A Direct Mapping of Relational Data to RDF

1 Introduction

Relational databases proliferate both because of their efficiency and their precise definitions, allowing for tools like SQL [SQLFN] to manipulate and examine the contents predictably and efficiently. Resource Description Framework (RDF) [RDF-concepts] is a data format based on a web-scalable architecture for identification and interpretation of terms. This document defines a mapping from relational representation to an RDF representation.

Strategies for mapping relational data to RDF abound. The direct mapping defines a simple transformation, providing a basis for defining and comparing more intricate transformations. It can also be used to materialize RDF graphs or define virtual graphs, which can be queried by SPARQL or traversed by an RDF graph API. This document includes an informal and a formal description of the transformation.

This specification has a companion, the R2RML mapping language [R2RML], that allows the creation of customized mapping from relational data to RDF. R2RML defines a relaxed variant of the Direct Mapping intended as a default mapping for further customization.

2 Direct Mapping Description (Informative)

The direct mapping defines an RDF Graph [RDF-concepts] representation of the data in a relational database. The direct mapping takes as input a relational database (data and schema), and generates an RDF graph that is called the direct graph. The algorithms in this document compose a graph of relative IRIs which must be resolved against a base IRI [RFC3987] to form an RDF graph.

Foreign keys in relational databases establish a reference from any row in a table to exactly one row in a (potentially different) table. The direct graph conveys these references, as well as each value in the row.

2.1 Direct Mapping Example

The concepts in direct mapping can be introduced with an example RDF graph produced by a relational database. Following is SQL (DDL) to create a simple example with two tables with single-column primary keys and one foreign key reference between them:

CREATE TABLE "Addresses" (
	"ID" INT, PRIMARY KEY("ID"), 
	"city" CHAR(10), 
	"state" CHAR(2)
)

CREATE TABLE "People" (
	"ID" INT, PRIMARY KEY("ID"), 
	"fname" CHAR(10), 
	"addr" INT, 
	FOREIGN KEY("addr") REFERENCES "Addresses"("ID")
)

INSERT INTO "Addresses" ("ID", "city", "state") VALUES (18, 'Cambridge', 'MA')
INSERT INTO "People" ("ID", "fname", "addr") VALUES (7, 'Bob', 18)
INSERT INTO "People" ("ID", "fname", "addr") VALUES (8, 'Sue', NULL)

HTML tables will be used in this document to convey SQL tables. The primary key of these tables will be marked with the PK class to convey an SQL primary key such as ID in CREATE TABLE "Addresses" ("ID" INT, ... PRIMARY KEY("ID")). Foreign keys will be illustrated with a notation like "→ Address(ID)" to convey an SQL foreign key such as CREATE TABLE "People" (... "addr" INT, FOREIGN KEY("addr") REFERENCES "Addresses"("ID")).

People
PK		→ Address(ID)
ID	fname	addr
7	Bob	18
8	Sue	NULL

Addresses
PK
ID	city	state
18	Cambridge	MA

Given a base IRI http://foo.example/DB/, the direct mapping of this database produces a direct graph:

@base <http://foo.example/DB/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .


<People/ID=7> rdf:type <People> .
<People/ID=7> <People#ID> 7 .
<People/ID=7> <People#fname> "Bob" .
<People/ID=7> <People#addr> 18 .
<People/ID=7> <People#ref-addr> <Addresses/ID=18> .
<People/ID=8> rdf:type <People> .
<People/ID=8> <People#ID> 8 .
<People/ID=8> <People#fname> "Sue" .

<Addresses/ID=18> rdf:type <Addresses> .
<Addresses/ID=18> <Addresses#ID> 18 .
<Addresses/ID=18> <Addresses#city> "Cambridge" .
<Addresses/ID=18> <Addresses#state> "MA" .

In this expression, each row, e.g. (7, "Bob", 18), produces a set of triples with a common subject. The subject is an IRI formed from the concatenation of the base IRI, table name (People), primary key column name (ID) and primary key value (7). The predicate for each column is an IRI formed from the concatenation of the base IRI, table name and the column name. The values are RDF literals formed from the lexical form of the column value. Each foreign key produces a triple with a predicate composed from the foreign key column names, the referenced table, and the referenced column names. The object of these triples is the row identifier (<Addresses/ID=18>) for the referenced triple. Note that these reference row identifiers must coincide with the subject used for the triples generated from the referenced row. The direct mapping does not generate triples for NULL values. Note that it is not known how to relate the behavior of the obtained RDF graph with the standard SQL semantics of the NULL values of the source RDB.

2.2 Foreign keys referencing candidate keys

More complex schemas include composite keys. In this example, the columns deptName and deptCity in the People table reference name and city in the Department table:

CREATE TABLE "Addresses" (
	"ID" INT, 
	"city" CHAR(10), 
	"state" CHAR(2), 
	PRIMARY KEY("ID")
)

CREATE TABLE "Department" (
	"ID" INT, 
	"name" CHAR(10), 
	"city" CHAR(10), 
	"manager" INT, 
	PRIMARY KEY("ID"), 
	UNIQUE ("name", "city")
)

CREATE TABLE "People" (
	"ID" INT, 
	"fname" CHAR(10), 
	"addr" INT, 
	"deptName" CHAR(10), 
	"deptCity" CHAR(10), 
	PRIMARY KEY("ID"), 
	FOREIGN KEY("addr") REFERENCES "Addresses"("ID"), 
	FOREIGN KEY("deptName", "deptCity") REFERENCES "Department"("name", "city") 
)

ALTER TABLE "Department" ADD FOREIGN KEY("manager") REFERENCES "People"("ID")

Following is an instance of this schema:

People
PK		→ Addresses(ID)	→ Department(name, city)
ID	fname	addr	deptName	deptCity
7	Bob	18	accounting	Cambridge
8	Sue	NULL	NULL	NULL

Addresses
PK
ID	city	state
18	Cambridge	MA

Department
PK	Unique Key		→ People(ID)
ID	name	city	manager
23	accounting	Cambridge	8

Per the People table's compound foreign key to Department:

The row in People with deptName="accounting" and deptCity="Cambridge" references a row in Department with a primary key of ID=23.
The predicate for this key is formed from "deptName" and "deptCity", reflecting the order of the column names in the foreign key.
The object of the above predicate is formed from the base IRI, the table name "Department" and the primary key value "ID=23".

Note: The order of a primary key constraint's columns is determined by the DDL statement used to create it. In SQL implementations that support the information schema, this order can be accessed through the INFORMATION_SCHEMA.KEY_COLUMN_USAGE.ORDINAL_POSITION column.

In this example, the direct mapping generates the following triples:

@base <http://foo.example/DB/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<People/ID=7> rdf:type <People> .
<People/ID=7> <People#ID> 7 .
<People/ID=7> <People#fname> "Bob" .
<People/ID=7> <People#addr> 18 .
<People/ID=7> <People#ref-addr> <Addresses/ID=18> .
<People/ID=7> <People#deptName> "accounting" .
<People/ID=7> <People#deptCity> "Cambridge" .
<People/ID=7> <People#ref-deptName;deptCity> <Department/ID=23> .
<People/ID=8> rdf:type <People> .
<People/ID=8> <People#ID> 8 .
<People/ID=8> <People#fname> "Sue" .

