True Parallel Graph Transformations: an Algebraic Approach Based on Weak Spans

We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the form $L\xleftarrow{l}K \xleftarrow{i} I \xrightarrow{r} R$, called weak spans. A parallel coherent transformation is introduced and shown to be a conservative extension of the interleaving semantics of parallel independent direct transformations. A categorical construction of finitely attributed structures is proposed, in which parallel coherent transformations can be built in a natural way. These notions are introduced and illustrated on detailed examples.

SROIQsigma is decidable

We consider a dynamic extension of the description logic $\mathcal{SROIQ}$. This means that interpretations could evolve thanks to some actions such as addition and/or deletion of an element (respectively, a pair of elements) of a concept (respectively, of a role). The obtained logic is called $\mathcal{SROIQ}$ with explicit substitutions and is written $\mathcal{SROIQ^\sigma}$. Substitution is not treated as meta-operation that is carried out immediately, but the operation of substitution may be delayed, so that sub-formulae of $\mathcal{SROIQ}^\sigma$ are of the form $\Phi\sigma$, where $\Phi$ is a $\mathcal{SROIQ}$ formula and $\sigma$ is a substitution which encodes changes of concepts and roles. In this paper, we particularly prove that the satisfiability problem of $\mathcal{SROIQ}^\sigma$ is decidable.