On graded semantics of abstract argumentation: Extension-based case
- URL: http://arxiv.org/abs/2012.10592v2
- Date: Sun, 27 Dec 2020 01:41:18 GMT
- Title: On graded semantics of abstract argumentation: Extension-based case
- Authors: Lixing Tan, Zhaohui Zhu, Jinjin Zhang
- Abstract summary: This paper considers some issues on extension-based semantics for abstract argumentation framework (AAF)
An alternative fundamental lemma is given, which generalizes the corresponding result obtained in [1].
A number of fundamental semantics for AAF, including conflict-free, admissible, complete and stable semantics, are shown to be closed under reduced meet modulo an ultrafilter.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Based on Grossi and Modgil's recent work [1], this paper considers some
issues on extension-based semantics for abstract argumentation framework (AAF,
for short). First, an alternative fundamental lemma is given, which generalizes
the corresponding result obtained in [1]. This lemma plays a central role in
constructing some special extensions in terms of iterations of the defense
function. Applying this lemma, some flaws in [1] are corrected and a number of
structural properties of various extension-based semantics are given. Second,
the operator so-called reduced meet modulo an ultrafilter is presented. A
number of fundamental semantics for AAF, including conflict-free, admissible,
complete and stable semantics, are shown to be closed under this operator.
Based on this fact, we provide a concise and uniform proof method to establish
the universal definability of a family of range related semantics. Thirdly,
using model-theoretical tools, we characterize the class of extension-based
semantics that is closed under reduced meet modulo any ultrafilter, which
brings us a metatheorem concerning the universal definability of range related
semantics. Finally, in addition to range related semantics, some graded
variants of traditional semantics of AAF are also considered in this paper,
e.g., ideal semantics, eager semantics, etc.
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