Answering Queries with Negation over Existential Rules

TL;DR

This paper introduces a new semantics for answering negated queries over existential rules using universal core models, providing syntactic conditions for safe evaluation and new reasoning techniques.

Contribution

It proposes universal core models for negation in existential rules, and identifies syntactic query fragments suitable for current chase implementations.

Findings

Defined universal core models for negation semantics

Identified syntactic query fragments for safe evaluation

Developed new reasoning techniques for existential rules with negation

Abstract

Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon semantics or standard implementation. Stratification, as used for Datalog, is not enough for existential rules, since the latter still admit multiple universal models that can differ on negative queries. We therefore propose universal core models as a basis for a meaningful (non-monotonic) semantics for queries with negation. Since cores are hard to compute, we identify syntactic descriptions of queries that can equivalently be answered over other types of models. This leads to fragments of queries with negation that can safely be evaluated by current chase implementations. We establish new techniques to estimate how the core model differs from other universal models, and we incorporate our findings into a new reasoning approach for existential rules with negation.