Enhancing Magic Sets with an Application to Ontological Reasoning

Abstract

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/DLV for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the DLV system, and tested for ontological reasoning, confirming their effectiveness.Under consideration for publication in Theory and Practice of Logic Programming.

Optimizing the computation of overriding in DLN

“…The implementations of Datalog ± and its extensions sometimes adopt optimization techniques developed for deductive databases, such as magic sets, that -like module extraction -have the purpose of focussing reasoning on the symbols relevant to the query. Magic sets have been applied both to the implementation of (monotonic) Datalog ± [56], and to the implementation of Datalog with nonmonotonic negation and aggregates [57]. Therefore, magic sets constitute an appealing candidate for optimized implementations of nonmonotonic Datalog ± .…”

DaRLing: A Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries

“…In this former set of experiments, we first generated Clipper-Rew and DaRLing rewritings for all queries of LUBM, Adolena, Stock Exchange and Vicodì; then, over these rewritings and for all considered datasets, we executed I-DLV under two different scenarios: in the scenario materialize the system is forced to materialize the whole ontology and then prompted to answer to each query individually; in the scenario query-driven the system still runs each query one by one, but performs a more efficient evaluation tailored on the query at hand by enabling the magic sets technique (Alviano et al 2019). Figure 2 reports average running times in seconds of I-DLV executions over all datasets on LUBM, Adolena, Stock Exchange and Vicodì, respectively.…”

Large-scale Ontological Reasoning via Datalog

“…This idea has been also implemented in a specific branch of DLV2 [3], with promising results. The rewriting implemented by DLV2 is further processed by a new version of the magic sets algorithm [5], which inhibits the creation of new recursive dependencies and partially unroll the magic sets rewriting if binding information are lost. The inhibition of new recursive definitions is important because magic sets were originally introduced for Datalog programs [10], and their extension to programs with stratified negation was nontrivial; indeed, the perfect model semantics [48] is not applicable to the rewritten program if recursive negation is introduced by magic sets, and several semantics were considered in the literature to overcome this limitation [9,13,37,38,52].…”