Abstract. The area of inconsistent ontological knowledge base query answering studies the problem of inferring from an inconsistent ontology. To deal with such a situation, different semantics have been defined in the literature (e.g. AR, IAR, ICR). Argumentation theory can also be used to draw conclusions under inconsistency. Given a set of arguments and attacks between them, one applies a particular semantics (e.g. stable, preferred, grounded) to calculate the sets of accepted arguments and conclusions. However, it is not clear what are the similarities and differences of semantics from ontological knowledge base query answering and semantics from argumentation theory. This paper provides the answer to that question. Namely, we prove that: (1) sceptical acceptance under stable and preferred semantics corresponds to ICR semantics; (2) universal acceptance under stable and preferred semantics corresponds to AR semantics; (3) acceptance under grounded semantics corresponds to IAR semantics. We also prove that the argumentation framework we define satisfies the rationality postulates (e.g. consistency, closure).
The paper addresses the problem of explaining Boolean Conjunctive Query (BCQ) entailment in the presence of inconsistency within the Ontology-Based Data Access (OBDA) setting, where inconsistency is handled by the intersection of closed repairs semantics (ICR) and the ontology is represented by Datalog+/-rules. We address this problem in the case of both BCQ acceptance and failure by adopting a logical instantiation of abstract argumentation model; that is, in order to explain why the query is accepted or failed, we look for proponent or opponent sets of arguments in favor or against the query acceptance. We have also studied the computational complexity of the problem of finding an arbitrary explanation as well as all explanations.
This paper presents a graph-based knowledge representation and reasoning language. This language benefits from an important syntactic operation, which is called a graph homomorphism. This operation is sound and complete with respect to logical deduction. Hence, it is possible to do logical reasoning without using the language of logic but only graphical, thus visual, notions. This paper presents the main knowledge constructs of this language, elementary graphbased reasoning mechanisms, as well as the graph homomorphism, which encompasses all these elementary transformations in one global step. We put our work in context by presenting a concrete semantic annotation application example.
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