AI 中文总结
本文提出高阶四极论证框架HQAF，扩展双极框架以支持高阶攻击与三种支持交互，通过三值及模糊编码语义实现模型等价，并指出集体交互为未来方向。
AI 中文摘要
本文提出了高阶四极论证框架（HQAF），该框架扩展了双极框架，允许攻击和三种类型的支持——必要支持、演绎支持和证据支持——在高阶上进行交互。在HQAF中，每个交互的源和目标可以是论证、攻击或支持。我们通过相邻完全标注和方程系统提供了三值语义，并直接在命题逻辑中定义编码语义，主要使用Łukasiewicz三值逻辑处理三值情形，以及基于连续t-范数（Gödel、Product、Łukasiewicz）的模糊逻辑处理模糊情形。建立了HQAF与其正规编码之间的模型等价性。模糊方程语义被证明是模糊编码语义的一种特定形式，三元化将模糊模型与三值完全标注联系起来。本研究仅限于非集合HQAF；集体交互留待未来工作。
英文摘要
This paper introduces the Higher-Order Quadripolar Argumentation Framework (HQAF), which extends bipolar frameworks by allowing attacks and three types of supports---necessary, deductive, and evidential---to interact at higher order. In HQAF, each interaction may have as its source and target an argument, an attack, or a support. We provide a 3-valued semantics via adjacent complete labellings and equational systems, and define encoded semantics directly in propositional logics, mainly Łukasiewicz three-valued logic for the 3-valued case and fuzzy logics based on continuous t-norms (Gödel, Product, Łukasiewicz) for the fuzzy case. Model equivalence between HQAF and its normal encoding is established. The fuzzy equational semantics is shown to be a specific formalism of the fuzzy encoded semantics, and ternarization connects fuzzy models to 3-valued complete labellings. The study is confined to non-set HQAF; collective interactions are reserved for future work.
