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A parameterised hierarchy of argumentation semantics for extended logic programming and its application to the well-founded semantics

机译:用于扩展逻辑编程的论证语义的参数化层次结构及其在充分依据的语义中的应用

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Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSX_p. Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.
机译:通过将证明视为支持者和反对者通过底切(攻击论点的前提)互相攻击并反驳(攻击论点的结论)的过程,论证已证明是为基于假设的推理定义形式语义的有用工具。在本文中,我们通过咬边和反击的组合为扩展逻辑程序提出了多种攻击概念,并定义了由支持者和反对者选择的攻击概念所参数化的论证语义的一般层次。我们证明了语义之间的等价关系和子集关系,并研究了有关一致性和一致性原则的一些基本属性,这些属性与默认否定和显式否定相关。最重要的是,我们将文献中提出的现有语义放入我们的层次结构中,并确定一个特定的论点语义,通过证明其与显式否定的副一致的,有充分根据的语义WFSX_p等效。最后,我们提出一种基于对话树的通用证明理论,并证明它在论证语义学方面是健全而完整的。

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