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We extend the result model for precedent-based reasoning with incomplete case bases. In contrast to regular case bases, these consist of incomplete cases for which not all dimension values need to be specified, but rather each dimension is assigned a set of possible values. The outcome of cases then applies for each (combination of) the possible dimension values. Building on earlier proposed notions of justification and stability for incomplete focus cases, we introduce the notion of possible justification statuses, which are required to maintain consistency of the incomplete case base. We demonstrate how these theoretic notions can be applied in practice for human-in-the-loop decision support, discuss their computational complexity and provide efficient algorithms.

Computational argumentation is a promising research area, yet there is a gap between theoretical contributions and practical applications. Bridging this gap could potentially raise interest in this topic even more. We argue that one part of the bridge could be an open-source package of implementations of argumentation algorithms, visualised in a web interface. Therefore we present a new release of PyArg, providing various new argumentation-based functionalities – including multiple generators, a learning environment, implementations of theoretical papers and a showcase of a practical application – in a new interface with improved accessibility.

The relatively young area of forgetting is concerned with the removal of selective information, while preserving other knowledge. This might be useful or even necessary, for example, to simplify a knowledge base or to tend legal requests. In the last few years, there has been an ample amount of research in the field, in particular with respect to logic programs, spanning from theoretical considerations to more practical applications, starting at the conceptual proposal of forgetting, to suggestions of properties that should be satisfied, followed by characterizations of abstract classes of operators that satisfy these properties, and finally the definition of concrete forgetting procedures. In this work we present novel Python implementations of all the forgetting procedures that have been proposed to date on logic programs. We provide them in a web interface, and hope to thereby give anybody who is interested a low-barrier overview of the landscape.

Reasoning under incomplete information is an important research direction in AI argumentation. Most computational advances in this direction have so-far focused on abstract argumentation frameworks. Development of computational approaches to reasoning under incomplete information in structured formalisms remains to-date to a large extent a challenge. We address this challenge by studying the so-called stability and relevance problems---with the aim of analyzing aspects of resilience of acceptance statuses in light of new information---in the central structured formalism of ASPIC+. Focusing on the case of the grounded semantics and an ASPIC+ fragment motivated through application scenarios, we develop exact ASP-based algorithms for stability and relevance in incomplete ASPIC+ theories, and pinpoint the complexity of reasoning about stability (coNP-complete) and relevance (Sigma_2^P-complete), further justifying our ASP-based approaches. Empirically, the algorithms exhibit promising scalability, outperforming even a recent inexact approach to stability, with our ASP-based iterative approach being the first algorithm proposed for reasoning about relevance in ASPIC+.

This volume contains revised versions of the papers selected for the fourth volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.

We explore the computational complexity of stability and relevance in incomplete argumentation frameworks (IAFs), abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. IAFs can be specified by, e.g., making uncertain arguments or attacks certain; the justification status of arguments in an IAF is determined on the basis of the certain arguments and attacks. An argument is stable if its justification status is the same in all specifications of the IAF. For arguments that are not stable in an IAF, the relevance problem is of interest: which uncertain arguments or attacks should be investigated for the argument to become stable? We redefine stability and define relevance for IAFs and study their complexity.