Large-Scale Ontological Reasoning via Datalog

Reasoning over OWL 2 is a very expensive task in general, and therefore the W3C identified tractable profiles exhibiting good computational properties. Ontological reasoning for many fragments of OWL 2 can be reduced to the evaluation of Datalog queries. This paper surveys some of these compilations, and in particular the one addressing queries over Horn-SHIQ knowledge bases and its implementation in DLV2 enanched by a new version of the Magic Sets algorithm.

Enhancing Magic Sets with an Application to Ontological Reasoning

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.

Scaling-up reasoning and advanced analytics on BigData

BigDatalog is an extension of Datalog that achieves performance and scalability on both Apache Spark and multicore systems to the point that its graph analytics outperform those written in GraphX. Looking back, we see how this realizes the ambitious goal pursued by deductive database researchers beginning 40 years ago: this is the goal of combining the rigor and power of logic in expressing queries and reasoning with the performance and scalability by which relational databases managed BigData. This goal led to Datalog which is based on Horn Clauses like Prolog but employs implementation techniques, such as semi-naïve fixpoint and magic sets, that extend the bottom-up computation model of relational systems, and thus obtain the performance and scalability that relational systems had achieved, as far back as the 80s, using data-parallelization on shared-nothing architectures. But this goal proved difficult to achieve because of major issues at (i) the language level and (ii) at the system level. The paper describes how (i) was addressed by simple rules under which the fixpoint semantics extends to programs using count, sum and extrema in recursion, and (ii) was tamed by parallel compilation techniques that achieve scalability on multicore systems and Apache Spark. This paper is under consideration for acceptance in Theory and Practice of Logic Programming.

A declarative extension of horn clauses, and its significance for datalog and its applications

FS-rules provide a powerful monotonic extension for Horn clauses that supports monotonic aggregates in recursion by reasoning on the multiplicity of occurrences satisfying existential goals. The least fixpoint semantics, and its equivalent least model semantics, hold for logic programs with FS-rules; moreover, generalized notions of stratification and stable models are easily derived when negated goals are allowed. Finally, the generalization of techniques such as seminaive fixpoint and magic sets, make possible the efficient implementation of DatalogFS, i.e., Datalog with rules with Frequency Support (FS-rules) and stratified negation. A large number of applications that could not be supported efficiently, or could not be expressed at all in stratified Datalog can now be easily expressed and efficiently supported in DatalogFS and a powerful DatalogFS system is now being developed at UCLA.

The magic of logical inference in probabilistic programming

Today, there exist many different probabilistic programming languages as well as more inference mechanisms for these languages. Still, most logic programming-based languages use backward reasoning based on Selective Linear Definite resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato's distribution semantics. We also contribute a novel approximate inference method that integrates forward reasoning with importance sampling, a well-known technique for probabilistic inference. In order to achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence.