This volume contains work on the decision problem done inKazan (Russia), Tallinn (Estonia), and Vienna (Austria). Theauthors met several times to discuss and exchange theirresults and finally decided to write this monographtogether. Besides a unified treatment of previouslypublished results there are many new results first presentedin this volume.The monograph opens with an introduction and a chapter onterminology, 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.