Motivation and Main Results. Over the past years, we have been witnessing an enormous growth of the Semantic Web through initiatives like Open Linked Data [5] and Open Government Data [14, 25]. As was noted by He et al. [13] and Madhavan et al. [17], to a large extent, the data accessible on the web still originates from relational databases. The design of these databases often follows speci c principles, called normal forms, developed in the beginnings of relational database research, see, e.g., [11, 12]. The goal of this work is to transfer these principles, in particular the BoyceCodd Normal Form (BCNF), to RDF graphs enhanced with RDFS statements. To establish and justify this normal form for RDF graphs, we need the following: (1) A mapping of relational databases to RDF graphs and (2) identi cation constraints that capture functional dependencies (FDs) over RDF graphs. For (1), W3C has recognized the importance of a standardized mapping of relational data to the Semantic Web data format RDF. To this end, the so-called direct mapping has been released as a W3C Recommendation [2]. Note that the direct mapping to RDF does not transfer the semantic information that may be present in the relational schema, e.g. functional or inclusion dependencies. We are going to study an enrichment of the direct mapping by transferring also important semantic information from relational to RDF data. Initial work on this includes the recent proposal to extend the direct mapping by the use of RDFS and OWL 2 vocabularies [21], achieving the transfer of primary and foreign keys. The mapping in [21] enjoys several important properties such as query-preservation. However, if the RDF graph resulting from such a mapping is later changed (through update, delete, or insert operations), then the correspondence between the relational and the RDF data may get lost. We therefore propose a further extension of the direct mapping that uses DL-LiteRDFS [3] | extended with disjointness | as basis. DL-LiteRDFS is a variant of DL-LiteA [7] and captures the Description Logic (DL) fragment of RDFS [6]. While this DL is simple and allows for e cient reasoning, it naturally captures conceptual modeling constructs, and hence can express dependencies over RDF graphs. We introduce a mapping d2r that produces from a database instance an RDF graph together with a mapping ? This is an extended abstract of [10]. The rst author has been partially supported by the Wolfgang Pauli Institute Vienna, and by the EU IP project Optique(grant agreement n. FP7-318338). The remaining authors have been partially supported by the Austrian Science Fund (FWF) project P25207-N23 and P25518-N23, and by the Vienna Science and Technology Fund (WWTF) project ICT12-15.
sm that outputs from a relational schema a DL TBox constraining RDF graphs. For this we use the well-known rei cation technique. We keep good properties of the mapping proposed in [21] { such as query preservation. In addition, we also introduce a mapping r2d that produces from an RDF graph (conforming to a DL TBox generated by sm) a database. This allows us to prove a desired one-to-one correspondence between relational databases and legal RDF graphs (i.e., RDF graphs satisfying the constraints of the TBox).
For (2), since functional dependencies (FDs) are a crucial building block in
database design [
As mentioned above, our goal is to nd BCNF-like conditions for RDF graphs. In relational schemas the purpose of using BCNF is to avoid update anomalies. A relational schema is in BCNF if the following holds: whenever a set of given FDs implies an FD from a subset S of the attributes to some attribute A 2= S, we have that S is a super-key, i.e., also implies an FD from S to every attribute of this schema. Our goal is to transfer the favorable properties of BCNF to the RDF world. To this end, we rst analyze how update anomalies can arise in the presence of tids. We identify several paths (stemming from the same tid) identifying the same object as a crucial source of redundancy and hence of update Entrance Hall room
is in 1600 PA Av address loc at
Oval Office room loc at Oval Office room is in
White House is in building
Entrance Hall
room
anomalies. This observation inspires the de nition of an RDF Normal Form
(RNF). Returning to the direct mapping, we prove that a relational schema is
in BCNF if and only if the corresponding TBox with its constraints guarantees
RNF. As a kind of surprise, it turns out that | for relational schemas in BCNF
| the additional expressive power of tree-based ids is not needed to capture FDs.
Indeed, under the restriction to BCNF, the original form of ids introduced by
Calvanese, De Giacomo, and Lenzerini [
Example 1. Consider the two RDF graphs in Figure 1. Both RDF graphs store
data about buildings. Each building has several rooms with an address. Clearly,
all rooms in the same building have the same address. Such a restriction can be
expressed using a tid. In the left RDF graph of Figure 1, the information that the
"White House" is located in "16000 PA Av" is stored redundantly, due to the
design, where rooms in a building have addresses rather than the building has the
address itself. We can avoid such a redundancy by storing the address connected
directly to the building concept, as it is in the right RDF graph of Figure 1. Our
de nition of RNF detects such problems in the design of DL TBoxes with tids.
Future Work On top of our agenda for future research is the extension of our
work on RNF. So far, we have concentrated on preserving BCNF of a relational
schema under the direct mapping of relational data to RDF. However, normal
forms for eliminating redundancies in the data would be an interesting topic for
the design of TBoxes in general. We thus see three main directions to continue our
work. First, we would like to extend the de nition of our RNF to other, maybe
more expressive, DLs than DL-LiteRDFS;tid , e.g. also to the DL CF D introduced
by Toman and Wedell. Note that this raises highly non-trivial questions concerning
the recognizability of the normal form, since our PTIME-membership result for
this task crucially depends on the language restrictions of DL-LiteRDFS;tid .
Second, we also want to investigate relaxations of our de nition of RNF. In our
current de nition, we request that a set of tids must be equivalent to a set of
fully local ids. This allows us to capture BCNF in DL-LiteRDFS;tid . However, for
the de nition of a normal form of more expressive DLs, the equivalence of tids
to a richer class of ids { such as local pids considered by Calvanese et al. [