Polarized unification grammar (PUG) is a linguistic formalism which uses polarities to better control the way grammar fragments interact. The grammar combination operation of PUG was conjectured to be associative. We show that PUG grammar combination is not associative, and even attaching polarities to objects does not make it order-independent. Moreover, we prove that no non-trivial polarity system exists for which grammar combination is associative. We then redefine the grammar combination operator, moving to the powerset domain, in a way that guarantees associativity. The method we propose is general and is applicable to a variety of tree-based grammar formalisms.
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Acknowledgements This research was supported by The Israel Science Foundation (grant no. 136/01). We are grateful to Yannick Parmentier for his help and support, including very useful comments on earlier versions of this paper. We wish to thank Claire Gardent for giving us the opportunity to present some of these results at the XMG Workshop in LORIA Nancy in 2007. We also benefited from constructive comments by three anonymous referees. All remaining errors and misconceptions are, of course, our own.
- Grammar combination
- Grammatical formalisms
- Polarized unification grammar
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Linguistics and Language