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.

中文翻译：

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计算机说，一个（简化的）至尊存在必然存在：G\"odel 的本体论论证的计算探索变体

采用经典高阶逻辑中的普遍（元）逻辑推理方法来探索和研究 Kurt G\"odel 模态本体论论证的简化。一些论证前提被修改，其他论证前提被删除，避免了模态崩溃，有效性是已经在弱模态逻辑 K 和 T 中显示出来。 G\"odel 原始理论获得简化的关键是利用拓扑中滤波器和超滤波器概念的链接。该论文说明了用于量化非经典逻辑的现代知识表示和推理技术如何为其他学科贡献新知识。贡献的材料也非常适合支持课堂上非平凡逻辑形式主义的教学。