Anthony P. Young

Vibhor Agarwal, Anthony P. Young, Sagar Joglekar et al.

Online forums that allow for participatory engagement between users have been transformative for the public discussion of many important issues. However, such conversations can sometimes escalate into full-blown exchanges of hate and misinformation. Existing approaches in natural language processing (NLP), such as deep learning models for classification tasks, use as inputs only a single comment or a pair of comments depending upon whether the task concerns the inference of properties of the individual comments or the replies between pairs of comments, respectively. But in online conversations, comments and replies may be based on external context beyond the immediately relevant information that is input to the model. Therefore, being aware of the conversations' surrounding contexts should improve the model's performance for the inference task at hand. We propose GraphNLI, a novel graph-based deep learning architecture that uses graph walks to incorporate the wider context of a conversation in a principled manner. Specifically, a graph walk starts from a given comment and samples "nearby" comments in the same or parallel conversation threads, which results in additional embeddings that are aggregated together with the initial comment's embedding. We then use these enriched embeddings for downstream NLP prediction tasks that are important for online conversations. We evaluate GraphNLI on two such tasks - polarity prediction and misogynistic hate speech detection - and found that our model consistently outperforms all relevant baselines for both tasks. Specifically, GraphNLI with a biased root-seeking random walk performs with a macro-F1 score of 3 and 6 percentage points better than the best-performing BERT-based baselines for the polarity prediction and hate speech detection tasks, respectively.

Anthony P. Young, David Kohan Marzagao, Josh Murphy

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.

Anthony Peter Young

This note reviews Section 2 of Dung's seminal 1995 paper on abstract argumentation theory. In particular, we clarify and make explicit all of the proofs mentioned therein, and provide more examples to illustrate the definitions, with the aim to help readers approaching abstract argumentation theory for the first time. However, we provide minimal commentary and will refer the reader to Dung's paper for the intuitions behind various concepts. The appropriate mathematical prerequisites are provided in the appendices.

Anthony P. Young

In his seminal paper that inaugurated abstract argumentation, Dung proved that the set of complete extensions forms a complete semilattice with respect to set inclusion. In this note we demonstrate that this proof is incorrect with counterexamples. We then trace the error in the proof and explain why it arose. We then examine the implications for the grounded extension. [Reason for withdrawal continued] Page 4, Example 2 is not a counterexample to Dung 1995 Theorem 25(3). It was believed to be a counter-example because the author misunderstood ``glb'' to be set-theoretic intersection. But in this case, ``glb'' is defined to be other than set-theoretic intersection such that Theorem 25(3) is true. The author was motivated to fully understand the lattice-theoretic claims of Dung 1995 in writing this note and was not aware that this issue is probably folklore; the author bears full responsibility for this error.

Anthony P. Young, Sanjay Modgil, Odinaldo Rodrigues

We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the conclusions of the justified arguments correspond to the PDL extensions. We will first assume that the default priority is total, and then generalise to the case where it is a partial order. This provides a characterisation of non-monotonic inference in PDL as an exchange of argument and counter-argument, providing a basis for distributed non-monotonic reasoning in the form of dialogue.

Anthony P. Young, Sanjay Modgil, Odinaldo Rodrigues

We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions. Argumentation semantics for PDL will allow for the application of argument game proof theories to the process of inference in PDL, making the reasons for accepting a conclusion transparent and the inference process more intuitive. This also opens up the possibility for argumentation-based distributed reasoning and communication amongst agents with PDL representations of mental attitudes.