Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Partial meet pseudo-contractions

In the AGM paradigm for belief revision, epistemic states are represented by logically closed sets of sentences, the so-called belief sets. An alternative approach uses belief bases, arbitrary sets of sentences. Both approaches have their problems when it comes to contraction operations. Belief bases are more expressive, but, at the same time, they present a serious syntax dependence. Between those two extremes lie a whole gamut of operations called pseudo-contractions, some of which may be interesting alternatives to the classical ones, providing a good balance between syntax dependence and expressivity. In this paper we explore some very natural and general constructions for pseudo-contractions, showing some of their properties and giving their axiomatic characterizations. We also illustrate possible practical scenarios where they can be employed