Affiliation:
1. Department of Philosophy, Tsinghua University, Beijing 100084, China
Abstract
Abstract
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.
Funder
Major Program of the National Social Science Foundation of China
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
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