Reasoning in RDFS is Inherently Serial, At Least in The Worst Case

There have recently been several papers presenting scalable distributed inference systems for the W3C Resource Description Framework Schema language (RDFS). These papers have made claims to the effect that they can produce the RDFS closure for billions of RDF triples using parallel hardware. For example, Urbani et al claim “a distributed technique to perform materialization under the RDFS [. . . ] semantics using the MapReduce programming model” [4]. Their initial algorithm used a small number of simple MapReduce passes in sequence to perform distributed materialization. In each pass all all triples are distributed according to the processing performed during that pass, but as well all schema triples (triples with predicate rdfs:domain, rdfs:range, rdfs:subPropertyOf, or rdfs:subClassOf) are sent to all reduce nodes. To handle some of the issues described here, later versions of their algorithm looped through the passes until no new inferences were made. Similarly, Weaver and Hendler claim to be “materializing the complete [emphasis added] finite RDFS closure in a scalable manner” [6]. Their algorithm uses a single MapReduce pass and sends ontological triples (schema triples plus triples with predicate rdf:type and object rdfs:Datatype, rdfs:Class, or rdfs:ContainerMembershipProperty) to all reduce nodes. However, the algorithm distributes the other triples evenly, without regard to contents. Each reduce node then produces the finite RDFS closure of its input and these results are finally combined. They call their algorithm “embarrassingly parallel” because the inference part can be split into many independent pieces.