Modeling structured objects by labellings on graphs I / II Tutorial Boris Flach Abstract: We introduce a formalism describing sets of graph labellings by means of local conjunctive predicates. This formalism might be seen as a generalization of regular string grammars. We discuss the computational problems arising in this framework in the context of sharp, fuzzy and statistical recognition and give an unified formulation. In the second part of the tutorial we present subclasses of these problems, which can be solved with polynomial time complexity.