Coordination in an Axiomatic Grammar

For some time there has been interest in the idea of parsing as deduction. Here we present a grammat i cal tbrmalism, 'Axiomatic G r a m m a r ' , which is based upon a small number of linguistically motivated ax-toms and deduction rules. Each axiom or rule combines a 'category ' with a string of words to form a further category. This contrasts with the usual 'trees t ructure ' approach to syntactic analysis where consti tuents are combined with each other to form a further constituent. We describe a g rammar for English which has a good coverage of 'non-consti tuent ' coordination. The g rammar has been integrated with a toy semantics, and has been implemented in a left-toright parser with incremental semantic interpretation. The parser does not suffer fi'om spurious ambiguity. I I n t r o d u c t i o n Coordi:uation is a particularly troublesome phenomenon to account for in theories of syntax based upon phrase structure rules. Acceptable examples of 'non-const i tuent ' coordination such as: (1) Jolhn gave Mary a book and Peter a paper (2) Ben likes and Fred admires Mary have led some to abandon a single level of grammatical description, and others to abandon phrase structure rules. An example of the former approach is Modifier Structure G r a m m a r (Dahl and McCord, 1983), which was justified as tbllows: ... it appears that a proper and general t reatment must recognise coordination as a "metagrmnmatieal ' construction, in the sense that metarules, general system operations, or 'second-pass' operations such as t ransformations, are needed for its formulation. Modifier Structure G r a m m a r embeds its rules for coordination into the parsing algorithm (there are close *This research was supported by an SE[IC resem'ch studentship. parallels with the SYSCONJ system (Woods, 1973)). In order to parse sentence (2), the state of the parser at the point immediately before 'Fred' is matched to the state immediately before 'Ben'. 'Fred admires' is then parsed, and the resulting state is merged with the state after parsing 'lien likes'. The alternative approach to dealing with coordination uses a single level of grammatical description, but uses a weaker notion of constituency than phrase structure grammar . It is presently exemplified by proposals to extend Categorial G r a m m a r with Forward Composition, the Product operator, Subject Type-Raising etc. Categorial Grammar , just like phrase structure grammar , is based upon the combination of one or more constituents to form a further constituent. In order to deal with coordination, the category ( X \ X ) / X 1 is assigned to the conjunction, or, n ] o r e usually, a phrase structure rule is invoked of the form: