Download Direct Mapping DM

On Directly Mapping Relational
Databases to RDF and OWL
Juan F. Sequeda
Marcelo Arenas
Daniel P. Miranker
Agenda
 Direct
Mapping and Property
 Direct Mapping DM
 Properties of DM
 Extended DM
 Conclusion
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

Fundamental Properties
 Information

If direct mapping does not lose any
information about the relational instance
being translated.
 Query

Preservation
Preservation
if every query over a relational database
can be translated into an equivalent query
over the RDF graph resulting from the
mapping.
Desirable Properties
 Monotonicity

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.
Direct Mapping DM
 Storing
relational databases
 Storing an ontology
 Translating relational schemas into OWL
 Translating database instances into RDF
 Example
Storing relational databases

REL(r)


ATTR(a,r)


e.g. PK("SID","STUDENT")
FK(a,r,b,s)


e.g. ATTR("NAME","STUDENT")
PK(a,r)


e.g. REL("STUDENT")
e.g. FK("CODE","COURSE","DID","DEPT")
VALUE(v,a,t,r)

e.g. VALUE("1","SID","id1","STUDENT")
Storing an ontology
 Class(c)

c is a class
 OPn(p1,…,pn,d,r)

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.
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")

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")

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")

Storing an ontology(cont'd)
 Identifying
data type properties:
DTP(A,R) ←
ATTR(A,R), ¬ISBINREL(R)
 E.g.
DTP("NAME","STUDENT")

Translating schemas into OWL
 Generating

IRI
Class
CLASSIRI(R,X) ←
CLASS(R),CONCAT(base,R,X)
E.g.
http://example.edu/db/STUDENT

Data type property
DTP_IRI(A,R,X) ← DTP(A,R),
CONCAT(base,R,"#",A,X)
E.g.
http://example.edu/db/STUDENT#NAME
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.
http://example.edu/db/ENROLLED#SID,CID,SID,CID
OP_IRI(X,Y,S,T,X) ←
OP(X,Y,S,T),
CONCAT(base,S,",",T,"#",X,",",Y,X)
E.g.
http://example.edu/db/COURSE,DEPT#CODE,DID
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)
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)
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:
http://example.edu/db/STUDENT#SID=1


BLANKNODE(T,R,X) ←
VALUE(V,A,T,R), CONCAT("_:",R,T,X)
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)
TUPLEID(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("http://example.edu/db/STUDENT#SID=1",
"rdf:type",
"http://example.edu/db/STUDENT")
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("http://example.edu/db/STUDENT#SID=1",
"http://example.edu/db/ENROLLED#SID,CID,SID,CID",
"http://example.edu/db/COURSE#CID=1")
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("http://example.edu/db/COURSE#CID=1",
"http://example.edu/db/COURSE,DEPT#CODE,DID",
"http://example.edu/db/DEPT#DID=1")
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("http://example.edu/db/STUDENT#SID=1",
"http://example.edu/db/STUDENT#NAME",
"John")
Properties of DM
 Information
preservation
 Query preservation
 Monotonicity
 Semantics preservation
Query Preservation of DM
 Translate
relational algebra into
equivalent SPARQL query

selection projection rename join union
difference

SPARQL query generated by
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.
Extended DM: DMpk

Extended rules
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
Extended DM: DMpk+fk

Extended rules
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
Conclusion
 Direct
mapping DM
Information preservation
 Query preservation
 Monotocity

 Extended
DM
DMpk
 DMpk+fk

 “No
monotone direct mapping is
semantics preserving”
The End