<Addresses/ID=18> rdf:type <Addresses> .
<Addresses/ID=18> <Addresses#ID> 18 .
<Addresses/ID=18> <Addresses#city> "Cambridge" .
<Addresses/ID=18> <Addresses#state> "MA" .

<Department/ID=23> rdf:type <Department> .
<Department/ID=23> <Department#ID> 23 .
<Department/ID=23> <Department#name> "accounting" .
<Department/ID=23> <Department#city> "Cambridge" .
<Department/ID=23> <Department#manager> 8 .
<Department/ID=23> <Department#ref-manager> <People#ID=8> .

The green triples above are generated by considering the new elements in the augmented database. Note:

The Reference Triple <People/ID=7> <People#ref-deptName;deptCity> <Department/ID=23> is generated by considering a foreign key referencing a candidate key (different from the primary key).

2.3 Multi-column primary keys

Primary keys may also be composite. If, in the above example, the primary key for Department were (name, city) instead of ID, the identifier for the only row in this table would be <Department/name=accounting;city=Cambridge>. The triples involving <Department/ID=23> would be replaced with the following triples:

<People/ID=7> <People#ref-deptName;deptCity> <Department/name=accounting;city=Cambridge> . 
<Department/name=accounting;city=Cambridge> rdf:type <Department> . 
<Department/name=accounting;city=Cambridge> <Department#ID> 23 . 
<Department/name=accounting;city=Cambridge> <Department#name> "accounting" .
<Department/name=accounting;city=Cambridge> <Department#city> "Cambridge" .

2.4 Empty (non-existent) primary keys

If there is no primary key, each row implies a set of triples with a shared subject, but that subject is a blank node. A Tweets table can be added to the above example to keep track of employees' tweets in Twitter:

CREATE TABLE "Tweets" (
	"tweeter" INT,
	"when" TIMESTAMP,
	"text" CHAR(140),
	FOREIGN KEY("tweeter") REFERENCES "People"("ID")
)

The following is an instance of table Tweets:

Tweets
→ People(ID)
tweeter	when	text
7	2010-08-30T01:33	I really like lolcats.
7	2010-08-30T09:01	I take it back.

Given that table Tweets does not have a primary key, each row in this table is identified by a Blank Node. In fact, when translating the above table the direct mapping generates the following triples:

@base <http://foo.example/DB/>
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

_:a rdf:type <Tweets> .
_:a <Tweets#tweeter> "7" .
_:a <Tweets#ref-tweeter> <People/ID=7> .
_:a <Tweets#when> "2010-08-30T01:33"^^xsd:dateTime .
_:a <Tweets#text> "I really like lolcats." .

_:b rdf:type <Tweets> .
_:b <Tweets#tweeter> "7" .
_:b <Tweets#ref-tweeter> <People/ID=7> .
_:b <Tweets#when> "2010-08-30T09:01"^^xsd:dateTime .
_:b <Tweets#text> "I take it back." .

2.5 Referencing tables with empty primary keys

Rows in tables with no primary key may still be referenced by foreign keys. (Relational database theory tells us that these rows must be unique as foreign keys reference candidate keys and candidate keys are unique across all the rows in a table.) References to rows in tables with no primary key are expressed as RDF triples with blank nodes for objects, where that blank node is the same node used for the subject in the referenced row.

Here is DDL for a schema with references to a Projects table which has no primary key:

CREATE TABLE "Projects" (
	"lead" INT,
	FOREIGN KEY ("lead") REFERENCES "People"("ID"),
	"name" VARCHAR(50), 
	UNIQUE ("lead", "name"), 
	"deptName" VARCHAR(50), 
	"deptCity" VARCHAR(50),
	UNIQUE ("name", "deptName", "deptCity"),
	FOREIGN KEY ("deptName", "deptCity") REFERENCES "Department"("name", "city")
)

CREATE TABLE "TaskAssignments" (
	"worker" INT,
	FOREIGN KEY ("worker") REFERENCES "People"("ID"),
	"project" VARCHAR(50), 
	PRIMARY KEY ("worker", "project"), 
	"deptName" VARCHAR(50), 
	"deptCity" VARCHAR(50),
	FOREIGN KEY ("worker") REFERENCES "People"("ID"),
	FOREIGN KEY ("project", "deptName", "deptCity") REFERENCES "Projects"("name", "deptName", "deptCity"),
	FOREIGN KEY ("deptName", "deptCity") REFERENCES "Department"("name", "city")
)

The following is an instance of the preceding schema:

Projects
Unique key
	Unique key
→ People(ID)		→ Department(name, city)
lead	name	deptName	deptCity
8	pencil survey	accounting	Cambridge
8	eraser survey	accounting	Cambridge

TaskAssignments
PK
	→ Projects(name, deptName, deptCity)
→ People(ID)		→ Departments(name, city)
worker	project	deptName	deptCity
7	pencil survey	accounting	Cambridge

In this case, the direct mapping generates the following triples from the preceding tables:

@base <http://foo.example/DB/>
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

_:c rdf:type <Projects> .
_:c <Projects#lead> <People/ID=8> .
_:c <Projects#name> "pencil survey" .
_:c <Projects#deptName> "accounting" .
_:c <Projects#deptCity> "Cambridge" .
_:c <Projects#ref-deptName;deptCity> <Department/ID=23> .

_:d rdf:type <Projects> .
_:d <Projects#lead> <People/ID=8> .
_:d <Projects#name> "eraser survey" .
_:d <Projects#deptName> "accounting" .
_:d <Projects#deptCity> "Cambridge" .
_:d <Projects#ref-deptName;deptCity> <Department/ID=23> .

<TaskAssignments/worker=7.project=pencil%20survey> rdf:type <TaskAssignments> .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#worker> 7 .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#ref-worker> <People/ID=7> .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#project> "pencil survey" .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#deptName> "accounting" .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#deptCity> "Cambridge" .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#ref-deptName;deptCity> <Department/ID=23> .
<TaskAssignments/worker=7.project=pencil%20survey> <TaskAssignments#ref-project;deptName;deptCity> _:c .

The absence of a primary key forces the generation of blank nodes, but does not change the structure of the direct graph or names of the predicates in that graph.

3 Direct Graph Definition

The Direct Graph is a formula for creating an RDF graph from the rows of each table and view in a database schema. A base IRI defines a web space for the IRIs in this graph; for the purposes of this specification, all IRIs are generated by appending to a base. Terms enclosed in <> are defined in the SQL specification [SQLFN].

An SQL table has a set of uniquely-named columns and has a set of foreign keys, each mapping a <column name list> to a <unique column list> (a list of columns in some table).

SQL table and column identifiers compose RDF IRIs in the direct graph. These identifiers are separated by the punctuation characters '#', ';', '/' and '='. All SQL identifiers are escaped following R2RML's escaping rules.

Definition percent-encode:

Replace the string with the IRI-safe form per section 7.3 of [R2RML].

