Restriction and Verbal Complexes in LFG - A Case Study for Danish

level of representation and permits grammaticality—as in usual LFG—to bedetermined on the phrasal and functional level of representation.A final note about the basic formal properties of the approaches. For traditional LFGgrammars (satisfying the Nonbranching Dominance Condition) the parsing problem isdecidable, since a grammar can assign to a string only a finite number of valid deriva-tions which guarantees the composition of the (decidable) context-free parsing and the(decidable) constraint satisfaction problem to be finitely bounded by the sentence length.Because of the decidability of the satisfiability problem for descriptions containing pro-jection and/or restriction constraints, decidability of the parsing problem follows for allthese extensions too.With respect to generation, however, the matter is different. We have seen that therestriction operator permits it to remove information when this information is assumedto be irrelevant for the f-structures finally assigned to the sentences. Thereby, it producesfloating structures that are not considered to be part of the actual f-structures. Since theinputs to the generator do not include the floating structures produced by restriction, gen-eration is here affected by the same problems as they arise in projection architectures.These assume only the f-structures, but not the complete fand m-structure configura-tions derived by the grammar to be given to the generator and depend thus also on theassumption that the inputs to the generator are underspecified.Unfortunately, the problem of whether or not there are any strings associated withan underspecified input structure had been shown to be undecidable in general (see, forexample, Wedekind 1999). Since there is in general no structural relation between the(underspecified) inputs and the fully specified structures, it is in principle possible torestrict/project off structures whose size is not bounded by the size of the actual inputf-structures. And this permits the computation of some in general undecidable problemsto be encoded in the structures restricted/projected off the f-structures.However, for auxiliary constructions we have seen that the depth of the required DEPembeddings is always finitely bounded (up to three or four, depending on the language),so that at least for grammars analyzing those particular constructions by restriction orprojection decidability of the generation problem can still be established.AcknowledgmentsMost of the research described here was supported by The Nordic Council of Ministers. We are indebted toMary Dalrymple, Helge Dyvik, Ron Kaplan, John Maxwell and Victoria Rosén for many helpfuldiscussions. In addition, we would like to acknowledge the Palo Alto Research Center for supporting ourgrammar development by equipping us with the XLE platform. Special thanks go to John Maxwell forimplementing the restriction operator and suggesting syntactic rules for passivization.ReferencesButt, M., M. E. Niño, and F. Segond. 1996. Multilingual Processing of Auxiliaries in LFG. In D. Gibbon,editor, Natural Language Processing and Speech Technology: Results of the 3rd KONVENS Conference.Bielefeld, pages 111–122.Butt, M., T. Holloway King, M. E. Niño, and F. Segond. 1999. A Grammar Writer’s Cookbook. CSLIPublications, Stanford, CA.Dyvik, H. 1999. The Universality of f-Structure: Discovery or Stipulation? The Case of Modals. In M. Buttand T. Holloway King, editors, The Proceedings of the LFG ’99 Conference. University of Manchester.Engdahl, E. 1999. The Choice between bli-Passive and s-Passive in Danish, Norwegian and Swedish.NORDSEM Report 3, Göteborg University.