Statements about RDF statements, or meta triples, provide additional information about individual triples, such as the source, the occuring time or place, or the certainty. Integrating such meta triples into semantic knowledge bases would enable the querying and reasoning mechanisms to be aware of provenance, time, location, or certainty of triples. How- ever, an efficient RDF representation for such meta knowledge of triples remains challenging. The existing reification approach allows such meta knowledge of RDF triples to be expressed using RDF by two steps. The first step is representing the triple by a Statement instance which has subject, predicate, and object indicated separately in three different triples. The second step is creating assertions about that instance as if it is a statement. While reification is simple and intuitive, this approach does not have formal semantics and is not commonly used in practice as described in the RDF Primer. In this paper, we propose a novel approach called Singleton Property for representing meta triples and provide a for- mal semantics for it. We explain how this singleton property approach fits well with the existing syntax and formal semantics of RDF, and the syntax of SPARQL query lan- guage. We also demonstrate the use of singleton property in the representation and querying of meta knowledge in two examples of Semantic Web knowledge bases: YAGO2 and BKR. This approach, which is also simple and intuitive, can be easily adopted for representing and querying statements about statements in other knowledge bases.

1. Don’t like RDF Reification?
Making Statements about Statements
Using Singleton Property
Vinh Nguyen
Kno.e.sis
Wright State University
Olivier Bodenreider
National Library of Medicine
National Institute of Health
Amit Sheth
Kno.e.sis
Wright State University
WWW 2014, Seoul

2. Linked Open Data
• > 70% Metadata
• Relation Extraction from
unstructured text (PubMed, Wiki)
• Evidences
• Judgement
2

3. Motivation Scenario
Starts Ends
1965-11-22 1977-06-29
1986-06-## 1992-10-##
Facts:
Meta Queries:
Query type Sample query
Provenance P1. Where is this fact from?
P2. When was it created?
P3. Who created this fact?
Time T1. When did this fact occur?
T2. What is the time span of this fact?
T3. Which events happened in the same year?
Location L1. What is the location associated with this fact?
L2. Which events happened at the same place?
Certainty C1. What is the author confidence of this fact?
3
Subject Predicate Object
Bob Dylan marriedTo Sarah Lownds
Bob Dylan marriedTo Carolyn Dennis

4. Form of Triples: Standard RDF Reification
Subject Predicate Object Starts Ends
Bob Dylan marriedTo Sarah Lownds 1965-11-22 1977-06-29
Standard RDF Reification
Pros:
1. Intuitive, easy to understand
Cons:
1. Takes 3N triples (4N if including
Statement typing) to represent a
statement => Not scalable
2. No formal semantics defined =>
Semantics is unclear
3. Discouraged in LOD!
Time-aware Facts:
4
Subject Predicate Object
#stmt1 type Statement
#stmt1 hasSubject BobDylan
#stmt1 hasProperty marriedTo
#stmt1 hasObject Sara Lownds
Bob Dylan marriedTo Sarah Lownds
#stmt1 starts 1965-11-22
#stmt1 ends 1977-06-29

5. RDF Reification vs. Singleton Property
Time-aware Facts:
Subject Predicate Object Starts Ends
Bob Dylan marriedTo Sarah Lownds 1965-11-22 1977-06-29
Standard RDF Reification
Subject Predicate Object
#stmt1 type Statement
#stmt1 hasSubject BobDylan
#stmt1 hasProperty marriedTo
#stmt1 hasObject Sara Lownds
Bob Dylan marriedTo Sarah Lownds
#stmt1 starts 1965-11-22
#stmt1 ends 1977-06-29
Singleton Property
Subject Predicate Object
marriedTo#1 rdf:sp marriedTo
BobDylan marriedTo#1 Sarah Lownds
marriedTo#1 starts 1965-11-22
marriedTo#1 ends 1977-06-29
5

6. Form of Triples: PaCE
Subject Predicate Object Source DateExtracted
Bob Dylan marriedTo Sarah Lownds wikipage:Bob_Dylan 2009-06-07
Pros:
1. Save ~50% number of triples
compared to reification thanks
to the repeated subject,
predicate, and object.
Cons:
1. Not intuitive, hard to
understand
2. Limited expressiveness
Provenance-aware Facts:
6
Provenance-aware Context Entity
Subject Predicate Object
BobDylan_wp rdf:type Bob Dylan
SaraLownds_wp rdf:type Sara Lownds
BobDylan_wp marriedTo SaraLownds_wp
BobDylan_wp hasSource wiki:Bob_Dylan
BobDylan_wp hasDateExt 2009-06-07
Satya S. Sahoo, Olivier Bodenreider, Pascal Hitzler, Amit Sheth, and Krishnaprasad Thirunarayan. 2010.
Provenance context entity (PaCE): scalable provenance tracking for scientific RDF data. In Proceedings
of the 22nd international conference on Scientific and statistical database management (SSDBM'10),

