Organizations: Data Science Group, Heinz Nixdorf Institute, Paderborn University, Germany · School of Computing Science, University of Glasgow, United Kingdom · School of Computer Science, University of Sheffield, United Kingdom · Institut für Theoretische Informatik, Leibniz Universität Hannover, Germany
The connection between subset-maximal repairs for inconsistent databases involving various integrity constraints and acceptable sets of arguments within argumentation frameworks has recently drawn growing interest. In this paper, we contribute to this domain by establishing a new connection when integrity constraints (ICs) include denial constraints and local-as-view tuple-generating dependencies. It turns out that SET-based Argumentation Frameworks (SETAFs), an extension of Dung's argumentation frameworks (AFs) allowing collective attacks, are needed. It is known that subset-maximal repairs under denial constraints correspond to the naive extensions, which also coincide with the preferred and stable extensions in the resulting SETAFs. Our main findings establish that repairs under the considered fragment of tuple-generating dependencies correspond to the preferred extensions. Moreover, for these dependencies, additional preprocessing allows computing a unique extension that is stable and naive. Allowing both types of constraints breaks this relationship, and even the pre-processing does not help as only preferred semantics captures these repairs. Finally, while it is known that functional dependencies do not require set-based attacks, we prove the same regarding inclusion dependencies. Thus, one can translate inconsistent databases under these restricted classes of ICs to plain AFs with attacks only between arguments.
In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.
This work proposes novel splitting techniques for argumentation formalisms that incorporate supports between defeasible elements. We base our studies on bipolar set-based argumentation frameworks (BSAFs) which generalize argumentation frameworks with collective attacks (SETAFs), as well as bipolar argumentation frameworks (BAFs), by incorporating both collective attacks and supports. Notably, BSAFs establish a crucial link to structured argumentation as they naturally capture general (potentially non-flat) assumption-based argumentation. The increase in expressiveness calls for diverse forms of splitting. We consider splits over collective attacks (thereby generalizing the recently proposed splitting techniques for SETAFs), splits over collective supports, as well as splits over both collective attacks and supports. We establish suitable splitting schemata and prove their correctness for the most common argumentation semantics.
Matti Berthold, Lydia Blümel, Giovanni Buraglio +1
The same arguments often need to be evaluated under different external regimes. An agent with influence over the regime has a strategic lever that standard formalisms do not directly capture. We introduce context-dependent argumentation frameworks (CDAFs), an extension of Dung's theory in which a defeat function determines, per context, which attacks succeed. A perspective-labeled specialisation derives the defeat function from a relevance set ρ and a priority π. The relevance set is the agent's action space. In a small worked example, the agent's target argument is rejected under every full-relevance injective priority, yet accepted under partial activations, one of which no VAF audience can mirror. We define the corresponding decision problem, ACTIVATION-MANIPULATION, and record baseline complexity bounds. Tight bounds and multi-agent variants are left open.