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.
Previously studied fuzzy bipolar conditions of type "and if possible" are made of a mandatory condition c and an optional condition w. They allow expressing complex preferences of a conjunctive nature. We define in this paper, a new kind of fuzzy bipolar conditions of the form "or else" which express complex preferences of a disjunctive nature. We show that the "or else" form can be used as a negation operator of the "and if possible" form and vice versa. We also show that these both forms are compatible and, therefore, fuzzy bipolar conditions of both types can be used together in the same bipolar query.
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