There is either a blank node or IRI assigned to each each row in a table:

Definition row node:

If the table has a primary key, the row node is a relative IRI obtained by concatenating:
- the percent-encoded form of the table name,
- the SOLIDUS character '/',
- for each column in the primary key, in order:
  - the percent-encoded form of the column name,
  - a EQUALS SIGN character '=',
  - the percent-encoded lexical form of the canonical RDF literal representation of the column value as defined in R2RML section 10.2 Natural Mapping of SQL Values [R2RML],
  - if it is not the last column in the primary key, a SEMICOLON character ';'
If the table has no primary key, the row node is a fresh blank node that is unique to this row.

A table forms a table IRI:

Definition table IRI: the relative IRI consisting of the percent-encoded form of the table name.

A column in a table forms a literal property IRI:

Definition literal property IRI: the concatenation of:

the percent-encoded form of the table name,
the hash character '#',
the percent-encoded form of the column name.

A foreign key in a table forms a reference property IRI:

Definition reference property IRI: the concatenation of:

the percent-encoded form of the table name,
the string '#ref-',
for each column in the foreign key, in order:
- the percent-encoded form of the column name,
- if it is not the last column in the foreign key, a SEMICOLON character ';'

Any input database with a given schema has a direct graph defined as:

Definition direct graph: the union of the table graphs for each table in a database schema.

Definition table graph: the union of the row graphs for each row in a table.

Definition row graph: an RDF graph consisting of the following triples:

the row type triple.
a reference triple for each <column name list> in a table's foreign keys where none of the column values is NULL.
a literal triple for each column in a table where the column value is non-NULL.

Definition row type triple: an RDF triple with:

subject: the row node for the row.
predicate: the RDF IRI rdf:type.
object: the table IRI for the table name.

Definition literal triple: an RDF triple with:

subject: the row node for the row.
predicate: the literal property IRI for the column.
object: the R2RML natural RDF literal representation of the column value as defined in R2RML section 10.2 Natural Mapping of SQL Values.

Definition reference triple: an RDF triple with:

subject: the row node for the row.
predicate: the reference property IRI for the columns.
object: the row node for the referenced row.

4 References

R2RML: R2RML: RDB to RDF Mapping Language , Souripriya Das, Seema Sundara, Richard Cyganiak, Editors. World Wide Web Consortium, 27 September 2012. This version is http://www.w3.org/TR/2012/REC-r2rml-20120927/. The latest version is http://www.w3.org/TR/r2rml/. This document is work in progress.
SPARQL: SPARQL Query Language for RDF, Eric Prud'hommeaux and Andy Seaborne 2008. (See http://www.w3.org/TR/rdf-sparql-query/.)
SQLFW: SQL. ISO/IEC 9075-1:2008 SQL – Part 1: Framework (SQL/Framework) International Organization for Standardization, 27 January 2009.
SQLFN: ISO/IEC 9075-2:2008 SQL – Part 2: Foundation (SQL/Foundation) International Organization for Standardization, 27 January 2009.
RDF-concepts: Resource Description Framework (RDF): Concepts and Abstract Syntax, G. Klyne, J. J. Carroll, Editors, W3C Recommendation, 10 February 2004 (See http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/.)
ReuseableIDs: Reusable Identifiers in the RDB2RDF mapping language, Michael Hausenblas and Themis Palpanas, 2009. (See http://esw.w3.org/topic/Rdb2RdfXG/ReusableIdentifier.)
URI: RFC3986 - Uniform Resource Identifier (URI): Generic Syntax (See http://tools.ietf.org/html/rfc3986.)
RFC3987: RFC3987 - Internationalized Resource Identifier (IRIs) (See http://tools.ietf.org/html/rfc3987.)
SQL2SW: Translating SQL Applications to the Semantic Web. Syed Hamid Tirmizi, Juan Sequeda and Daniel Miranker. 2008 (See http://www.springerlink.com/content/mv58805364k31734/.)
DMSurvey: Survey of directly mapping SQL databases to the Semantic Web. Juan Sequeda, Syed Hamid Tirmizi, Oscar Corcho, Daniel P. Miranker. 2011 (See http://journals.cambridge.org/abstract_S0269888911000208.)

A Direct Mapping Algebra (Informative)

A.1 Notations

The RDB and RDF data models make use of the commonly defined Abstract Data Types Set, List and MultiSet, used here as type constructors. For example, Set(A) denotes the type for the sets of elements of type A. We assume that they come with their common operations, such as the function size : Set → Int.

The definitions follow a type-as-specification approach; thus the models are based on dependent types. For example, { s:Set(A) | size(s) ≤ 1 } is a type denoting the sets for elements of type A, such that those sets have at most one element.

The denotational RDF semantics makes use of the set-builder notation for building the RDF sets.

The buttons below can be used to show or hide the available syntaxes.

A.2 Relational Data Model

A.2.1 RDB Abstract Data Type

[1]	`Database`	::=	`Set(Table)`
[1]	`Database`	::=	`{ Table }`
A relational database is a set of tables.
[2]	`Table`	::=	`(TableName, Set((ColumnName, Datatype)), Set(CandidateKey), Set(PrimaryKey) \| size() ≤ 1, Set(ForeignKey), Body)`
[2]	`Table`	::=	`( TableName, { ColumnName → Datatype }, { CandidateKey }, PrimaryKey?, { ForeignKey }, Body )`
A relation has a name uniquely defining this table in the database; an associative array mapping each column to a SQL datatype; a potentially empty list of candidate keys, possibly including a primary key; a potentially empty set of foreign keys; a body containing the rows of data.
[3]	`Body`	::=	`MultiSet(Row)`
[3]	`Body`	::=	`[ Row ]`
A body is a set of potentially duplicate rows.
[4]	`Row`	::=	`Set((ColumnName, CellValue))`
[4]	`Row`	::=	`{ ColumnName → CellValue }`
A row is a associative array mapping each column in a row to a value.
[5]	`CellValue`	::=	`Value \| NULL`
[5]	`CellValue`	::=	`Value \| Null`
A cell value is either a lexical value or NULL, denoting the absence of value.
[6]	`ForeignKey`	::=	`(List(ColumnName), Table, CandidateKey)`
[6]	`ForeignKey`	::=	`{ [ColumnName] → ( Table, [ColumnName] ) }`
A foreign key constrains the values of a <column name list> to be equivalent (by the SQL `=` operator) to the values of a <unique column list> in some row of the referenced table.
[7]	`PrimaryKey`	::=	`CandidateKey`
[7]	`PrimaryKey`	::=	`CandidateKey`
A primary key is a candidate key with the additional constraint that none of the columns can have a NULL value.
[8]	`CandidateKey`	::=	`List(ColumnName)`
[8]	`CandidateKey`	::=	`[ ColumnName ]`
A candidate key is an SQL <unique column list> in some table. This constrains that no two rows in the table have values for the <unique column list> which are all equivalent (by the SQL `=` operator).
[9]	`Datatype`	::=	`Int \| Float \| Date \| …`
[9]	`Datatype`	::=	`{ INT \| FLOAT \| DATE \| TIME \| TIMESTAMP \| CHAR \| VARCHAR \| STRING }`
A datatype is a common SQL datatype.
[10]	`TableName`	::=	`String`
[10]	`TableName`	::=	`String`
A table name is a string.
[11]	`ColumnName`	::=	`String`
[11]	`ColumnName`	::=	`String`
A column name is a string.

