this type of semiproductive lexical rule. In Section 7 we consider the extent to which our approach to lexical rules will generalize to other types of putatively lexical processes.</Paragraph>
  </Section>
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