An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal collapse is avoided and validity is shown already in weak modal logics K and T. Key to the gained simplifications of G\"odel's original theory is the exploitation of a link to the notions of filter and ultrafilter from topology. The paper illustrates how modern knowledge representation and reasoning technology for quantified non-classical logics can contribute new knowledge to other disciplines. The contributed material is also well suited to support teaching of non-trivial logic formalisms in classroom.
翻译:在古典高阶逻辑中采用普遍(元)逻辑推理方法来探索和研究Kurt G\“odel”模式理论的简化。一些论点的前提被修改,其他论点被删除,模型崩溃被避免,而弱的模型逻辑K和T已经表明了有效性。G\“odel”的原始理论简化的关键是利用与地形学过滤和超过滤器概念的联系。论文说明了量化非经典逻辑的现代知识代表性和推理技术如何能为其他学科提供新知识。所提供的资料也非常适合支持课堂中非三重逻辑形式主义的教学。