7. Facts and Provenance:
Subject Predicate Object Source DateExtracted
Bob Dylan marriedTo Sarah Lownds wikipage:Bob_Dylan 2009-06-07
Provenance-aware Context Entity
Subject Predicate Object
BobDylan_wp rdf:type Bob Dylan
SaraLownds_wp rdf:type Sara Lownds
BobDylan_wp marriedTo SaraLownds_wp
BobDylan_wp hasSource wiki:Bob_Dylan
BobDylan_wp hasDateExt 2009-06-07
7
PaCE vs. Singleton Property
Singleton Property
Subject Predicate Object
marriedTo#1 rdf:sp marriedTo
BobDylan marriedTo#1 Sarah Lownds
marriedTo#1 hasSource wp:Bob_Dylan
marriedTo#1 hasDateExt 2009-06-07

8. Form of Quadruples: Named Graph
Subject Predicate Object Starts Ends
Bob Dylan marriedTo Sarah Lownds 1965-11-22 1977-06-29
Named Graph
Subject Predicate Object NG
Bob Dylan marriedTo Sarah Lownds ng_1
ng_1 starts 1965-11-22 Prov_graph
ng_2 ends 1977-06-29 Prov_graph
Pros:
1. Intuitive --creating # named graphs
for # sources
2. Attach metadata for a set of triples
3. SPARQL supported
Cons
:
1. Defined for provenance only
2. Ambiguous semantics while
associating different types of
metadata at triple level
Time-aware Facts:
8
* Carroll, Jeremy J., et al. "Named graphs, provenance and trust." Proceedings of the 14th international conference on World Wide Web. ACM, 2005.

9. Named Graph vs. Singleton Property
Time-aware Facts:
Subject Predicate Object Starts Ends
Bob Dylan marriedTo Sarah Lownds 1965-11-22 1977-06-29
Named Graph
Subject Predicate Object NG
Bob Dylan marriedTo Sarah Lownds ng_1
ng_1 starts 1965-11-22 Prov_graph
ng_2 ends 1977-06-29 Prov_graph
Singleton Property
Subject Predicate Object
marriedTo#1 rdf:sp marriedTo
Bob Dylan marriedTo#1 Sarah Lownds
marriedTo#1 starts 1965-11-22
marriedTo#1 ends 1977-06-29 9

10. Facts and Temporal Information:
RDF+:
Form of Quintuples: RDF+
Subject Predicate Object Meta Property Meta value
Bob Dylan marriedTo Sarah Lownds starts 1965-11-22
Bob Dylan marriedTo Sarah Lownds ends 1977-06-29
Cons
1. The r:epresentation is not in the form of RDF. Statement identifiers are used
internally. Require the mappings from RDF to RDF+ and vice versa.
2. The SPARQL query syntax and semantics need to be extended to support RDF+
* Dividino, Renata, et al. "Querying for provenance, trust, uncertainty and other meta knowledge in RDF." Web
Semantics: Science, Services and Agents on the World Wide Web 7.3 (2009): 204-219.
10
Subject Predicate Object Starts Ends
Bob Dylan marriedTo Sarah Lownds 1965-11-22 1977-06-29

11. Overall Goal
A mechanism to make statements about statements
should meet these requirements:
1. Intuitive, easy to understand 2. Formal semantics defined
3. Scalable, e.g., to LOD
4. Compatible with existing standards
5. Multiple types of metadata
11

12. Generic Property vs. Singleton Property
Facts and Provenance:
Subject Predicate Object Source MarriageDate
Bob Dylan marriedTo Sarah Lownds wikipage:Bob_Dylan 1965-11-22
BarackObama marriedTo MichelleObama wikipage:Barack_Obama 1992-10-03
Generic Property:
1. marriedTo is an RDF property
instanceOf
2. marriedTo => {
(Bob Dylan, Sarah Dylan),
(Barack Obama, Michelle Obama),
…
…
}
3. Any assertion to marriedTo is
applicable to all pairs of entities!
Singleton Property:
1. marriedTo#1, marriedTo#2 are
RDF property
2. Different property instances:
marriedTo#1,
marriedTo#2,
…
marriedTo#n
3. Any assertion to
marriedTo#1/marriedTo#2/…/mar
riedTo#n is applicable to only ONE
pair <= KEY
12

