Generating from a Deep Structure

1 Introduct ion not derivable under G. Representa t ions tha t cannot be der ived under a g r ammar G are said to be noncanonical with respect to G. In this paper, we present a generat ion a lgor i thm for Unification Categoria l G r a m m a r [6] ( , c a ) which addresses the problem raised by non-canonicM input (section 2 and 3). An interest ing upshot of the s t ra tegy we propose is that it allows :['or language independent generat ion. Section 4 i l lustrates this point by considering how, s tar t ing from one semantic representa t ion, two sentences can be generated: one in English and one in French. Section 5 relates our work to previous proposals by Van Noord and Shieber. Two major requirements on a genera tor is that it be correct and complete. A generator is said to be correct if given two semant ic representat ions R1 and R.~ which are not semant ical ly equivalent, R1 and R2 do not generate the same string. A generator is said to be complete if any two senmn tically equivalent representat ions generate the same set of strings. An obvious case of incompleteness occurs when the generator fails to t e rmina te on some well-defined input. Ano ther less obvious cause for incompleteness can be explMned as follows. Consider a g rammar G and its associated semant ic representat ion language L. It is often the case that syntact ical ly different strings of L will have equivalent semantics. A simple case in point is the semantic equivalence holding between ¢ A ¢ and ¢ A ¢ in e.g. proposi t ional logic. On the other hand, it is also often the case tha t the same g r ammar G will not derive for a given string all the formulae which may represent its meaning. From the point of view of generat ion, this means that given two semanticMly equivalent representat ions R1 and R2 there is always a possibility that R1 generates a s t r ing S but that R2 doesn ' t because R2 is *The work reported here has been carried out ,as part of the ESPRIT project P393 ACORD on "The Construction and Interrogation of Knowledge-B~es using Natural Language Text and Graphics". It is the result of joint work with Michael Reape of the Center for Cognitive Science, University of Edinburgh (Scotland, UK). 2 Generat ing from a deep structure It is somet imes the case that a g r ammar will assign to a string several possible der ivat ions with equivalent sementies. This phenomena is par t icular ly acute in categorial g rammars [2] and is referred to in the l i tera ture as that of spurious ambiguity. In g rammars where the semantics is buil t by unification, the syntac t ic differences holding between these equivalent semantics resides in the relat ive ordering of the subformulae within the formula. Tha t is, there is a direct relat ionship between the syntact ic shape of a semantic formula and the der ivat ional history of the corresponding string. Consequently, a given formula will be non-canonk:al wrt to a par t icular g rammar G if the relat ive sequencing of its subformulae does not reflect a possible der ivat ion in C . Hence, to allow for generat ion from non-canonical input , we need to abs t rac t away from the der ivat ional informat ion reflected in the l inear ordering of the input formula. Three major a l ternat ives come to mind. First , we could try to generate all sentences whose semantics are logically equivalent to the input semantics. In uc(~, this means tha t generat ion is carried out with the two addi t ional logical axioms of associativity and commuta t iv i ty . However, this solution produces a search space factorial in the number of conjunct ion s and must thus be rejected as computa t iona l ly intractable .