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The LogAnswer system is an application of automated reasoning to the field of open domain question answering. In order to find answers to natural language questions regarding arbitrary topics, the system integrates an automated theorem prover in a framework of natural language processing tools. The latter serve to construct an extensive knowledge base automatically from given textual sources, while the automated theorem prover makes it possible to derive answers by deductive reasoning. In the paper, we discuss the requirements to the prover that arise in this application, especially concerning efficiency and robustness. The proposed solution rests on incremental reasoning, relaxation of the query (if no proof of the full query is found), and other techniques. In order to improve the robustness of the approach to gaps of the background knowledge, the results of deductive processing are combined with shallow linguistic features by machine learning.

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Abstract. In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for paramodulation are drawn (only) from a set of positive unit clauses, the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition-style theorem proving. Our main theoretical result is the soundness and completeness of the calculus. The calculus is implemented, and we also report on practical experiments.