Matthias König

Wolfgang Dvořák, Matthias König, Markus Ulbricht et al.

Argumentation Frameworks (AFs) are a key formalism in AI research. Their semantics have been investigated in terms of principles, which define characteristic properties in order to deliver guidance for analysing established and developing new semantics. Because of the simple structure of AFs, many desired properties hold almost trivially, at the same time hiding interesting concepts behind syntactic notions. We extend the principle-based approach to Argumentation Frameworks with Collective Attacks (SETAFs) and provide a comprehensive overview of common principles for their semantics. Our analysis shows that investigating principles based on decomposing the given SETAF (e.g. directionality or SCC-recursiveness) poses additional challenges in comparison to usual AFs. We introduce the notion of the reduct as well as the modularization principle for SETAFs which will prove beneficial for this kind of investigation. We then demonstrate how our findings can be utilized for incremental computation of extensions and give a novel parameterized tractability result for verifying preferred extensions.

Matthias König, Xiyue Zhang, Holger H. Hoos et al.

The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification techniques offer provable guarantees for all robustness queries but struggle to scale beyond small neural networks. To overcome this computational intractability, incomplete verification methods often rely on convex relaxation to over-approximate the nonlinearities in neural networks. Progress in tighter approximations has been achieved for piecewise linear functions. However, robustness verification of neural networks for general activation functions (e.g., Sigmoid, Tanh) remains under-explored and poses new challenges. Typically, these networks are verified using convex relaxation techniques, which involve computing linear upper and lower bounds of the nonlinear activation functions. In this work, we propose a novel parameter search method to improve the quality of these linear approximations. Specifically, we show that using a simple search method, carefully adapted to the given verification problem through state-of-the-art algorithm configuration techniques, improves the average global lower bound by 25% on average over the current state of the art on several commonly used local robustness verification benchmarks.

Wolfgang Dvořák, Matthias König, Johannes P. Wallner et al.

In this solver description we present ASPARTIX-V, in its 2021 edition, which participates in the International Competition on Computational Models of Argumentation (ICCMA) 2021. ASPARTIX-V is capable of solving all classical (static) reasoning tasks part of ICCMA'21 and extends the ASPARTIX system suite by incorporation of recent ASP language constructs (e.g. conditional literals), domain heuristics within ASP, and multi-shot methods. In this light ASPARTIX-V deviates from the traditional focus of ASPARTIX on monolithic approaches (i.e., one-shot solving via a single ASP encoding) to further enhance performance.