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The ability to conduct logical reasoning is a fundamental aspect of intelligent human behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, logic-based symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human logical reasoning qualities. More recently, however, there has been an increasing interest in using machine learning rather than logic-based symbolic formalisms to tackle these tasks. In this paper, we employ state-of-the-art methods for training deep neural networks to devise a novel model that is able to learn how to effectively perform logical reasoning in the form of basic ontology reasoning. This is an important and at the same time very natural logical reasoning task, which is why the presented approach is applicable to a plethora of important real-world problems. We present the outcomes of several experiments, which show that our model is able to learn to perform highly accurate ontology reasoning on very large, diverse, and challenging benchmarks. Furthermore, it turned out that the suggested approach suffers much less from different obstacles that prohibit logic-based symbolic reasoning, and, at the same time, is surprisingly plausible from a biological point of view.