We present a new approach for computing complete, stable and preferred extensions of abstract argumentation frameworks. Unlike existing approaches that reduce these problems to the propositional satisfiability problem and solve them with the help of SAT-solvers, our approach solves them directly by making use of the fact that the mentioned extensions are contained in certain closure systems. Our algorithms enumerate these closed sets and filter the searched extensions. Experimental results show that our approach outperforms the existing approaches for a large number of the test cases.

We present a probably approximately correct algorithm for learning the terminological part of a description-logic knowledge base via subsumption queries. The axioms we learn are concept inclusions between conjunctions of concepts from a specified set of concept descriptions. By varying the distribution of queries posed to the oracle, we adapt the algorithm to improve the recall when using the resulting TBox for ontology-mediated query answering. Experimental evaluation on OWL 2 EL ontologies suggests that our approach helps significantly improve recall while maintaining a high precision of query answering. • A PAC algorithm for learning DL ontologies via subsumption queries. • A method to fine-tune query distribution during learning to boost recall in ontology-mediated query answering. • Experimental evaluation.

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining ℰℒ⊥ bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining ℰℒ⊥ bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all ℰℒ⊥ concept inclusions holding in the interpretation, not only the ones up to a fixed role depth. We also consider the case of confident ℰℒ⊥ bases, which requires that some proportion of the domain of the interpretation satisfies the base, instead of the whole domain. This case is useful to cope with noisy data.

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.