Expressiveness of guarded existential rule languages

Abstract

The so-called existential rules have recently gained attention, mainly due to their adequate expressiveness for ontological query answering. Several decidable fragments of such rules have been introduced, employing restrictions such as various forms of guardedness to ensure decidability. Some of the more well-known languages in this arena are (weakly) guarded and (weakly) frontier-guarded fragments of existential rules. In this paper, we explore their relative and absolute expressiveness. In particular, we provide a new proof that queries expressed via frontier-guarded and guarded rules can be translated into plain Datalog queries. Since the converse translations are impossible, we develop generalizations of frontier-guarded and guarded rules to nearly frontierguarded and nearly guarded rules, respectively, which have exactly the expressive power of Datalog. We further show that weakly frontier-guarded rules can be translated into weakly guarded rules, and thus, weakly frontier-guarded and weakly guarded rules have exactly the same expressive power. Such rules cannot be expressed in Datalog since their query answering problem is ExpTime-complete in data complexity. We strengthen this completeness result by proving that on ordered databases with input negation available, weakly guarded rules capture all queries computable in exponential time. We then show that weakly guarded rules extended with stratified negation are expressive enough to capture all database queries decidable in exponential time, without any assumptions on the input databases. Finally, we note that the translations of this paper are, in general, exponential in size, but lead to worst-case optimal algorithms for query answering with the considered languages.

Functional Dependencies Unleashed for Scalable Data Exchange

“…It would be interesting to see how the two approaches can be combined. As shown in [10], guarded existential rules, that ensure the decidability of query answering tasks, can be translated into plain Datalog rules, in order to possibly leverage Datalog optimization techniques. However, Datalog rewriting is orthogonal to our approach and a comparison of the performances of the two complementary approaches falls beyond the scope of our work and is left for future investigation.…”

“…Research on DE has led to a very wide and rich range of results [17,5,6]. Many existing approaches have aimed at rewriting the dependencies, so as to further leverage the power of an external, general evaluation engine, such as a traditional RDBMS [17,15] or a Datalog engine [12,10]. Alternatively, custom chase engines have been used and optimized for computing DE solutions [7,16].…”

Reasoning Web. Web Logic Rules

“…Indeed, in the absence of existential quantification, most of the Horn DLs we have discussed in this chapter could be expressed as Datalog rules. 5 to reduce the OMQA problem for existential rules to plain Datalog reasoning [97]. Since Datalog with existential quantification is well known to be undecidable, these extensions must be done in a cautious and controlled way, and restrictions must be imposed, such as certain acyclicity conditions or allowing only guarded quantification.…”

Containment for Rule-Based Ontology-Mediated Queries

“…Interestingly, some of these challenges are by now well-studied; most notably (a) query evaluation [8,24,25,27]: given an OMQ Q = (S, Σ, q), a database D over S, and a tuple of constantsc, doesc belong to the evaluation of q over every extension of D that satisfies Σ, or, equivalently, isc a certain answer for Q over D? and (b) relative expressiveness [19,42,43]: how does the expressiveness of OMQs compare to the one of other query languages? Surprisingly, despite its prominence, no work to date has carried out an in-depth investigation of containment for OMQs based on tgds and UCQs.…”

“…The OMQ language based on guarded tgds is not UCQ rewritable, which forces us to develop different tools to study its containment problem. Let us remark that guarded OMQs can be rewritten as guarded Datalog queries (by exploiting the translations devised in [9,43]), for which containment is decidable in 2ExpTime [20]. But, again, the known rewritings are very large [43], and hence the reduction of containment for guarded OMQs to containment for guarded Datalog does not yield optimal upper bounds.…”