A.2.2 RDB accessor functions

[12]	`tablename`	:	`Table → TableName`
Given a table, tablename returns its name.
[13]	`header`	:	`Table → Set((ColumnName, Datatype))`
Given a table, header returns its header.
[14]	`candidateKeys`	:	`Table → List(CandidateKey)`
Given a table, candidateKeys returns the list of candidate keys.
[15]	`primaryKey`	:	`Table → { s:Set(CandidateKey) \| size(s) ≤ 1 }`
Given a table, primaryKey returns a set containing the primary key if it exists, otherwise it returns an empty set.
[16]	`foreignKeys`	:	`Table → Set(ForeignKey)`
Given a table, foreignKeys returns the set of foreign keys.
[17]	`unary`	:	`ForeignKey → Boolean`
Given a foreign key, unary tells if this is a unary foreign key, meaning it has exactly one column.
[18]	`lexicals`	:	`Table → Set({ c:ColumnName \| ! unary(c) })`
Given a table, lexicals returns the set of columns that do not constitute a unary foreign key.
[19]	`body`	:	`Table → Body`
Given a table, body returns its body.
[20]	`datatype`	:	`{ h:Set((ColumnName, Datatype)) } → { c:ColumnName \| ∃ d, (c,d) ∈ h } → { d:Datatype \| (c,d) ∈ h }`
Given a header and a column in this header, datatype returns the datatype associated with this column.
[21]	`table`	:	`{ r:Row } → { t:Table \| r ∈ t }`
Given a row, table returns the table to which this row belongs.
[22]	`value`	:	`{ r:Row } → { a:ColumnName \| a ∈ r } → CellValue`
Given a row and a column in this row, value returns the cell value (can be NULL) for this column.
[23]	`dereference`	:	{ r:Row } → { fk:ForeignKey \| fk ∈ foreignKeys(table(r)) } → { targetRow:Row \| let (columnNames, targetTable, ck) = fk in targetRow ∈ body(targetTable) and ∀ c_i^fk ∈ columnNames, ∀ c_j^ck ∈ ck, ∀ (c_k^r, v_k^r) ∈ r, ∀ (c_l^target, v_l^target) ∈ targetRow, i = j → c_i^fk = c_k^r → c_j^ck = c_l^target → v_k^r = v_l^target }
Given a row and a foreign key from the table containing this row, dereference returns the row which is referenced by this foreign key, i.e. the row for which the values of the foreign key's <unique column list> are all equivalent (by the SQL `=` operator) to the values for the foreign key's <column name list> in the referring table.

A.3 RDF Data Model

Per RDF Concepts and Abstract Syntax, an RDF graph is a set of triples of a subject, predicate and object. The subject may be an IRI or a blank node, the predicate must be an IRI and the object may be an IRI, blank node, or an RDF literal.

This section recapitulates for convience the formal definition of RDF.

[24]	`Graph`	::=	`Set(Triple)`
[24]	`Graph`	::=	`{ Triple }`
An RDF graph is a set of RDF triples.
[25]	`Triple`	::=	`(Subject, Predicate, Object)`
[25]	`Triple`	::=	`( Subject, Predicate, Object )`
An RDF triple is composed of a subject, predicate and object.
[26]	`Subject`	::=	`IRI \| BlankNode`
[26]	`Subject`	::=	`IRI \| BlankNode`
A subject is either an IRI or a blank node.
[27]	`Predicate`	::=	`IRI`
[27]	`Predicate`	::=	`IRI`
A predicate is always an IRI.
[28]	`Object`	::=	`IRI \| BlankNode \| Literal`
[28]	`Object`	::=	`IRI \| BlankNode \| Literal`
An object is either an IRI, a blank node, or a literal.
[29]	`BlankNode`	::=	`RDF blank node`
[29]	`BlankNode`	::=	`RDF blank node`
A blank node is an arbitrary term used only to establish graph connectivity.
[30]	`Literal`	::=	`PlainLiteral \| TypedLiteral`
[30]	`Literal`	::=	`PlainLiteral \| TypedLiteral`
A literal is either a plain literal or a typed literal.
[31]	`PlainLiteral`	::=	`lexicalForm \| (lexicalForm, langageTag)`
[31]	`PlainLiteral`	::=	`(lexicalForm) \| (lexicalForm, langageTag)`
A plain literal has a lexical form and an optional language tag.
[32]	`TypedLiteral`	::=	`(lexicalForm, IRI)`
[32]	`TypedLiteral`	::=	`(lexicalForm, IRI)`
An typed literal is composed of lexical form and a datatype IRI.
[33]	`IRI`	::=	`RDF URI-reference as subsequently restricted by SPARQL`
[33]	`IRI`	::=	`RDF URI-reference as subsequently restricted by SPARQL`
An IRI is an RDF URI reference as subsequently restricted by SPARQL.
[34]	`lexicalForm`	::=	`a Unicode String`
[34]	`lexicalForm`	::=	`a Unicode String`
SQL string representing a value.

A.4 Denotational semantics

In this model, Databases are inhabitants of RDB and they are denoted by mathematical objects living in the RDF domain. This denotational semantics is what we call the Direct Mapping.

The url-encoding function renders strings in a form suitable to insert into IRIs. Data values are expressed in the XML Schema canonical form before url-encoding.

[35]	`ue`	:	`String → String`
[35]	`UE(s)`	=	s percent-encoded.
Replace the string with the IRI-safe form per section 7.3 of [R2RML].
	`⟦ , ⟧_canon`	:	`(Row, Column) → String`
[36]	`⟦r, c⟧_canon`	=	`let v = value(r, c) in let d = header(table(r)) in canonical RDF literal(v, d)`
[36]	`canon(A)`	=	`canonical RDF literal(A)`
lexical form of the canonical RDF literal representation of the column value as defined in R2RML section 10.2 Natural Mapping of SQL Values [R2RML]

Most of the functions defining the Direct Mapping are higher-order functions parameterized by a function φ(r) row_node(r) which maps any row to a unique IRI or Blank Node.

[37]	`φ`	:	`∀ db:Database, ∀ r:Row, r ∈ db if primaryKey(table(r)) ≠ ∅ then ue(tablename(table(r))) + '/' + ue(c₀) + '=' + ue(canon(r, c₀)) + ';' + ⋯ + ';' + ue(c_n-1) + '=' + ue(canon(r, c_n-1)) else a BlankNode unique to r`
[37]	`row_node`	=	`if (pk(R) ≠ ∅) then IRI(UE(R.name) + "/" + (join(';', UE(A.name) + '=' + UE(canon(A))) ∣ A ∈ As )) else a BlankNode unique to r`
If the table has a primary key, the row node is a relative IRI obtained by concatenating: the percent-encoded form of the table name, the SOLIDUS character '/', for each column in the primary key, in order: the percent-encoded form of the column name, a EQUALS SIGN character '=', the percent-encoded lexical form of the canonical RDF literal representation of the column value as defined in R2RML section 10.2 Natural Mapping of SQL Values, if it is not the last column in the primary key, a SEMICOLON character ';' If the table has no primary key, the row node is a fresh blank node that is unique to this row.
	`⟦ ⟧_tableIRI`	:	`TableName → IRI`
[38]	`⟦t⟧_tableIRI`	=	ue(tablename(t))
[38]	`table_IRI(R)`	=	`IRI(R.name)`
the relative IRI consisting of the percent-encoded form of the table name.
	`⟦ , ⟧_litcol`	:	`(Row, Column) → IRI`
[39]	`⟦r, c⟧_litcol`	=	`ue(tablename(table(r))) + '#' + ue(c))`
[39]	`literal_property_IRI(R, A)`	=	`IRI(UE(R.name) + "#" + UE(A.name))`
the concatenation of: the percent-encoded form of the table name, the hash character '#', the percent-encoded form of the column name.
	`⟦ , ⟧_refcol`	:	`(Row, ForeignKey) → IRI`
[40]	`⟦r, fk⟧_refcol`	=	`let(from, reftable, to) = fk in ue(tablename(table(r))) + '/ref-' + ue(from₀) + ';' + ⋯ + ';' + ue(from_n-1)`
[40]	`reference_property_IRI(R, As)`	=	`IRI(UE(R.name) + "#ref-" + join(';', UE(A.name)) ∣ A ∈ As )`
the concatenation of: the percent-encoded form of the table name, the string '#ref-', for each column in the foreign key, in order: the percent-encoded form of the column name, if it is not the last column in the foreign key, a SEMICOLON character ';'

The Direct Mapping is defined by induction on the structure of RDB. Thus it is defined for any relational database. The entry point for the Direct Mapping is the function ⟦ ⟧^φ_database direct_graph(r).

	`⟦ ⟧^φ_database`	:	`Database → Graph`
[41]	`⟦db⟧^φ_database`	=	`{ triple \| triple ∈ ⟦t⟧^φ_table \| t ∈ db }`
[41]	`direct_graph()`	=	`{ table_graph(R) ∣ R ∈ DB }`
the union of the table graphs for each table in a database schema.
	`⟦ ⟧^φ_table`	:	`Table → Set(Triple)`
[42]	`⟦t⟧^φ_table`	=	`{ triple \| triple ∈ ⟦r⟧^φ_row \| r ∈ body(t) }`
[42]	`table_graph(R)`	=	`{ row_graph(T, R) ∣ T ∈ R.Body }`
the union of the row graphs for each row in a table.
	`noNULLs`	:	`Row → ForeignKey → Boolean`
[43]	`noNULLs(r, fk)`	=	`let (columnNames, _, _) = fk in ∀ c ∈ columnNames, value(r, c) ≠ NULL`
[43]	`noNULLs(T, As)`	=	`∄(T(A) = Null ∣ A ∈ As)`
	`⟦ ⟧^φ_row`	:	`Row → Set(Triple)`
[44]	`⟦r⟧^φ_row`	=	`let s = φ(r) in { ⟦r⟧^φ_type } ⋃ { ⟦r, c⟧^φ_lex \| value(r, c) ≠ NULL \| c ∈ lexicals(r) } ⋃ { ⟦r, fk⟧^φ_ref \| noNULLs(r, fk) \| fk ∈ foreignKeys(table(r)) }`
[44]	`row_graph(T, R)`	=	`{ type_triple(R) } ∪ { literal_triple(R, A) ∣ A ≠ Null ∧ [A] ∉ R.ForeignKeys(T) } ∪ { reference_triple(As, T) ∣ noNULLs(T, As) ∧ As ≠ R.PrimaryKey ∣ As ∈ R.ForeignKeys(T)`
an RDF graph consisting of the following triples: the row type triple. a reference triple for each <column name list> in a table's foreign keys where none of the column values is NULL. a literal triple for each column in a table where the column value is non-NULL.
	`⟦ ⟧_type`	:	`(Row) → Triple`
[45]	`⟦r⟧_type`	=	`let s = φ(r) in let t = table(r) in let o = ⟦t⟧_tableIRI in { (s, rdf:type, o) }`
[45]	`type_triple(R)`	=	`triple(row node(R), rdf:type, table-IRI(R))`
an RDF triple with: subject: the row node for the row. predicate: the RDF IRI `rdf:type`. object: the table IRI for the table name.
	`⟦ , ⟧_lex`	:	`(Row, Column) → Triple`
[46]	`⟦r, c⟧_lex`	=	`let s = φ(r) in let p = ⟦table(r), c⟧_litcol in let v = value(r, c) in let d = header(table(r)) in if v is NULL then ∅ else let o = natural RDF literal(v, d) in { (s, p, o) }`
[46]	`literal_triple(R, A)`	=	`triple(row node(R), literal_property_IRI(R, [A]), natural RDF literal(A))`
an RDF triple with: subject: the row node for the row. predicate: the literal property IRI for the column. object: the R2RML natural RDF literal representation of the column value as defined in R2RML section 10.2 Natural Mapping of SQL Values.
	`⟦ , ⟧_ref`	:	`(Row, ForeignKey) → Triple`
[47]	`⟦r, fk⟧_ref`	=	`let s = φ(r) in let targetSpec = dereference(r, fk) in let p = ⟦table(r), fk⟧_refcol in let o = φ(row(targetSpec)) in (s, p, o)`
[47]	`reference_triple(R, As)`	=	`triple(row node(R), reference_property_IRI(R, As), row_node(row referenced by (R, As)))`
an RDF triple with: subject: the row node for the row. predicate: the reference property IRI for the columns. object: the row node for the referenced row.

B Direct Mapping as Rules (Informative)

In this section, we formally present the Direct Mapping as rules in Datalog syntax, inspired by the previous approaches in [SQL2SW] [DMSurvey]. The left hand side of each rule is the RDF Triple output. The right hand side of each rule consists of a sequence of predicates from the relational database and built-in predicates. The built-in predicates are divided into four groups. The first group contains some built-in predicates for dealing with repeated rows in a table without a primary key.

card(r, l, k): Given a table name r without a primary key and the list l of values [v₁, ..., v_n] for a row of table r, it returns in k the multiplicity of l in r (that is, k is the number of times row l appears in r)
n ≤ m: This is the usual order on positive integer values (given positive integers n and m, it holds if n is smaller than or equal to m)

The second group contains a predicate to deal with null values.

nonNull(v): Given a value v, it holds if v is not null

The third group of built-in predicates is used to generate IRIs for identifying tables and the columns in a table, and to generate IRIs or blank nodes for identifying each row in a table.

generateTableIRI(r, i): Given a table name r, it generates the table IRI i of r
generateLiteralPropertyIRI(r, a, i): Given a table name r and an attribute name a, it generates the literal property IRI i for a
generateReferencePropertyIRI(r, l, i): Given a table name r and a non-empty list of columns l, it generates the reference property IRI i for l
generateRowIRI(r, l₁, l₂, i): Given a table name r, a non-empty list l₁ of columns and a non-empty list l₂ of values (for the columns in l₁), it generates the row node (or Row IRI) i for the given row
generateRowBlankNode(r, l, n, i): Given a table name r without a primary key, a list l of values for a row of table r and a positive integer n, it generates the row node i for the n-th occurrence of row l in r (which is a Blank Node in this case). It is assumed that n is smaller than or equal to the multiplicity of l in r (that is, if card(r, l, k) holds, then 1 ≤ n ≤ k)

Finally, the fourth group of built-in predicates is used to generate typed literals.

generateTypedLiteral(u, a, r, v): Given a value u, an attribute name a and a table name r, it generates an R2RML natural RDF literal v representation of the column value u, given the type of a in r and as defined in R2RML section 10.2 Natural Mapping of SQL Values.

