Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations

Rewriting Guarded Existential Rules into Small Datalog Programs

The goal of this paper is to understand the relative expressiveness of the query language in which queries are specified by a set of guarded (disjunctive) tuple-generating dependencies (TGDs) and an output (or \u27answer\u27) predicate. Our main result is to show that every such query can be translated into a polynomially-sized (disjunctive) Datalog program if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant. To overcome the challenge that Datalog has no direct means to express the existential quantification present in TGDs, we define a two-player game that characterizes the satisfaction of the dependencies, and design a Datalog query that can decide the existence of a winning strategy for the game. For guarded disjunctive TGDs, we can obtain Datalog rules with disjunction in the heads. However, the use of disjunction is limited, and the resulting rules fall into a fragment that can be evaluated in deterministic single exponential time. We proceed quite differently for the case when the TGDs are not disjunctive and we show that we can obtain a plain Datalog query. Notably, unlike previous translations for related fragments, our translation requires only polynomial time if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant

The Impact of Active Domain Predicates on Guarded Existential Rules

It is realistic to assume that a database management system provides access to the active domain via built-in relations. Therefore, databases that include designated predicates that hold the active domain, which we call product databases, form a natural notion that deserves our attention. An important issue then is to look at the consequences of product databases for the expressiveness and complexity of central existential rule languages. We focus on guarded-based existential rules, and we investigate the impact of product databases on their expressive power and complexity. We show that the queries expressed via (frontier-)guarded rules gain in expressiveness, and in fact, they have the same expressive power as Datalog. On the other hand, there is no impact on the expressiveness of the queries specified via weakly-(frontier-)guarded rules since they are powerful enough to explicitly compute the predicates needed to access the active domain. We also observe that there is no impact on the complexity of the query languages in question

The Impact of Active Domain Predicates on Guarded Existential Rules

We claim it is realistic to assume that a database management system provides access to the active domain via built-in relations. Therefore, product databases, i.e., databases that include designated predicates that hold the active domain, form a natural notion that deserves our attention. An important issue then is to look at the consequences of product databases for the expressiveness and complexity of central existential rule languages. We focus on guarded existential rules, and we investigate the impact of product databases on their expressive power and complexity. We show that the queries expressed via (frontier-)guarded rules gain in expressiveness, and in fact, they have the same expressive power as Datalog. On the other hand, there is no impact on the expressiveness of the queries specified via weakly-(frontier-)guarded rules since they are powerful enough to explicitly compute the predicates needed to access the active domain. We also observe that there is no impact on the complexity of the languages in question

Relaxing and restraining queries for OBDA (extended abstract)

We investigate query reformulation rules in OBDA to obtain either more or less answers. We extend DL-Lite with complex role inclusions and define rules that produce query relaxations/restrictions over any dataset.We also introduce a set of data-driven rules to get more fine-grained reformulations