Unifying Parallels

Unifying Parallels Claire Gardent Computational Linguistics University of the Saarland Saarbriicken, Germany claire0coli, uni-sb, de Abstract I show that the equational treatment of ellipsis proposed in (Dalrymple et al., 1991) can further be viewed as modeling the effect of parallelism on semantic interpretation. I illustrate this claim by showing that the account straightfor- wardly extends to a general treatment of sloppy identity on the one hand, and to deaccented foci on the other. I also briefly discuss the results obtained in a prototype implementation. 1 Introduction (Dalrymple et al., 1991; Shieber et al., 1996) (henceforth DSP) present a treatment of VP- ellipsis which can be sketched as follows. An el- liptical construction involves two phrases (usu- ally clauses) which are in some sense struc- turally parallel. Whereas the first clause (we refer to it as the source) is semantically com- plete, the second (or target) clause is missing semantic material which can be recovered from the source. Formally the analysis consists of two com- ponents: the representation of the overall dis- course (i.e. source and target clauses) and an equation which permits recovering the missing semantics. I Representation Equation I S A R(T1, • • •, Tn) R(S1,..., Sn) = S I S is the semantic representation of the source, $1,..., Sn and T1,... ,Tn are the semantic rep- resentations of the parallel elements in the source and target respectively and R represents the relation to be recovered. The equation is solved using Higher-Order Unification (HOU): Given any solvable equation M = N, HOU yields a substitution of terms for free variables that makes M and N equal in the theory of a/~v-identity. The following example illustrates the work- ings of this analysis: (1) Jon likes Sarah and Peter does too. In this case the semantic representation and the equation associated with the overall discourse ar e: Equation R(j) = like(j,s) For this equation, HOU yields the substitution1: {R x.like(x,s)} and as a result, the resolved semantics of the target is: Ax.like(x, s)(p) - like(p, s) The DSP approach has become very influen- tial in computational linguistics for two main reasons. First, it accounts for a wide range of observations concerning the interaction of VP- ellipsis, quantification and anaphora. Second, it bases semantic construction on a tool, HOU, which is both theoretically and computationally attractive. Theoretically, HOU is well-defined and well-understood - this permits a clear un- derstanding of both the limitations and the pre- dictions of the approach. Computationally, it has both a declarative and a procedural inter- pretation - this supports both transparency and implementation. 1As (Dalrymple et al., 1991) themselves observe, HOU also yields other, linguistically invalid, solutions. For a proposal on how to solve this over-generation prob- lem, see (Gardent and Kohlhase, 1996b; Gardent et al., 1999). 49 In this paper, I start (section 2) by clari- fying the relationship between DSP's proposal and the semantic representation of discourse anaphors. In section 3 and 4, I then show that the HOU-treatment of ellipsis naturally extends to …

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