Throughout the section, boxes containing Direct Mapping rules and examples will appear. These boxes are color-coded. Yellow boxes contain Direct Mapping rules:

This box contains a Direct Mapping rule

Green boxes contain examples of applying the previous Direct Mapping rule:

This box contains examples of applying a Direct Mapping rule

Consider again the example from Section Direct Mapping Example. It should be noticed that in the rules presented in this section, a formula of the form Addresses(X, Y, Z) indicates that the variables X, Y and Z are used to store the values of a row in the three columns of the table Addresses (according to the order specified in the schema of the table, that is, X, Y and Z store the values of ID, city and state, respectively). In particular, uppercase letters like X, Y, Z, S, P and O are used to denote variables. Moreover, double quotes are used in the rules to refer to the string with the name of a table or a column. For example, a formula of the form generateRowIRI("Addresses", ["ID"], [X], S) is used to generate the row node (or Row IRI) for the row of table "Addresses" whose value in the primary key "ID" is the value stored in the variable X. The value of this Row IRI is stored in the variable S.

B.1 Generating Row Type Triples

B.1.1 Table has a primary key

Assume that r is a table with columns a₁, ..., a_m and such that [a_p₁, ..., a_{p_n}] is the primary key of r, where 1 ≤ n ≤ m and 1 ≤ p₁ < ... < p_n ≤ m. Then the following is the direct mapping rule to generate row type triples from r:

Triple(S, "rdf:type", O) ← r(X₁, ..., X_m), generateRowIRI("r", ["a_p₁", ..., "a_{p_n}"], [X_p₁, ..., X_{p_n}], S), generateTableIRI("r", O)

For example, table Addresses in the Direct Mapping Example has columns ID, city and state, and it has column ID as its primary key. Then the following is the direct mapping rule to generate row type triples from Addresses:

Triple(S, "rdf:type", O) ← Addresses(X₁, X₂, X₃), generateRowIRI("Addresses", ["ID"], [X₁], S), generateTableIRI("Addresses", O)

As a second example, consider table Department from the example in Section Foreign keys referencing candidate keys, which has columns ID, name, city and manager, and assume that (name, city) is the multi-column primary key of this table (instead of ID). Then the following is the direct mapping rule to generate row type triples from Department:

Triple(S, "rdf:type", O) ← Department(X₁, X₂, X₃, X₄), generateRowIRI("Department", ["name","city"], [X₂, X₃], S), 
                            generateTableIRI("Department", O)

B.1.2 Table does not have a primary key

Assume that r is a table with columns a₁, ..., a_m and such that r does not have a primary key. Then the following is the direct mapping rule to generate row type triples from r:

Triple(S, "rdf:type", O) ← r(X₁, ..., X_m), card("r", [X₁, ..., X_m], U), V ≤ U, generateRowBlankNode("r", [X₁, ..., X_m], V, S),
                            generateTableIRI("r", O)

For example, table Tweets from Section Empty (non-existent) primary keys has columns tweeter, when and text, and it does not have a primary key. Then the following is the direct mapping rule to generate row type triples from Tweets:

Triple(S, "rdf:type", O) ← Tweets(X₁, X₂, X₃), card("Tweets", [X₁, X₂, X₃], U), V ≤ U, generateRowBlankNode("Tweets", [X₁, X₂, X₃], V, S),
                            generateTableIRI("Tweets", O)

B.2 Generating Literal Triples

B.2.1 Table has a primary key

Assume that r is a table with columns a₁, ..., a_m and such that [a_p₁, ..., a_{p_n}] is the primary key of r, where 1 ≤ n ≤ m and 1 ≤ p₁ < ... < p_n ≤ m. Then for every a_j (1 ≤ j ≤ m), the direct mapping includes the following rule for r and a_j to generate literal triples:

Triple(S, P, V) ← r(X₁, ..., X_m), nonNull(X_j), generateRowIRI("r", ["a_p₁", ..., "a_{p_n}"], [X_p₁, ..., X_{p_n}], S),
                   generateLiteralPropertyIRI("r", "a_j", P), generateTypedLiteral(X_j, "a_j", "r", V)

For example, table Addresses in the Direct Mapping Example has columns ID, city and state, and it has column ID as its primary key. Then the following are the direct mapping rules to generate literal triples from Addresses:

Triple(S, P, V) ← Addresses(X₁, X₂, X₃), nonNull(X₁), generateRowIRI("Addresses", ["ID"], [X₁], S),
                   generateLiteralPropertyIRI("Addresses", "ID", P), generateTypedLiteral(X₁, "ID", "Addresses", V)
Triple(S, P, V) ← Addresses(X₁, X₂, X₃), nonNull(X₂), generateRowIRI("Addresses", ["ID"], [X₁], S), 
                   generateLiteralPropertyIRI("Addresses", "city", P), generateTypedLiteral(X₂, "city", "Addresses", V)
Triple(S, P, V) ← Addresses(X₁, X₂, X₃), nonNull(X₃), generateRowIRI("Addresses", ["ID"], [X₁], S),
                   generateLiteralPropertyIRI("Addresses", "state", P), generateTypedLiteral(X₃, "state", "Addresses", V)

As a second example, consider again table Department from the example in Section Foreign keys referencing candidate keys, which has columns ID, name, city and manager, and assume that (name, city) is the multi-column primary key of this table (instead of ID). Then the following are the direct mapping rules to generate literal triples from Department:

Triple(S, P, V) ← Department(X₁, X₂, X₃, X₄), nonNull(X₁), generateRowIRI("Department", ["name", "city"], [X₂, X₃], S), 
                   generateLiteralPropertyIRI("Department", "ID", P), generateTypedLiteral(X₁, "ID", "Department", V)
Triple(S, P, V) ← Department(X₁, X₂, X₃, X₄), nonNull(X₂), generateRowIRI("Department", ["name", "city"], [X₂, X₃], S), 
                   generateLiteralPropertyIRI("Department", "name", P), generateTypedLiteral(X₂, "name", "Department", V)
Triple(S, P, V) ← Department(X₁, X₂, X₃, X₄), nonNull(X₃), generateRowIRI("Department", ["name", "city"], [X₂, X₃], S), 
                   generateLiteralPropertyIRI("Department", "city", P), generateTypedLiteral(X₃, "city", "Department", V)
Triple(S, P, V) ← Department(X₁, X₂, X₃, X₄), nonNull(X₄), generateRowIRI("Department", ["name", "city"], [X₂, X₃], S), 
                   generateLiteralPropertyIRI("Department", "manager", P), generateTypedLiteral(X₄, "manager", "Department", V)

