In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents . This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are induced by the extended (hypersequent-based) frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics (like the intermediate logic LC , the modal logic S5 , and the relevance logic RM ), which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties.

中文翻译：

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基于超序列的逻辑论证的广义证明理论方法

在本文中，我们通过基于逻辑的论证和归纳蕴涵关系介绍了基于超序列的框架，用于可废止推理的建模。这些结构是基于序列的论证框架的扩展，其中论证和它们之间的攻击关系不仅由 Gentzen 风格的序列表达，而且由更一般的表达式表达，称为超序列。这种概括使我们能够克服逻辑论证框架的一些已知弱点，并证明由扩展的（基于超序列的）框架引起的蕴涵的几个理想属性。它还允许我们将一些众所周知的逻辑（如中间逻辑 LC 、模态逻辑 S5 和相关逻辑 RM ）合并为我们形式主义的演绎基础，缺乏无切割的连续演算，因此不足以用于标准的基于序列的论证。我们表明，基于超序列的论证产生了这些逻辑的强大的可废止变体​​，具有许多理想的特性。