Applying Lexical Rules Under Subsumption

Lexical rules are used in constraintbased g rammar formalisms such as llead-Driven l)hrase Structure Gram m ar ( I IPSG) (Pollard and Sag 1994) to express generalizations atnong lexical entries. '['his paper discusses a number of lexical rules from recent I[PSG analyses of German (tlinri<;hs and Nakazawa 1994) and shows that the g r am m ar in some cases vastly overgenerates and in other cases introduces massive spurious structural ambiguity, if lexical rules ap: ply under unification. Such l)rot)lems of overgeneration or spurious ambiguity do not arise, if a lexical rule al)plies to a given lexical ent;ry iff the lexical entry is subsumed by the left:hand side of the lexical rule. I,'inally, the paper discusses computat ional consequcnce~s of at)plying lexical rules under subsuml)tion. 1 I n t r o d u c t i o n Current linguistic theories place an increasing amount of grammatical information in the lexicon and employ a variety of mechanisms to express generalizations across lexical entries: templates (Flickinger 1987, Shieber 1986), inheritance hierarchies (Flickinger 1987, Pollard and Sag 11994), and lexical rules (Bresnan 1982, I)owty 1982, Gazd a r e t al. 1985, Pollard and Sag 1994). Lexical rules (henceibrth: LRs) have been subjected to particularly close s<:rutiny. 'Fhis research has tbcused on two important issues: 1. how the use of LRs affects the generative power of g rammar formalisms and the computat ional complexity of parsing algorithms (Uszkoreit and Peters 1986, Carpenter 1991), and 2. how to provide a denotational semantics for LRs (Calcagno and PoP lard 1995, Meurers 1995). In this paper we address neither of these two issues. Instead we will concentrate on a question that we cro cess LRs in a coml)utational system for I IPSG. Itowever, as discussed in section 6, it is worth noting that the subsumption test for I,l{ application <'.an be integrated straightforwardly into two recent proposals by van Noord and Bouma (:1994) and by Meurers and Minnen (1995) of how to implement l a b in a processing system for HPSG. l'Fhis paper will not provide a formal definition of subsumption or nnificiation for typed feature structures. Instead, we refer the reader to the standard definitions of Kasper and Rounds (1986) and Carpentel: (1992), among many <)tilers. Informally speaking, two feature structures are unifiable itf they do not cont ab incompatible information. One feature structure subsumes another iff the intormation contained in the former is less specific than in the latter.