B.2.2 Table does not have a primary key

Assume that r is a table with columns a₁, ..., a_m and such that r does not have a primary key. Then for every a_j (1 ≤ j ≤ m), the direct mapping includes the following rule for r and a_j to generate literal triples:

Triple(S, P, V) ← r(X₁, ..., X_m), nonNull(X_j), card("r", [X₁, ..., X_m], U), V ≤ U, generateRowBlankNode("r", [X₁, ..., X_m], V, S), 
                   generateLiteralPropertyIRI("r", "a_j", P), generateTypedLiteral(X_j, "a_j", "r", V)

For example, table Tweets from Section Empty (non-existent) primary keys has columns tweeter, when and text, and it does not have a primary key. Then the following are the direct mapping rules to generate literal triples from Tweets:

Triple(S, P, V) ← Tweets(X₁, X₂, X₃), nonNull(X₁), card("Tweets", [X₁, X₂, X₃], U), V ≤ U, generateRowBlankNode("Tweets", [X₁, X₂, X₃], V, S), 
                   generateLiteralPropertyIRI("Tweets", "tweeter", P), generateTypedLiteral(X₁, "tweeter", "Tweets", V)
Triple(S, P, V) ← Tweets(X₁, X₂, X₃), nonNull(X₂), card("Tweets", [X₁, X₂, X₃], U), V ≤ U, generateRowBlankNode("Tweets", [X₁, X₂, X₃], V, S), 
                   generateLiteralPropertyIRI("Tweets", "when", P), generateTypedLiteral(X₂, "when", "Tweets", V)
Triple(S, P, V) ← Tweets(X₁, X₂, X₃), nonNull(X₃), card("Tweets", [X₁, X₂, X₃], U), V ≤ U, generateRowBlankNode("Tweets", [X₁, X₂, X₃], V, S), 
                   generateLiteralPropertyIRI("Tweets", "text", P), generateTypedLiteral(X₃, "text", "Tweets", V)

B.3 Generating Reference Triples

For each foreign key from a table r₁ to a table r₂, one of the following four cases is applied.

B.3.1 Table r₁ has a primary key and table r₂ has a primary key

Assume that:

r₁ is a table with columns a₁, ..., a_i and such that [a_p₁, ..., a_{p_j}] is the primary key of r₁, where 1 ≤ j ≤ i and 1 ≤ p₁ < ... < p_j ≤ i
r₂ is a table with columns c₁, ..., c_k and such that [c_q₁, ..., c_{q_m}] is the primary key of r₂, where 1 ≤ m ≤ k and 1 ≤ q₁ < ... < q_m ≤ k
the foreign key indicates that the columns a_s₁, ..., a_{s_n} of r₁ reference the columns c_t₁, ..., c_{t_n} of r₂, where (1) 1 ≤ s₁, ..., s_n ≤ i, (2) 1 ≤ t₁, ..., t_n ≤ k, and (3) n ≥ 1

Then the direct mapping includes the following rule for r₁ and r₂ to generate Reference Triples:

Triple(S, P, O) ← r₁(X₁, ..., X_i), generateRowIRI("r₁", ["a_p₁", ..., "a_{p_j}"], [X_p₁, ..., X_{p_j}], S), 
                   r₂(Y₁, ..., Y_k), generateRowIRI("r₂", ["c_q₁", ..., "c_{q_m}"], [Y_q₁, ..., Y_{q_m}], O), 
                   nonNull(X_s₁), ..., nonNull(X_{s_n}), X_s₁ = Y_t₁, ...,  X_{s_n} = Y_{t_n},  generateReferencePropertyIRI("r₁", ["a_s₁", ..., "a_{s_n}"], P)

For example, table Addresses in the Direct Mapping Example has columns ID, city and state, where column ID is the primary key. Table People in this example has columns ID, fname and addr, where column ID is the primary key, and it has a foreign key in the column addr that references the column ID in the table Addresses. In this case, the following is the direct mapping rule to generate Reference Triples:

Triple(S, P, O) ← People(X₁, X₂, X₃), generateRowIRI("People", ["ID"], [X₁], S),  
                   Addresses(Y₁, Y₂, Y₃), generateRowIRI("Addresses", ["ID"], [Y₁], O),  
                   nonNull(X₃), X₃ = Y₁,  generateReferencePropertyIRI("People", ["addr"], P)

B.3.2 Table r₁ has a primary key and table r₂ does not have a primary key

Assume that:

r₁ is a table with columns a₁, ..., a_i and such that [a_p₁, ..., a_{p_j}] is the primary key of r₁, where 1 ≤ j ≤ i and and 1 ≤ p₁ < ... < p_j ≤ i
r₂ is a table with columns c₁, ..., c_k, and it does not have a primary key
the foreign key indicates that the columns a_s₁, ..., a_{s_n} of r₁ reference the columns c_t₁, ..., c_{t_n} of r₂, where (1) 1 ≤ s₁, ..., s_n ≤ i, (2) 1 ≤ t₁, ..., t_n ≤ k, and (3) n ≥ 1

Then the direct mapping includes the following rule for r₁ and r₂ to generate Reference Triples:

Triple(S, P, O) ← r₁(X₁, ..., X_i), generateRowIRI("r₁", ["a_p₁", ..., "a_{p_j}"], [X_p₁, ..., X_{p_j}], S),
                   r₂(Y₁, ..., Y_k), card("r₂", [Y₁, ..., Y_k], U), V ≤ U, generateRowBlankNode("r₂", [Y₁, ..., Y_k], V, O), 
                nonNull(X_s₁), ..., nonNull(X_{s_n}), X_s₁ = Y_t₁, ...,  X_{s_n} = Y_{t_n},  generateReferencePropertyIRI("r₁", ["a_s₁", ..., "a_{s_n}"], P)

For example, assume that table Addresses in the Direct Mapping Example has columns ID, city and state, and that column ID is a candidate key (instead of a primary key), so that table Addresses does not have a primary key. Moreover, assume that table People in this example has columns ID, fname and addr, it has column ID as its primary key, and it has a foreign key in the column addr to the candidate key ID in the table Addresses. In this case, the following is the direct mapping rule to generate Reference Triples:

Triple(S, P, O) ← People(X₁, X₂, X₃), generateRowIRI("People", ["ID"], [X₁], S), 
                   Addresses(Y₁, Y₂, Y₃), card("Addresses", [Y₁, Y₂, Y₃], U), V ≤ U, generateRowBlankNode("Addresses", [Y₁, Y₂, Y₃], V, O), 
                   nonNull(X₃), X₃ = Y₁,  generateReferencePropertyIRI("People", ["addr"], P)

B.3.3 Table r₁ does not have primary key and table r₂ has a primary key

Assume that:

r₁ is a table with columns a₁, ..., a_i, and it does not have a primary key
r₂ is a table with columns c₁, ..., c_k and such that [c_q₁, ..., c_{q_m}] is the primary key of r₂, where 1 ≤ m ≤ k and 1 ≤ q₁ < ... < q_m ≤ k
the foreign key indicates that the columns a_s₁, ..., a_{s_n} of r₁ reference the columns c_t₁, ..., c_{t_n} of r₂, where (1) 1 ≤ s₁, ..., s_n ≤ i, (2) 1 ≤ t₁, ..., t_n ≤ k, and (3) n ≥ 1

