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

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 local graph extension grammars.

Generating Semantic Graph Corpora with Graph Expansion Grammar

“…• In this paper, context nodes can be mapped to arbitrary nodes in the argument graph of a graph expansion operation, provided that labels match. In [7], admissible mappings are specified by counting monadic second-order logic, which is a much more powerful mechanism not yet implemented in LOVELACE. • Finally, we do not make use of the mechanism of cloning context nodes.…”

“…Note that the process of identifying docks of Φ with ports of the argument graph G may merge ports of G if dock contains repetitions. The expansion operations defined here are thus more general than those in [7]. In fact, readers familiar with hyperedge replacement grammars will easily be able to see that this allows us to simulate hyperedge replacement.…”

“…Further deviations from [7] are that the definition above does not make use of the cloning of context nodes, and that the logic formula that determines which mappings of context nodes to nodes in the argument graph are allowed has been replaced by the much simpler condition that node labels must match. The cloning ability is not needed here since we consider expansion operations rather than the special case of extension operations as in [7] (see below), which means that cloning can be implemented by repeated application of expansion. The latter has been dropped in the current paper for simplicity, and because it is not yet implemented in LOVELACE anyway.…”

“…To address these problems, we provide the software LOVELACE 2 that generates well-formed graphs with respect to a graph expansion grammar (GEG) [7]. GEGs are hyperedge replacement grammars [5,10,8] that have been extended by a type of contextual rules inspired by [9].…”

“…Assuming that a given subterm has already been evaluated to a graph, which will become a subgraph of the generated graph, the evaluation of an operation on top of it adds new nodes with edges pointing to already existing nodes of the subgraph. In [7], the placement of these edges can be restricted by a formula in counting monadic second-order logic. LOVELACE does not currently make use of such a powerful mechanism, which we leave for future extensions.…”