@article{LambersOrejas2021,
  author    = {Lambers, Leen and Orejas, Fernando},
  title     = {Transformation rules with nested application conditions},
  series = {Theoretical computer science},
  volume    = {884},
  journal   = {Theoretical computer science},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3975},
  doi       = {10.1016/j.tcs.2021.07.023},
  pages     = {44 -- 67},
  year      = {2021},
  abstract  = {Recently, initial conflicts were introduced in the framework of M-adhesive categories as an important optimization of critical pairs. In particular, they represent a proper subset such that each conflict is represented in a minimal context by a unique initial one. The theory of critical pairs has been extended in the framework of M-adhesive categories to rules with nested application conditions (ACs), restricting the applicability of a rule and generalizing the well-known negative application conditions. A notion of initial conflicts for rules with ACs does not exist yet. In this paper, on the one hand, we extend the theory of initial conflicts in the framework of M-adhesive categories to transformation rules with ACs. They represent a proper subset again of critical pairs for rules with ACs, and represent each conflict in a minimal context uniquely. They are moreover symbolic because we can show that in general no finite and complete set of conflicts for rules with ACs exists. On the other hand, we show that critical pairs are minimally M-complete, whereas initial conflicts are minimally complete. Finally, we introduce important special cases of rules with ACs for which we can obtain finite, minimally (M-)complete sets of conflicts.},
  language  = {en}
}
@article{NavarroOrejasPinoetal.2021,
  author    = {Navarro, Marisa and Orejas, Fernando and Pino, Elvira and Lambers, Leen},
  title     = {A navigational logic for reasoning about graph properties},
  series = {Journal of logical and algebraic methods in programming},
  volume    = {118},
  journal   = {Journal of logical and algebraic methods in programming},
  publisher = {Elsevier Science},
  address   = {Amsterdam [u.a.]},
  issn      = {2352-2208},
  doi       = {10.1016/j.jlamp.2020.100616},
  pages     = {33},
  year      = {2021},
  abstract  = {Graphs play an important role in many areas of Computer Science. In particular, our work is motivated by model-driven software development and by graph databases. For this reason, it is very important to have the means to express and to reason about the properties that a given graph may satisfy. With this aim, in this paper we present a visual logic that allows us to describe graph properties, including navigational properties, i.e., properties about the paths in a graph. The logic is equipped with a deductive tableau method that we have proved to be sound and complete.},
  language  = {en}
}
@article{SchneiderLambersOrejas2021,
  author    = {Schneider, Sven and Lambers, Leen and Orejas, Fernando},
  title     = {A logic-based incremental approach to graph repair featuring delta preservation},
  series = {International journal on software tools for technology transfer : STTT},
  volume    = {23},
  journal   = {International journal on software tools for technology transfer : STTT},
  number    = {3},
  publisher = {Springer},
  address   = {Berlin ; Heidelberg},
  issn      = {1433-2779},
  doi       = {10.1007/s10009-020-00584-x},
  pages     = {369 -- 410},
  year      = {2021},
  abstract  = {We introduce a logic-based incremental approach to graph repair, generating a sound and complete (upon termination) overview of least-changing graph repairs from which a user may select a graph repair based on non-formalized further requirements. This incremental approach features delta preservation as it allows to restrict the generation of graph repairs to delta-preserving graph repairs, which do not revert the additions and deletions of the most recent consistency-violating graph update. We specify consistency of graphs using the logic of nested graph conditions, which is equivalent to first-order logic on graphs. Technically, the incremental approach encodes if and how the graph under repair satisfies a graph condition using the novel data structure of satisfaction trees, which are adapted incrementally according to the graph updates applied. In addition to the incremental approach, we also present two state-based graph repair algorithms, which restore consistency of a graph independent of the most recent graph update and which generate additional graph repairs using a global perspective on the graph under repair. We evaluate the developed algorithms using our prototypical implementation in the tool AutoGraph and illustrate our incremental approach using a case study from the graph database domain.},
  language  = {en}
}