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In automated theorem proving, there are some problems that need information on the inequality of certain constants. In most cases this information is provided by adding facts which explicitly state that two constants are unequal. Depending on the number of constants, a huge amount of this facts can clutter the knowledge base and distract the author and readers of the problem from its actual proposition. For most cases it is save to assume that a larger knowledge base reduces the performance of a theorem prover, which is another drawback of explicit inequality facts. Using the unique name assumption in those reasoning tasks renders the introduction of inequality facts obsolete as the unique name assumptions states that two constants are identical iff their interpretation is identical. Implicit handling of non-identical constants makes the problems easier to comprehend and reduces the execution time of reasoning. In this thesis we will show how to integrate the unique name assumption into the E-hyper tableau calculus and that the modified calculus is sound and complete. The calculus will be implemented into the E-KRHyper theorem prover and we will show, by empiric evaluation, that the changed implementation, which is able to use the unique name assumption, is superior to the traditional version of E-KRHyper.

This dissertation investigates the usage of theorem provers in automated question answering (QA). QA systems attempt to compute correct answers for questions phrased in a natural language. Commonly they utilize a multitude of methods from computational linguistics and knowledge representation to process the questions and to obtain the answers from extensive knowledge bases. These methods are often syntax-based, and they cannot derive implicit knowledge. Automated theorem provers (ATP) on the other hand can compute logical derivations with millions of inference steps. By integrating a prover into a QA system this reasoning strength could be harnessed to deduce new knowledge from the facts in the knowledge base and thereby improve the QA capabilities. This involves challenges in that the contrary approaches of QA and automated reasoning must be combined: QA methods normally aim for speed and robustness to obtain useful results even from incomplete of faulty data, whereas ATP systems employ logical calculi to derive unambiguous and rigorous proofs. The latter approach is difficult to reconcile with the quantity and the quality of the knowledge bases in QA. The dissertation describes modifications to ATP systems in order to overcome these obstacles. The central example is the theorem prover E-KRHyper which was developed by the author at the Universität Koblenz-Landau. As part of the research work for this dissertation E-KRHyper was embedded into a framework of components for natural language processing, information retrieval and knowledge representation, together forming the QA system LogAnswer.
Also presented are additional extensions to the prover implementation and the underlying calculi which go beyond enhancing the reasoning strength of QA systems by giving access to external knowledge sources like web services. These allow the prover to fill gaps in the knowledge during the derivation, or to use external ontologies in other ways, for example for abductive reasoning. While the modifications and extensions detailed in the dissertation are a direct result of adapting an ATP system to QA, some of them can be useful for automated reasoning in general. Evaluation results from experiments and competition participations demonstrate the effectiveness of the methods under discussion.