1. On Directly Mapping Relational Databases to RDF and OWL
Juan F. Sequeda
Marcelo Arenas
Daniel P. Miranker

2. Agenda Direct Mapping and Property Direct Mapping DM Properties of DM
Extended DM
Conclusion

3. Direct Mapping
A direct mapping is a default and automatic way of translating a relational database to RDF.
A direct mapping M is a total function from RC to G.
RC is the set of all triples of the form(R,Σ,I)
R is relational schema
Σ is a set of PKs and FKs over R
I is an instance of R
G is the set of all RDF graph

4. Fundamental Properties
Information Preservation
If direct mapping does not lose any information about the relational instance being translated.
Query Preservation
if every query over a relational database can be translated into an equivalent query over the RDF graph resulting from the mapping.

5. Desirable Properties Monotonicity Semantics Preservation
if we insert new data to the database, then the elements of the mapping that are already computed are unaltered.
Semantics Preservation
A direct mapping is semantics preserving if the satisfaction of a set of PKs and FKs by a relational database is encoded in the translation process.

6. Direct Mapping DM Storing relational databases Storing an ontology
Translating relational schemas into OWL
Translating database instances into RDF
Example

7. Storing relational databases
REL(r)
e.g. REL("STUDENT")
ATTR(a,r)
e.g. ATTR("NAME","STUDENT")
PK(a,r)
e.g. PK("SID","STUDENT")
FK(a,r,b,s)
e.g. FK("CODE","COURSE","DID","DEPT")
VALUE(v,a,t,r)
e.g. VALUE("1","SID","id1","STUDENT")

8. Storing an ontology Class(c) OPn(p1,…,pn,d,r) DTP(p,d) c is a class
p1,...,pn (n ≥ 1) form an object property with domain d and range r.
DTP(p,d)
p is a data type property with domain d.

9. Storing an ontology(cont'd)
Identifying binary relations:
BINREL(R,A,B,S,C,T,D)←
PK(A,B,R),¬THREEATTR(R),
FK(A,R,C,S),R≠S,
FK(B,R,D,T),R≠T,
¬TWOFK(A,R),¬TWOFK(B,R),
¬ONEFK(A,B,R),¬FKTO(R)
BINREL("ENROLLED","SID","CID", "STUDENT","SID","COURSE","CID")

10. Storing an ontology(cont'd)
Identifying class:
CLASS(X) ← REL(X),¬ISBINREL(X)
ISBINREL(X) ← BINREL(X,A,B,S,C,T,D)
E.g.
CLASS("DEPT")
CLASS("STUDENT")

11. Storing an ontology(cont'd)
Identifying object properties:
OP(X,Y,S,T) ←
FK(X,S,Y,T), ¬ ISBINREL(S)
E.g. OP("CODE","DID","COURSE","DEPT")

12. Storing an ontology(cont'd)
Identifying data type properties:
DTP(A,R) ←
ATTR(A,R), ¬ISBINREL(R)
E.g.
DTP("NAME","STUDENT")

13. Translating schemas into OWL
Generating IRI
Class
CLASSIRI(R,X) ← CLASS(R),CONCAT(base,R,X)
E.g.
Data type property
DTP_IRI(A,R,X) ← DTP(A,R), CONCAT(base,R,"#",A,X)

14. Translating schemas into OWL(cont’d)
Generating IRI
Object property
OP_IRI(R,A,B,S,C,T,D,X) ←
BINREL(R,A,B,S,C,T,D),
CONCAT(base,R,"#",A,",",B,",",C,",",D,X)
E.g.
OP_IRI(X,Y,S,T,X) ←
OP(X,Y,S,T),
CONCAT(base,S,",",T,"#",X,",",Y,X)

15. Translating schemas into OWL(cont’d)
Translating relational schemas
Class
TRIPLE(U,"rdf:type","owl:Class") ←
CLASS(R),CLASSIRI(R,U)
Data type property
TRIPLE(U,"rdf:type","owl:DatatypeProperty") ←
DTP(A,R), DTP_IRI(A,R,U)
TRIPLE(U,"rdfs:domain",W) ←
DTP(A,R), DTP_IRI(A,R,U), CLASSIRI(R,W)

