Reasoning in Combinations of TheoriesCarsten IhlemannDissertationzur Erlangung des Grades desDoktors der Naturwissenschaftender Naturwissenschaftlich-Technischen Fakult¨atender Universit¨at des SaarlandesSaarbru¨cken2010Tag des Kolloquiums: 25. August 2010Dekan: Prof. Dr. Holger HermannsPru¨fungsausschussVorsitzender: Prof. Dr. Gert SmolkaBerichterstattende: PD Dr. Viorica Sofronie-StokkermansProf. Dr. Bernd FinkbeinerProf. Dr. Silvio Ghilardi, MailandAkademischer Mitarbeiter: Dr. Thomas HillenbrandMeinen Eltern gewidmetAcknowledgementsI am grateful to a number of people for their contribution to this dissertation.First of all I would like to thank my advisor Viorica Sofronie-Stokkermansfor her scientific and personal support. Without her unstinting encourage-ment and advice this thesis would not have been possible. Over the years Ihave become a better mathematician under her guidance.Many thanks also to Christoph Weidenbach for creating an environmentconducive to research, to Bernd Finkbeiner and Silvio Ghilardi for agreeingto be on the reading committee and to my colleagues Thomas Hillenbrandand Swen Jacobs for fruitful discussions.My personal thanks go foremost to my parents for everything they havedone for me.Many thanks also to my friends Annette Soelter, Frank Quante, KeithBecker (in order of appearance) and my sister Caren for sustaining methrough the process.