On the semantics of SPARQL queries with optional matching under entailment regimes

We study the semantics of SPARQL queries with optional matching features under entailment regimes. We argue that the normative semantics may lead to answers that are in conflict with the intuitive meaning of optional matching, where unbound variables naturally represent unknown information. We propose an extension of the SPARQL algebra that addresses these issues and is compatible with any entailment regime satisfying the minimal requirements given in the normative specification. We then study the complexity of query evaluation and show that our extension comes at no cost for regimes with an entailment relation of reasonable complexity. Finally, we show that our semantics preserves the known properties of optional matching that are commonly exploited for static analysis and optimisation