A Tutorial on Graph Transformation

Abstract

Graph transformation or graph rewriting has been developed for nearly 50 years and has become a mature and manifold formal technique. Basically, rewrite rules are used to manipulate graphs. These rules are given by a left-hand side and a right-hand side graph and the application comprises matching the left-hand side and replacing it with the right-hand side of the rule. In this contribution we give a tutorial on graph transformation that explains the so-called double-pushout approach to graph transformation in a rigorous, but non-categorical way, using a gluing construction. We explicate the definitions with several small examples. We also introduce attributes and attributed graph transformation in a lightweight form. The paper is concluded by a more extensive example on a leader election protocol, the description of tool support and pointers to related work.

Applications of the Metadata Standards

“…that which is evaluated by an assertion is an "object" in the sense of Peircean semiotics; this is a context-sensitive rule, since the relabelling of the vertex (individual) is contingent on one of the edges, namely, an incoming edge with the label vivo:evaluates. Beyond this, more complex graph transformation rules [40] can be applied in the case that the transformation goes beyond relabelling, i.e. if vertices or edges in the knowledge graph need to be eliminated or created by applying m : n property chain correspondences [38].…”

Reliable and interoperable computational molecular engineering: 2. Semantic interoperability based on the European Materials and Modelling Ontology

“…3. In more expressive logics, e.g., first-order logic or description logics that extend OWL DL [5], or by rewriting rules constituting, e.g., a graph transformation system [24]. While these formalisms are undecidable in general, their particular application to the OMP might restrict formulae and rules in a way that keeps them decidable and tractable computationally; this will be addressed by future work, since as discussed below, OWL DL is insufficient to capture a number of typical and relevant cases.…”

“…( 12), from i = 10, expresses the rule that "if :X osmo:has aspect paradigmatic content :Y, where :X is a osmo:materials relation and :Y is a evmpo:material, then there is an individual :Z such that :Y emmo-models:has model :Z and :Z emmo-mereotopology:has proper part :X." Statements like these can easily be formulated in first-order logic, extensions of OWL DL by additional operators (see above), or by graph transformation systems [24] which would apply to graph representations of the scenarios (see the Appendix).…”

Creating and Maintaining Ifc–citygml Conversion Rules

“…Graph transformation (or graph grammar) is a well-known approach applicable to a range of problems in the software engineering domain where the problems can be represented as graph structures, see e.g. König et al (2018) for an introduction. Ehrig et al (2006) have worked out a seminal theory of algebraic graph transformation and also applied it to model transformation and integration problems Ehrig et al (2015).…”