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A Structured Argumentation Framework for Modeling Debates in the Formal Sciences

机译:用于在正式科学中建模辩论的结构性论证框架

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Abstract Scientific research in the formal sciences comes in multiple degrees of formality: fully formal work; rigorous proofs that practitioners know to be formalizable in principle; and informal work like rough proof sketches and considerations about the advantages and disadvantages of various formal systems. This informal work includes informal and semi-formal debates between formal scientists, e.g. about the acceptability of foundational principles and proposed axiomatizations. In this paper, we propose to use the methodology of structured argumentation theory to produce a formal model of such informal and semi-formal debates in the formal sciences. For this purpose, we propose ASPIC-END, an adaptation of the structured argumentation framework ASPIC+ which can incorporate natural deduction style arguments and explanations. We illustrate the applicability of the framework to debates in the formal sciences by presenting a simple model of some arguments about proposed solutions to the Liar paradox, and by discussing a more extensive—but still preliminary—model of parts of the debate that mathematicians had about the Axiom of Choice in the early twentieth century.
机译:摘要正式科学的科学研究有多项形式:全面的工作;严谨的证据,从业者认为是原则上可操作的;和非正式的工作,如粗略的迹象草图和关于各种形式系统的优缺点的思考。这种非正式的工作包括正式科学家之间的非正式和半正式辩论,例如,关于基础原则的可接受性和提出的公理化。在本文中,我们建议使用结构性论证理论的方法,以在正式科学中制作各种非正式和半正式辩论的正式模型。为此目的,我们提出了Apic-End,适应结构化的论证框架Aspic +,它可以包含自然扣除风格的论点和解释。我们通过展示关于骗子悖论的拟议解决方案的一些论据的简单模型,并通过讨论数学家对数学家的辩论的更广泛但仍然是初步模型,展示了一个简单的一些论据的辩论二十世纪初选择的公理。

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