Concept formation using graph grammars

2009

Many graph mining tasks involve search over languages of graphs. Several approaches to generate graphs exist, but for some applications, however, it is desirable to constrain the search and only consider a subclass of all graphs. For this, the use of language bias has been considered, eg in the field of inductive logic programming. In the context of graph mining, one would expect of a similar general language bias mechanism that it allows one to specify many different classes of graphs in a declarative way.

Theoretical Computer Science, 1982

The proposed transformation module performs mapping be-tween two di®erent knowledge representation forms used in grammar induction systems. The kernel knowledge representation form is a special predicate centered conceptual graph called ECG. The ECG provides a semantic-based, language independent description of the environment. The other base representation form is some kind of language. The sentences of the language should meet the corresponding grammatical rules. The pilot project demonstrates the functionality of a translator module using this transformation engine between the ECG graph and the Hungarian language.

Fundamenta Informaticae, 2016

Though graph grammars have been widely investigated for 40 years, few learning results exist for them. The main reasons come from complexity issues that are inherent when graphs, and a fortiori graph grammars, are considered. The picture is however different if one considers drawings of graphs, rather than the graphs themselves. E.g., it has recently been proved that the isomorphism and pattern searching problems could be solved in polynomial time for plane graphs, that is, planar embedding of planar graphs. In this paper, we introduce the Plane Graph Grammars (PGG) and detail how they differ to usual graph grammar formalisms while at the same time they share important properties with string context-free grammars. In particular, the parsing of a graph with a given PGG is polynomial for languages with appropriate restrictions. We demonstrate that PGG are well-shaped for learning: we show how recent results on string grammars can be extended to PGG by providing a learning algorithm that identifies in the limit the class of substitutable plane graph languages. Our algorithm runs in polynomial time assuming the same restriction used for polynomial parsing, and the amount of data needed for convergence is comparable to the one required in the case of strings.

this document. This thesis would not have been possible without the help of drs. Frits Vereijken and

Proceedings of the 2006 SIAM International Conference on Data Mining, 2006

In this paper we describe an approach to learning node replacement graph grammars. This approach is based on previous research in frequent isomorphic subgraphs discovery. We extend the search for frequent subgraphs by checking for overlap among the instances of the subgraphs in the input graph. If subgraphs overlap by one node we propose a node replacement grammar production. We also can infer a hierarchy of productions by compressing portions of a graph described by a production and then infer new productions on the compressed graph. We validate this approach in experiments where we generate graphs from known grammars and measure how well our system infers the original grammar from the generated graph.

International Journal on Artificial Intelligence Tools, 2008

We describe an algorithm and experiments for inference of edge replacement graph grammars. This method generates candidate recursive graph grammar productions based on isomorphic subgraphs which overlap by two nodes. If there is no edge between the two overlapping nodes, the method generates a recursive graph grammar production with a virtual edge. We guide the search for the graph grammar based on the size of the grammar and the portion of the graph described by the grammar. We show experiments where we generate graphs from known graph grammars, use our method to infer the grammar from the generated graphs, and then measure the error between the original and inferred grammars. Experiments show that the method performs well on several types of grammars, and specifically that error decreases with increased numbers of unique labels in the graph.

1997

Abstract. Object Grammars define mappings between text and object graphs. Parsing recognizes syntactic features and creates the corresponding object structure. In the reverse direction, formatting recognizes object graph features and generates an appropriate textual presentation. The key to Object Grammars is the expressive power of the mapping, which decouples the syntactic structure from the graph structure.

Taxonomies play a central role in conceptual domain modeling having a direct impact in areas such as knowledge representation, ontology engineering, software engineering, as well as in knowledge organization in information sciences. Despite their key role, there is in the literature little guidance on how to build high-quality taxonomies, with notable exceptions such as the OntoClean methodology, and the ontology-driven conceptual modeling language OntoUML. These techniques take into account the ontological meta-properties of types to establish well-founded rules for forming taxonomic structures. In this paper, we show how to leverage on the formal rules underlying these techniques to build taxonomies which are correct by construction. We define a set of correctness-preserving operations to systematically introduce types and subtyping relations into taxonomic structures. To validate our proposal, we formalize these operations as a graph grammar. Moreover, to demonstrate our claim of correctness by construction , we use automatic verification techniques over the grammar language to show that: (i) all taxonomies produced by the grammar rules are correct; and (ii) the rules can generate all correct taxonomies.