13. Model-Theoretic Semantics
Original* Simple Interpretation I :
• Given a vocabulary V,
New simple Interpretation I :
satisfies additional criteria as follows:
• IPS: a subset of IR, called the set of
singleton properties of I,
• IS_EXT (ps): is a function assigning to each
singleton property a pair of entities from
IR.
New RDF Interpretation I :
satisfies additional criteria as follows:
• xs ∈ IPs if
⟨xs, rdf:SingletonPropertyI⟩ ∈ IEXT (rdf:typeI)
• IR: a non-empty set of resources,
alternatively called domain or
universe of discourse of I.
• IP: the set of generic properties of I
• IEXT: a function assigning to each
property a set of pairs from IR
where IEXT (p) is called the extension
of property p
• IEXT : IP → 2IR X IR
• IS: a function, mapping URIs from
V into the union set of IR and IP,
• IL: a function from the typed
literals from V into the set of
resources IR,
• LV: a subset of IR, called the set of
literal values.
IS_EXT : IPS→ IR X IR.
• xs ∈ IPs if
⟨xs, xI⟩ ∈ IEXT (rdf:singletonPropertyOfI),
and x∈IP, IS_EXT (xs) = <s1, s2>
13

14. Model-Theoretic Semantics: Example
IR = {α, β, γ, δ, θ, λ, σ, ϕ}
IP = {δ, θ, λ, σ, ϕ}
LV = {1965-11-22, 1977-06-29,
1986-06-##, 1992-10-##}
IEXT = θ → {⟨α, β⟩}
λ → {⟨α, γ⟩}
σ → {⟨θ, 1965-11-22 ⟩,
⟨λ, 1986-06-## ⟩}
φ → {⟨θ, 1977-06-29⟩,
⟨λ, 1992-10-## ⟩}
rdf:sp → {⟨θ, δ⟩, ⟨λ, δ⟩}
δ → {⟨α, β⟩, ⟨α, γ⟩}
IPS = {θ, λ}
IS_EXT= θ→⟨α,β⟩
λ → ⟨α,γ⟩
Example of vocabulary VEX:
RDF Interpretation of VEX:
Subject Predicate Object
BobDylan isMarriedTo Sarah Lownds
BobDylan isMarriedTo#1 SaraLownds
isMarriedTo#1 rdf:sp isMarriedTo
isMarriedTo#1 hasStart 1965-11-22
isMarriedTo#1 hasEnd 1977-06-29
BobDylan isMarriedTo CarolynDennis
BobDylan isMarriedTo#2 CarolynDennis
isMarriedTo#2 rdf:sp isMarriedTo
isMarriedTo#2 hasStart 1986-06-##
isMarriedTo#2 hasEnd 1992-10-##
IS:
BobDylan → α
SaraLownds → β
CarolynDennis → γ
isMarriedTo → δ
isMarriedTo#1 → θ
isMarriedTo#2 → λ
hasStart → σ
hasEnd → φ
14

15. Querying Meta Triples Using SPARQL
Singleton Graph Pattern
Triple Type Subject Predicate Object
Instantiating singleton property predicate_i rdf:sp predicate
Singleton triple subject predicate_i object
Meta triple predicate_i meta-predicate_j meta-value_j
Data Query:
1. Who married whom?
2. SPARQL query
SELECT ?person1 ?person2
WHERE {
?person1 ?married_sp ?person2 .
?married_sp rdf:sp :marriedTo .
}
Meta Query:
1. Who married whom and when?
2. SPARQL query
SELECT ?person1 ?person2 ?time
WHERE {
?person1 ?married_sp ?person2 .
?married_sp rdf:sp :marriedTo .
?married_sp :happenedOn ?date .
}
15

16. Use Case: Temporal and Spatial YAGO2S
16
FactID in Yago2s
FactID Subject Predicate Object
#1 GratefulDead performed TheClosingOfWinterLand
#2 #1 occursIn SanFrancisco
#3 #1 occursOn 1978-12-31
Singleton Property
Subject Predicate Object
performed_12345 rdf:singletonPropertyOf performed
GratefulDead performed_12345 TheClosingOfWinterLand
performed_12345 occursIn SanFrancisco
performed_12345 occursOn 1978-12-31

17. Experiment: BKR with Provenance
• Five data sets generated from the same seed BKR
 Singleton Property (SP)
 Reification (R)
 PaCE C1 (C1)
 PaCE C2 (C2)
 PaCE C3 (C3)
All datasets are available at http://wiki.knoesis.org/index.php/Singleton_Property 17

18. Experiment Results
(A) random-value queries vs. fixed-value queries in msec.
(B) query length and execution time in msec. 18

19. Conclusion
Does the singleton property approach meet these
3. Scalable, e.g., to LOD
requirements?
1. Intuitive, easy to understand 2. Formal semantics defined
4. Compatible with existing standards
5. Multiple types of metadata
19

20. Further information, please visit
http://wiki.knoesis.org/index.php/Singleton_Property
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