This volume contains work on the decision problem done in Kazan (Russia), Tallinn (Estonia), and Vienna (Austria). The authors met several times to discuss and exchange their results and finally decided to write this monograph together. Besides a unified treatment of previously published results there are many new results first presented in this volume. The monograph opens with an introduction and a chapter on terminology, followed by chapters on: - Semantic clash resolution as decision procedure, - Completeness of ordering refinements, - Semantic tree based resolution variants, - Deciding the class K by an ordering refinement, - A resolution based method for building finite models. A final chapter on applications completes the volume.