Abstract Assumption-based argumentation is one of the most prominent formalisms for logical (or structured) argumentation, with tight links to different forms of defeasible reasoning. In this paper we study the Dung semantics for extended forms of assumption-based argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible assumptions are expressed by arbitrary formulas in that logic. We show that unless the falsity propositional constant is part of the defeasible assumptions, the grounded and the well-founded semantics for ABFs lack most of the desirable properties they have in abstract argumentation frameworks (AAFs), and that for simple definitions of the contrariness operator and the attacks relations, preferred and stable semantics are reduced to naive semantics. We also show the redundancy of the closure condition in the standard definition of Dung's semantics for ABFs, and investigate the use of disjunctive attacks in this setting. Finally, we show some close relations of reasoning with ABFs to reasoning with maximally consistent sets of premises, and consider some properties of the induced entailments, such as being cumulative, preferential, or rational relations that satisfy non-interference.

中文翻译：

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基于对立假设的简单论证框架

摘要 基于假设的论证是逻辑（或结构化）论证最突出的形式主义之一，与不同形式的可废止推理密切相关。在本文中，我们研究了基于假设的论证框架 (ABF) 的扩展形式的 Dung 语义，该框架基于任何对逆命题逻辑，并且其可废止的假设由该逻辑中的任意公式表达。我们表明，除非假命题常数是可废止假设的一部分，否则 ABF 的有根据和有根据的语义缺乏它们在抽象论证框架 (AAF) 中的大部分理想属性，以及矛盾算子的简单定义并将攻击关系、首选和稳定语义简化为朴素语义。我们还在 ABF 的 Dung 语义的标准定义中展示了闭合条件的冗余，并研究了在此设置中使用析取攻击的情况。最后，我们展示了 ABF 推理与具有最大一致前提集的推理的一些密切关系，并考虑了归纳蕴涵的一些属性，例如满足非干涉的累积、优先或理性关系。