Notes on Abstract Argumentation Theory

Young, Anthony P.

doi:10.48550/arxiv.1806.07709

Cited by 3 publications

(9 citation statements)

References 11 publications

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“…Proof. This follows from [6,Theorem 25(3)] and [27,Theorem 6.30], respectively. We will give an example of subsolutions in Section 4 (Example 8).…”

Section: Complete Extensions Correspond To Subsolutionsmentioning

confidence: 79%

“…We now understand how an abstract game IM P, → , which is also an uncountably infinite digraph, arises from a game G. Dung interprets IM P, → as an abstract AF, where each argument is an argument for a given payoff distribution, and each attack denotes the possibility for a subset of agents to defect from the grand coalition. Corollary 1 states that such an AF has uncountably infinite arguments, but this is not a problem because Dung's argumentation semantics and their properties hold for AFs of arbitrary cardinalities [1,6,27]. Dung then proved that various methods of resolving conflicts in IM P, → as an AF correspond to meaningful solution concepts of G. The following result is straightforward to show.…”

Section: From Cooperative Game Theory To Abstract Argumentationmentioning

confidence: 99%

“…To determine which sets of arguments are justifiable we say S is a complete extension iff S is admissible and d(S) ⊆ S. 4 Further, S is a preferred extension iff it is a ⊆-maximal complete extension [27,Theorem 7.11], S is a stable extension iff n(S) = S and S is the grounded extension iff it is the ⊆-least complete extension. These four semantics are collectively called the Dung semantics, and each defines sets of winning arguments given A, R .…”

Section: Abstract Argumentation Theorymentioning

confidence: 99%

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Applying Abstract Argumentation Theory to Cooperative Game Theory

Young,

Marzagao,

Murphy

2019

Preprint

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We apply ideas from abstract argumentation theory to study cooperative game theory. Building on Dung's results in his seminal paper, we further the correspondence between Dung's four argumentation semantics and solution concepts in cooperative game theory by showing that complete extensions (the grounded extension) correspond to Roth's subsolutions (respectively, the supercore). We then investigate the relationship between well-founded argumentation frameworks and convex games, where in each case the semantics (respectively, solution concepts) coincide; we prove that three-player convex games do not in general have well-founded argumentation frameworks.

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“…Proof. This follows from [6,Theorem 25(3)] and [27,Theorem 6.30], respectively. We will give an example of subsolutions in Section 4 (Example 8).…”

Section: Complete Extensions Correspond To Subsolutionsmentioning

confidence: 79%

Section: From Cooperative Game Theory To Abstract Argumentationmentioning

confidence: 99%

Section: Abstract Argumentation Theorymentioning

confidence: 99%

See 1 more Smart Citation

Applying Abstract Argumentation Theory to Cooperative Game Theory

Young,

Marzagao,

Murphy

2019

Preprint

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“…While MPs are guided by political issues, many discussion platforms have UIs that allow for readers to sort the comments, say from most liked to least liked. This seems to rely on a "wisdom of the crowds" effect to have the best points float to the top as indicated by the number of likes, allowing for the user to read the top few points made [31]. [2] has argued that such comment sorting and structuring mechanisms, including flagging, moderation and ways of detecting relevancy and novelty, can help increase user participation on news comments, improve the quality of comments, and promote constructive discussions.…”

Section: Social Media Analyticsmentioning

confidence: 99%

“…For example, in BBC's Have Your Say (recall Footnote 1, page 2), there are ways to sort the comments by their number of likes or by their time of posting. Following the suggestion in [31], suppose a user sorts the comments from most liked to least liked, then how many comments should a reader sample in order to get, say, 10% of the winning arguments? How about 50% of the winning arguments?…”

Section: More Ways To Samplementioning

confidence: 99%

Who Has the Last Word? Understanding How to Sample Online Discussions

et al. 2021

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In online debates, as in offline ones, individual utterances or arguments support or attack each other, leading to some subset of arguments (potentially from different sides of the debate) being considered more relevant than others. However, online conversations are much larger in scale than offline ones, with often hundreds of thousands of users weighing in, collaboratively forming large trees of comments by starting from an original post and replying to each other. In large discussions, readers are often forced to sample a subset of the arguments being put forth. Since such sampling is rarely done in a principled manner, users may not read all the relevant arguments to get a full picture of the debate from a sample. This article is interested in answering the question of how users should sample online conversations to selectively favour the currently justified or accepted positions in the debate. We apply techniques from argumentation theory and complex networks to build a model that predicts the probabilities of the normatively justified arguments given their location in idealised online discussions of comments and replies, which we represent as trees. Our model shows that the proportion of replies that are supportive, the distribution of the number of replies that comments receive, and the locations of comments that do not receive replies (i.e., the “leaves” of the reply tree) all determine the probability that a comment is a justified argument given its location. We show that when the distribution of the number of replies is homogeneous along the tree length, for acrimonious discussions (with more attacking comments than supportive ones), the distribution of justified arguments depends on the parity of the tree level, which is the distance from the root expressed as number of edges. In supportive discussions, which have more supportive comments than attacks, the probability of having justified comments increases as one moves away from the root. For discussion trees that have a non-homogeneous in-degree distribution, for supportive discussions we observe the same behaviour as before, while for acrimonious discussions we cannot observe the same parity-based distribution. This is verified with data obtained from the online debating platform Kialo. By predicting the locations of the justified arguments in reply trees, we can therefore suggest which arguments readers should sample, to grasp the currently accepted opinions in such discussions. Our models have important implications for the design of future online debating platforms.

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GraphNLI: A Graph-based Natural Language Inference Model for Polarity Prediction in Online Debates

Agarwal,

Joglekar,

Young

et al. 2022

Preprint

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Online forums that allow participatory engagement between users have been transformative for public discussion of important issues. However, debates on such forums can sometimes escalate into full blown exchanges of hate or misinformation. An important tool in understanding and tackling such problems is to be able to infer the argumentative relation of whether a reply is supporting or attacking the post it is replying to. This so called polarity prediction task is difficult because replies may be based on external context beyond a post and the reply whose polarity is being predicted. We propose GraphNLI, a novel graph-based deep learning architecture that uses graph walk techniques to capture the wider context of a discussion thread in a principled fashion. Specifically, we propose methods to perform root-seeking graph walks that start from a post and captures its surrounding context to generate additional embeddings for the post. We then use these embeddings to predict the polarity relation between a reply and the post it is replying to. We evaluate the performance of our models on a curated debate dataset from Kialo, an online debating platform. Our model outperforms relevant baselines, including S-BERT, with an overall accuracy of 83%.

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Notes on Abstract Argumentation Theory

Cited by 3 publications

References 11 publications

Applying Abstract Argumentation Theory to Cooperative Game Theory

Applying Abstract Argumentation Theory to Cooperative Game Theory

Who Has the Last Word? Understanding How to Sample Online Discussions

GraphNLI: A Graph-based Natural Language Inference Model for Polarity Prediction in Online Debates

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