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Simple contrapositive assumption-based argumentation frameworks

机译：简单的矛盾假设基数框架

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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. (C) 2020 Elsevier Inc. All rights reserved.
机译：基于假设的论证是逻辑（或结构化）论证中最突出的形式主义之一，具有与不同形式的缺陷推理的紧密联系。在本文中，我们基于任何用于任何矛盾的突出逻辑，研究了基于延长形式的基于假设的论证框架（ABF）的粪便语义，并且其逻辑中的任意公式表达了其缺陷的假设。我们表明，除非虚假命题常数是不可行的假设的一部分，否则ABFS的基础和良好的语义缺乏他们在抽象论证框架（AAF）中的大部分理想的属性，以及对违反运营商的简单定义。而攻击关系，优选和稳定的语义减少到幼稚语义。我们还展示了ABFS粪便语义的标准定义中封闭条件的冗余，并调查在此设置中使用析取攻击。最后，我们展示了与ABF的推理与最大一致的房屋的推理关系，并考虑了诱导的蕴涵的一些性质，例如累积，优先或合理关系，满足不干扰。 （c）2020 Elsevier Inc.保留所有权利。

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