16. Translating schemas into OWL(cont’d)
Translating relational schemas
Object property
TRIPLE(U,"rdf:type","owl:ObjectProperty") ←
OP(X,Y,S,T),OP_IRI(X,Y,S,T,U)
TRIPLE(U, "rdfs:domain",W) ←
OP(X,Y,S,T),OP_IRI(X,Y,S,T,U),CLASSIRI(S,W)
TRIPLE(U, "rdfs:range",W) ←
OP(X,Y,S,T),OP_IRI(X,Y,S,T,U),CLASSIRI(T,W)

17. Translating instances into RDF
Generating IRI
ROWIRI(V,A,T,R,X) ←
PK(A,R), VALUE(V,A,T,R),
CONCAT(base,R,"#",A,"=",V,X)
E.g.
Given VALUE("1","SID","id1","STUDENT") and PK("SID","STUDENT"),the IRI is:
BLANKNODE(T,R,X) ←
VALUE(V,A,T,R), CONCAT("_:",R,T,X)

18. Translating instances into RDF(cont’d)
Translating relational instances
CLASS
TUPLEID(T,R,X) ←
CLASS(R),PK(A,R),
VALUE(V,A,T,R),ROWIRI(V,A,T,R,X)
CLASS(R),¬HASPK(R),
VALUE(V,A,T,R),BLANKNODE(T,R,X)
TRIPLE(U,"rdf:type",W) ←
VALUE(V,A,T,R),TUPLEID(T,R,U),CLASSIRI(R,W)
E.g.
TRIPLE("
"rdf:type",
"

19. Translating instances into RDF(cont’d)
Translating relational instances
Object Property(from BINREL)
TRIPLE(U,V,W) ←
BINREL(R,A,B,S,C,T,D),
VALUE(V1,A,T1,R),VALUE(V1,C,T2,S),
VALUE(V2,B,T1,R),VALUE(V2,D,T3,T),
TUPLEID(T2,S,U),
OP_IRI(R,A,B,S,C,T,D,V),
TUPLEID(T3,T,W)
E.g.
TRIPLE(" "
"

20. Translating instances into RDF(cont’d)
Translating relational instances
Object Property(from FK)
TRIPLE(U,V,W) ←
OP(A,B,S,T),
VALUE(V1,A,T1,S),VALUE(V1,B,T2,T),
TUPLEID(T1,S,U),
OP_IRI(A,B,S,T,V),
TUPLEID(T2,T,W)
E.g.
TRIPLE(" "
"

21. Translating instances into RDF(cont’d)
Translating relational instances
Data type Property
TRIPLE(U,V,W) ←
DTP(A,R),VALUE(W,A,T,R),
W≠NULL,TUPLEID(T,R,U),DTP_IRI(A,R,V)
E.g.
TRIPLE("
"
"John")

22. Properties of DM Information preservation Query preservation
Monotonicity
Semantics preservation

23. Query Preservation of DM
Translate relational algebra into equivalent SPARQL query
selection projection rename join union difference
SPARQL query generated by

24. Semantics Preservation of DM
Example of PK violation
T1.SID = 1, T1.NAME = John
T2.SID = 1, T2.NAME = Peter
Database is inconsistent
Resulting RDF graph is consistent
DM is not semantics preserving.

25. Extended DM: DMpk Extended rules Properties of DMpk
TRIPLE(a,"owl:differentFrom",a) ← PK(X,R),
VALUE(V,X,T1,R),VALUE(V,X,T2,R),T1 ≠ T2
TRIPLE(a,"owl:differentFrom",a) ← PK(X,R),VALUE(V,X,T,R),V = NULL
Properties of DMpk
Information preservation
Query preservation
Monotonicity
Semantic preservation if considers only PKs

26. Extended DM: DMpk+fk Extended rules Properties of DMpk+fk
VIOLATION(S) ← FK(X,S,Y,T),
VALUE(V,X,T,S),V ≠ NULL,
¬ISVALUE(V,Y,T)
TRIPLE(a,"owl:differentFrom", a) ← VIOLATION(S)
Properties of DMpk+fk
Information preservation
Query preservation
Monotonicity
Semantic preservation

27. Conclusion Direct mapping DM Extended DM
Information preservation
Query preservation
Monotocity
Extended DM
DMpk
DMpk+fk
“No monotone direct mapping is semantics preserving”

28. The End
Thank You!