Since the early days of theorem proving and inductive logic programming several θ-subsumption algorithms have been developed. Recently, the focus came back to θ-subsumption due to its relevance in planning within first-order Markov Decision Processes. More than one formalism has been adopted to describe the language and the algorithms. Many experimental evaluations have been performed, but all focusing only on some algorithms and a particular domain. In this thesis, we will present the most popular θ-subsumption algorithms within a unified framework for a fair comparison. Further, we will describe the domains in which θsubsumption is used and present a huge experimental evaluation on data from these domains. In addition, we give arguments for which algorithm is best suited depending on some basic parameters. 2 Acknowledgment

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