Unsupervised graph anomaly detection (GAD) has received increasing attention in recent years, which aims to identify data anomalous patterns utilizing only unlabeled node information from graph-structured data. However, prevailing unsupervised GAD methods typically presuppose complete node attributes and structure information, a condition hardly satisfied in real-world scenarios owing to privacy, collection errors or dynamic node arrivals. Existing standard imputation schemes risk "repairing" rare anomalous nodes so that they appear normal, thereby introducing imputation bias into the detection process. In addition, when both node attributes and edges are missing simultaneously, estimation errors in one view can contaminate the other, causing cross-view interference that further undermines the detection performance. To overcome these challenges, we propose M$^2$V-UGAD, a multiple missing values-resistant unsupervised GAD framework on incomplete graphs. Specifically, a dual-pathway encoder is first proposed to independently reconstruct missing node attributes and graph structure, thereby preventing errors in one view from propagating to the other. The two pathways are then fused and regularized in a joint latent space so that normals occupy a compact inner manifold while anomalies reside on an outer shell. Lastly, to mitigate imputation bias, we sample latent codes just outside the normal region and decode them into realistic node features and subgraphs, providing hard negative examples that sharpen the decision boundary. Experiments on seven public benchmarks demonstrate that M$^2$V-UGAD consistently outperforms existing unsupervised GAD methods across varying missing rates.

Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following a recent trend in the literature, we tackle the open question of studying plausible instantiations of these abstract models. To do so, we ground the uncertainty of arguments in their components, structured within rules and premises. Our main technical contributions are: i) the introduction of a notion of expressivity that can handle abstract and structured formalisms, and ii) the presentation of both negative and positive expressivity results, comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results affect incomplete abstract argumentation frameworks, and their extension with dependencies, on the abstract side, and ASPIC+, on the structured side.

We establish a correspondence between (fragments of) $\mathcal{TEL}^\bigcirc$, a temporal extension of the $\mathcal{EL}$ description logic with the LTL operator $\bigcirc^k$, and some specific kinds of formal grammars, in particular, conjunctive grammars (context-free grammars equipped with the operation of intersection). This connection implies that $\mathcal{TEL}^\bigcirc$ does not possess the property of ultimate periodicity of models, and further leads to undecidability of query answering in $\mathcal{TEL}^\bigcirc$, closing a question left open since the introduction of $\mathcal{TEL}^\bigcirc$. Moreover, it also allows to establish decidability of query answering for some new interesting fragments of $\mathcal{TEL}^\bigcirc$, and to reuse for this purpose existing tools and algorithms for conjunctive grammars.

Node-level graph anomaly detection (GAD) plays a critical role in identifying anomalous nodes from graph-structured data in various domains such as medicine, social networks, and e-commerce. However, challenges have arisen due to the diversity of anomalies and the dearth of labeled data. Existing methodologies - reconstruction-based and contrastive learning - while effective, often suffer from efficiency issues, stemming from their complex objectives and elaborate modules. To improve the efficiency of GAD, we introduce a simple method termed PREprocessing and Matching (PREM for short). Our approach streamlines GAD, reducing time and memory consumption while maintaining powerful anomaly detection capabilities. Comprising two modules - a pre-processing module and an ego-neighbor matching module - PREM eliminates the necessity for message-passing propagation during training, and employs a simple contrastive loss, leading to considerable reductions in training time and memory usage. Moreover, through rigorous evaluations of five real-world datasets, our method demonstrated robustness and effectiveness. Notably, when validated on the ACM dataset, PREM achieved a 5% improvement in AUC, a 9-fold increase in training speed, and sharply reduce memory usage compared to the most efficient baseline.

This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC+'s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung's framework and its extensions to accommodate preferences.

The ASPIC+ framework is intermediate in abstraction between Dung's argumentation framework and concrete instantiating logics. This paper generalises ASPIC+ to accommodate classical logic instantiations, and adopts a new proposal for evaluating extensions: attacks are used to define the notion of conflict-free sets, while the defeats obtained by applying preferences to attacks, are exclusively used to determine the acceptability of arguments. Key properties and rationality postulates are then shown to hold for the new framework.