构建统一框架，融合证据支持与多值推理，解决论证系统中的复杂交互问题。
Evidential-Based Higher-Order Set Argumentation Framework
- 引入基于证据的高阶集合论证框架，统一处理支持链、集合来源和高阶关系。
- 提出两种语义：允许三值判断的邻近完整标注与严格依赖证据链的扩展语义。
- 通过逻辑编码实现可计算性，支持模糊逻辑下的连续推理与定性定量融合。
证据型论证通过要求论证及其互动基于源于初步要素的证据链，扩展了Dung的抽象论证理论。然而，现有形式化缺乏对证据支持、高阶关系（攻击与支持作用于任意元素）及集体互动（来源为集合）的统一处理。本文提出证据基础的高阶集合论证框架（EHSAF），在单一表达性设定中保守地推广多个现有框架。我们开发了两种完整的语义：一种是允许论证在支持环中取真、假、未决三值的邻近完整标注语义，反映对未来证据的开放认知态度；另一种是遵循严格证据主义立场的基于扩展的完整语义，仅接受具有稳固支持链的论证。我们证明两者在支持环存在时分歧，但在支持无环条件下等价。为支持计算推理，我们提供EHSAF的命题归约编码，并证明在三值卢卡西维茨逻辑中，其模型恰好对应邻近完整标注。进一步将该编码拓展至连续模糊逻辑（Gödel、Product、Łukasiewicz），定义连续模糊归约语义。我们证明该模糊语义满足连续性、单调性、边界条件及解的存在性，且其三值化在自然三角模条件下恢复邻近完整标注。本框架因此统一了表达性论证与有原则的三值与模糊语义，弥合了证据推理中定性与定量之间的鸿沟。
原文摘要 · Abstract (English)
Evidential argumentation extends Dung's abstract argumentation by requiring arguments and interactions to be backed by chains of evidence rooted in prima-facie elements. However, existing formalisms lack a unified treatment of evidential support, higher-order relations (attacks and supports targeting arbitrary elements), and collective interactions (sources as sets). In this paper, we introduce the Evidential-Based Higher-Order Set Argumentation Framework (EHSAF), which conservatively generalises several existing frameworks within a single expressive setting. We develop two complete semantics for EHSAFs: an \emph{adjacent complete labelling semantics} that admits multiple truth values (true, false, undecided) for arguments in support cycles, reflecting an open epistemic attitude toward future evidence; and an \emph{extension-based complete semantics} that follows a strict evidentialist stance, accepting only arguments with well-founded support chains. We show that these two semantics diverge in the presence of support cycles, and prove their equivalence under support-acyclicity. To enable computational reasoning, we provide a normal propositional encoding of EHSAFs and prove that, in three-valued Łukasiewicz logic, its models correspond precisely to the adjacent complete labellings. We further extend this encoding to continuous fuzzy logics (G{ö}del, Product, and Łukasiewicz), defining a continuous fuzzy normal encoded semantics. We establish that this fuzzy semantics satisfies key properties---continuity, monotonicity, boundary conditions, and solution existence---and that its ternarisation recovers the adjacent complete labellings under natural t-norm conditions. Our framework thus unifies expressive argumentation with principled three-valued and fuzzy semantics, bridging the gap between qualitative and quantitative reasoning about evidence.
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