Then the direct mapping includes the following rule for r₁ and r₂ to generate Reference Triples:

Triple(S, P, O) ← r₁(X₁, ..., X_i), card("r₁", [X₁, ..., X_i], U), V ≤ U, generateRowBlankNode("r₁", [X₁, ..., X_i], V, S), 
                   r₂(Y₁, ..., Y_k), generateRowIRI("r₂", ["c_q₁", ..., "c_{q_m}"], [Y_q₁, ..., Y_{q_m}], O), 
                   nonNull(X_s₁), ..., nonNull(X_{s_n}), X_s₁ = Y_t₁, ...,  X_{s_n} = Y_{t_n},  generateReferencePropertyIRI("r₁", ["a_s₁", ..., "a_{s_n}"], P)

For example, table People in the Direct Mapping Example has columns ID, fname and addr, and it has column ID as its primary key, while table Tweets from Section Empty (non-existent) primary keys has columns tweeter, when and text, it does not have a primary key, and it has a foreign key in column tweeter that references column ID in table People. In this case, the following is the direct mapping rule to generate Reference Triples:

Triple(S, P, O) ← Tweets(X₁, X₂, X₃), card("Tweets", [X₁, X₂, X₃], U), V ≤ U, generateRowBlankNode("Tweets", [X₁, X₂, X₃], V, S), 
                   People(Y₁, Y₂, Y₃), generateRowIRI("People", ["ID"], [Y₁], O), 
                   nonNull(X₁), X₁ = Y₁, generateReferencePropertyIRI("Tweets", ["tweeter"], P)

B.3.4 Table r₁ does not have primary key and table r₂ does not have a primary key

Assume that:

r₁ is a table with columns a₁, ..., a_i, and it does not have a primary key
r₂ is a table with columns c₁, ..., c_k, and it does not have a primary key
the foreign key indicates that the columns a_s₁, ..., a_{s_n} of r₁ reference the columns c_t₁, ..., c_{t_n} of r₂, where (1) 1 ≤ s₁, ..., s_n ≤ i, (2) 1 ≤ t₁, ..., t_n ≤ k, and (3) n ≥ 1

Then the direct mapping includes the following rule for r₁ and r₂ to generate Reference Triples:

Triple(S, P, O) ← r₁(X₁, ..., X_i), card("r₁", [X₁, ..., X_i], U₁), V₁ ≤ U₁, generateRowBlankNode("r₁", [X₁, ..., X_i], V₁, S), 
                   r₂(Y₁, ..., Y_k), card("r₂", [Y₁, ..., Y_k], U₂), V₂ ≤ U₂, generateRowBlankNode("r₂", [Y₁, ..., Y_k], V₂, O), 
                   nonNull(X_s₁), ..., nonNull(X_{s_n}), X_s₁ = Y_t₁, ...,  X_{s_n} = Y_{t_n},  generateReferencePropertyIRI("r₁", ["a_s₁", ..., "a_{s_n}"], P)

For example, assume that table People in the Direct Mapping Example has columns ID, fname and addr, and that column ID is a candidate key (instead of a primary key), so that People does not have a primary key. Moreover, assume that table Tweets from Section Empty (non-existent) primary keys has columns tweeter, when and text, it does not have a primary key, and it has a foreign in column tweeter that references candidate key ID in table People. In this case, the following is the direct mapping rule to generate Reference Triples:

Triple(S, P, O) ← Tweets(X₁, X₂, X₃), card("Tweets", [X₁, X₂, X₃], U₁), V₁ ≤ U₁, generateRowBlankNode("Tweets", [X₁, X₂, X₃], V₁, S), 
                   People(Y₁, Y₂, Y₃), card("People", [Y₁, Y₂, Y₃], U₂), V₂ ≤ U₂, generateRowBlankNode("People", [Y₁, Y₂, Y₃], V₂, O), 
                   nonNull(X₁), X₁ = Y₁, generateReferencePropertyIRI("Tweets", ["tweeter"], P)

A Direct Mapping of Relational Data to RDF

W3C Recommendation 27 September 2012

Abstract

Status of this Document

Table of Contents

Appendices

1 Introduction

2 Direct Mapping Description (Informative)

2.1 Direct Mapping Example

2.2 Foreign keys referencing candidate keys

2.3 Multi-column primary keys

2.4 Empty (non-existent) primary keys

2.5 Referencing tables with empty primary keys

3 Direct Graph Definition

4 References

A Direct Mapping Algebra (Informative)

A.1 Notations

A.2 Relational Data Model

A.2.1 RDB Abstract Data Type

A.2.2 RDB accessor functions

A.3 RDF Data Model

A.4 Denotational semantics

B Direct Mapping as Rules (Informative)

B.1 Generating Row Type Triples

B.1.1 Table has a primary key

B.1.2 Table does not have a primary key

B.2 Generating Literal Triples

B.2.1 Table has a primary key

B.2.2 Table does not have a primary key

B.3 Generating Reference Triples

B.3.1 Table r₁ has a primary key and table r₂ has a primary key

B.3.2 Table r₁ has a primary key and table r₂ does not have a primary key

B.3.3 Table r₁ does not have primary key and table r₂ has a primary key

B.3.4 Table r₁ does not have primary key and table r₂ does not have a primary key

A Direct Mapping of Relational Data to RDF

W3C Recommendation 27 September 2012

Abstract

Status of this Document

Table of Contents

Appendices

1 Introduction

2 Direct Mapping Description (Informative)

2.1 Direct Mapping Example

2.2 Foreign keys referencing candidate keys

2.3 Multi-column primary keys

2.4 Empty (non-existent) primary keys

2.5 Referencing tables with empty primary keys

3 Direct Graph Definition

4 References

A Direct Mapping Algebra (Informative)

A.1 Notations

A.2 Relational Data Model

A.2.1 RDB Abstract Data Type

A.2.2 RDB accessor functions

A.3 RDF Data Model

A.4 Denotational semantics

B Direct Mapping as Rules (Informative)

B.1 Generating Row Type Triples

B.1.1 Table has a primary key

B.1.2 Table does not have a primary key

B.2 Generating Literal Triples

B.2.1 Table has a primary key

B.2.2 Table does not have a primary key

B.3 Generating Reference Triples

B.3.1 Table r1 has a primary key and table r2 has a primary key

B.3.2 Table r1 has a primary key and table r2 does not have a primary key

B.3.3 Table r1 does not have primary key and table r2 has a primary key

B.3.4 Table r1 does not have primary key and table r2 does not have a primary key

B.3.1 Table r₁ has a primary key and table r₂ has a primary key

B.3.2 Table r₁ has a primary key and table r₂ does not have a primary key

B.3.3 Table r₁ does not have primary key and table r₂ has a primary key

B.3.4 Table r₁ does not have primary key and table r₂ does not have a primary key