Generation and Polynomial Parsing of Graph Languages with Non-Structural Reentrancies

Authors

Abstract

Graph-based semantic representations are popular in natural language processing (NLP), where it is often convenient to model linguistic concepts as nodes and relations as edges between them. Several attempts have been made to find a generative device that is sufficiently powerful to describe languages of semantic graphs, while at the same allowing efficient parsing. We contribute to this line of work by introducing graph extension grammar, a variant of the contextual hyperedge replacement grammars proposed by Hoffmann et al. Contextual hyperedge replacement can generate graphs with non-structural reentrancies, a type of node-sharing that is very common in formalisms such as abstract meaning representation, but which context-free types of graph grammars cannot model. To provide our formalism with a way to place reentrancies in a linguistically meaningful way, we endow rules with logical formulas in counting monadic second-order logic. We then present a parsing algorithm and show as our main result that this algorithm runs in polynomial time on graph languages generated by a subclass of our grammars, the so-called edge-agnostic graph extension grammars.

Author Biographies

  • Johanna Björklund, Umeå University
    Senior Lecturer, Dept. Computing Science
  • Frank Drewes, Umeå University
    Professor, Dept. Computing Science
  • Anna Jonsson, Umeå University
    Postdoc, Umeå University

Published

2024-11-14