We integrate Dung’s argumentation framework with a topological space to formalize Clark’s no false lemmas theory for solving the Gettier problem and study its logic. Our formalization shows that one of the two notions of knowledge proposed by Clark, justified belief with true grounds, satisfies Stalnaker’s axiom system of belief and knowledge except for the axiom of closure under conjunction. We propose a new notion of knowledge, justified belief with a well-founded chain of true grounds, which further improves on Clark’s two notions of knowledge. We pinpoint a seemingly reasonable condition which makes these three notions of knowledge collapse into the same one and explain why this result looks counter-intuitive. From a technical point of view, our formal analysis driven by the philosophical issues reveals the logical structure of the grounded semantics in Dung’s argumentation theory.

中文翻译：

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没有错误的论据和论证的拓扑

我们将Dung的论证框架与拓扑空间相结合，以形式化Clark的无虚假引理理论来解决Gettier问题并研究其逻辑。我们的形式化表明，由克拉克提出的两个知识概念之一，即具有真实根据的合理信念，满足了斯坦纳克的信念和知识公理体系，但不包括联合下的封闭公理。我们提出了一种新的知识观，一种有充分根据的合理信念一连串的真实依据，进一步完善了克拉克的两个知识观。我们指出了一种看似合理的条件，该条件使这三种知识观念陷入同一概念，并解释了为什么这一结果看起来违反直觉。从技术的角度来看，我们在哲学问题的驱动下进行的形式分析揭示了董氏论证理论中扎根语义的逻辑结构。