Reasoning under incomplete information is an important research direction in the study of computational argumentation. Most advances in this direction so far have focused on abstract argumentation frameworks. In particular, development of computational approaches to reasoning under incomplete information in structured formalisms remains to a large extent a challenge. We address this challenge by studying the problems of determining stability and relevance—with the aim of analyzing aspects of resilience of acceptance statuses in light of new information—in the central structured formalism of ASPIC+ . The specific ASPIC+ instantiation and grounded argumentation semantics we focus on are motivated by current applications in criminal investigation at the Netherlands Police. Our contributions consist of a theoretical analysis of the complexity of deciding stability and relevance as well as first exact algorithms for reasoning about stability and relevance in incomplete ASPIC+ theories. In terms of complexity results, we show that deciding stability is coNP-complete for incomplete ASPIC+ when assuming a preference ordering on defeasible rules via the last-link ordering, while deciding relevance is significantly more complex, namely NP^NP-complete. Complementing the complexity results, we develop practical algorithms for deciding stability and relevance based on the declarative paradigm of answer set programming (ASP). Furthermore, we provide an open-source implementation of the algorithms, and show empirically that the implementation exhibits promising scalability on both real-world and synthetic data. Our exact approach to stability is competitive with a previously proposed inexact approach, and the run times of our algorithms for both stability and relevance are sufficiently low on real-world data to be used in online settings.

Incomplete argumentation frameworks (IAFs) are abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. In a completion of an IAF, each uncertain argument or attack is either added (made certain) or removed. Given a completion, the acceptability of an argument is determined by its justification status. For arguments in an IAF that do not have the same justification status in each completion, it is interesting to study which uncertain arguments and attacks are relevant, in the sense that adding or removing them can lead to a different justification status. We propose algorithms based on Answer Set Programming for enumerating relevant arguments and attacks under grounded and complete semantics.

We propose a new layered visualization in PyArg for grounded labelings of abstract argumentation frameworks. Argument nodes are colored according to their label (IN, OUT, or UNDEC) and have a new length annotation, which is derived from provenance subgraphs. New edge annotations explain an attack-edge’s role in determining the value (label) of nodes in an argumentation framework.

We provide complexity results and algorithms for reasoning in the central structured argumentation formalism of ASPIC+. Considering ASPIC+ accommodated with preferences under the last-link principle, the results are made possible by rephrasing several argumentation semantics---admissible, complete, stable, preferred and grounded---in terms of defeasible elements of an ASPIC+ theory for both democratic and elitist last-link lifting. Via the rephrasing, we establish that acceptance is polynomial-time computable under grounded semantics, and complete for either NP, coNP, or Pi_P^2, depending on the reasoning mode and semantics. We also detail answer set programming encodings for deciding acceptance for the NP/coNP-complete reasoning tasks, and empirically show that it scales significantly better than first translating ASPIC+ reasoning tasks to abstract argumentation. Finally, we show that, in contrast to the last-link principle, it is NP-hard to compute the grounded extension under the weakest-link principle.

We define and study the notions of stability and relevance for precedent-based reasoning, focusing on Horty's result model of precedential constraint. According to this model, precedents constrain the possible outcomes for a focus case, which is a yet undecided case, where precedents and the focus case are compared on their characteristics (called dimensions). In this paper, we refer to the enforced outcome for the focus case as its justification status. In contrast to earlier work, we do not assume that all dimension values of the focus case have been established with certainty: rather, each dimension is assigned a set of possible values. We define a focus case as stable if its justification status is the same for every choice of the possible values. For focus cases that are not stable, we study the task of identifying relevance: which possible values should be excluded to make the focus case stable? We show how the tasks of identifying justification, stability and relevance can be exploited for human-in-the-loop decision support. Finally, we discuss the computational complexity of these tasks and provide efficient algorithms.

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.

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+.

We introduce PyArg, a Python-based solver and explainer for both abstract argumentation and ASPIC+. A large variety of extension-based semantics allows for flexible evaluation and several explanation functions are available.

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.

We study the dynamic argumentation task of detecting stability: given a specific structured argumentation setting, can adding information change the acceptability status of some propositional formula? Detecting stability is not tractable for every input, but efficient computation is essential in practical applications. We present a sound approximation algorithm that recognises stability for many inputs in polynomial time and we discuss several of its properties. In particular, we show under which constraints on the input our algorithm is complete. The proposed algorithm is currently applied for fraud inquiry at the Dutch National Police - we provide an English demo version that also visualises the output of the algorithm.

We propose an agent architecture for transparent human-in-the-loop classification. By combining dynamic argumentation with legal case-based reasoning, we create an agent that is able to explain its decisions at various levels of detail and adapts to new situations. It keeps the human analyst in the loop by presenting suggestions for corrections that may change the factors on which the current decision is based and by enabling the analyst to add new factors. We are currently implementing the agent for classification of fraudulent web shops at the Dutch Police.