@inproceedings{wittenburg-1993-adventures,
    title = "Adventures in Multi-dimensional Parsing: Cycles and Disorders",
    author = "Wittenburg, Kent",
    editor = "Bunt, Harry  and
      Berwick, Robert  and
      Church, Ken  and
      Joshi, Aravind  and
      Kaplan, Ronald  and
      Kay, Martin  and
      Lang, Bernard  and
      Nagao, Makoto  and
      Nijholt, Anton  and
      Steedman, Mark  and
      Thompson, Henry  and
      Tomita, Masaru  and
      Vijay-Shanker, K.  and
      Wilks, Yorick  and
      Wittenburg, Kent",
    booktitle = "Proceedings of the Third International Workshop on Parsing Technologies",
    month = aug # " 10-13",
    year = "1993",
    address = "Tilburg, Netherlands and Durbuy, Belgium",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-emnlp/1993.iwpt-1.26/",
    pages = "333--348",
    abstract = "Among the proposals for multidimensional grammars is a family of constraint-based grammatical frameworks, including Relational Grammars. In Relational languages, expressions are formally defined as a set of relations whose tuples are taken from an indexed set of symbols. Both bottom-up parsing and Earley-style parsing algorithms have previously been proposed for different classes of Relational languages. The Relational language class for Earley style parsing in Wittenburg (1992a) requires that each relation be a partial order. However, in some real-world domains, the relations do not naturally conform to these restrictions. In this paper I discuss motivations and methods for predictive, Earley-style parsing of multidimensional languages when the relations involved do not necessarily yield an ordering, e.g., when the relations are symmetric and/or nontransitive. The solution involves guaranteeing that a single initial start position for parsing can be associated with any member of the input set. The domains in which these issues are discussed involve incremental parsing in interfaces and off-line verification of multidimensional data."
}