Knowledge bases are deductive databases where the machinery of logic is used to represent domain-specific and general-purpose knowledge over existing data. In the existential rules framework, a knowledge base is composed of two layers: the data layer which represents the factual knowledge, and the ontological layer that incorporates rules of deduction and negative constraints. The main reasoning service in such framework is answering queries over the data layer by means of the ontological layer. As in classical logic, contradictions trivialize query answering since everything follows from a contradiction (ex falso quodlibet). Recently, inconsistency-tolerant approaches have been proposed to cope with such problem in the existential rules framework. They deploy repairing strategies on the knowledge base to restore consistency and overcome the problem of trivialization. However, these approaches are sometimes unintelligible and not straightforward for the end-user as they implement complex repairing strategies. This would jeopardize the trust relation between the user and the knowledge-based system. In this thesis we answer the research question: “How do we make query answering intelligible to the end-user in presence of inconsistency?”. To answer the question we consider the general framework of argumentation and we propose three types of explanations: (1) One-shot Argument-based Explanations, (2) Meta-level Dialectical Explanations, and (3) Object-level Dialectical Explanations. The first one is a set of arguments in favor or against the query in question. The two others take the form of a dialogue between the user and the reasoner about the entailment of a given query. We study these explanations in the framework of logic-based argumentation and dialectics and we study their properties and their impact on users.