Table Of ContentLogical Inferences with Contexts of RDF Triples
Vinh Nguyen Amit Sheth
Kno.e.sisCenter Kno.e.sisCenter
WrightStateUniversity WrightStateUniversity
Dayton,Ohio,USA Dayton,Ohio,USA
[email protected] [email protected]
ABSTRACT knowledge base, as a set of RDF triples, can be created us-
7 Logical inference, an integral feature of the Semantic Web, ingdifferentmethods. Existingdatafromastructuredform
1 istheprocessofderivingnewtriplesbyapplyingentailment (e.g., relational databases, text files, XML documents, or
0 HTML pages) can be transformed into RDF with ontolo-
rules on knowledge bases. The entailment rules are deter-
2 giesdescribingthedatabaseschema(e.g.,Bio2RDF[8]and
minedbythemodel-theoreticsemantics. Incorporatingcon-
PubChem [12]). A knowledge base can also be created by
n textofanRDFtriple(e.g.,provenance,time,andlocation)
extractingthetriplesintheformof(subject,predicate,ob-
a intotheinferencingprocessrequirestheformalsemanticsto
J be capable of describing the context of RDF triples also in ject)fromunstructureddatausingnaturallanguageprocess-
ing algorithms (e.g., Google Knowledge Vault [11], Yago2S
0 theformoftriples,orinotherwords,RDFcontextualtriples
[17], andDBpedia[20]). Ineithermethod, eachRDFtriple
2 about triples. The formal semantics should also provide the
in the resulting knowledge bases can be associated and en-
rules that could entail new contextual triples about triples.
riched with different types of contextual information, such
] Inthispaper,weproposethefirstinferencingmechanism
I asthetimedurationinwhichthetripleholdstrue, andthe
A that allows context of RDF triples, represented in the form
provenance specifying the source of the triple.
of RDF triples about triples, to be the first-class citizens in
. If a knowledge base is created and maintained by an or-
s the model-theoretic semantics and in the logical rules. Our
c inferencemechanismiswell-formalizedwithallnewconcepts ganization, the knowledge integrity can be validated within
[ thatorganization. Nowadays,itiscommonplaceforaknowl-
being captured in the model-theoretic semantics. This for-
malsemanticsalsoallowsustoderiveanewsetofentailment edge base to be created and shared by anyone on the Web,
1
orintheLinkedOpenData. Therefore,webelievethatthe
v rules that could entail new contextual triples about triples.
contextofeveryfactorassertionshouldbeprovidedforcon-
4 To demonstrate the feasibility and the scalability of the
sumerstovalidateandassessthereliabilityoftheknowledge
2 proposedmechanism,weimplementanewtoolinwhichwe
before using it. The contextual information of a triple may
7 transformtheexistingknowledgebasestoourrepresentation
providethetimeintervalorthetimeinstantwhenthetriple
5 ofRDFtriplesabouttriplesandprovidetheoptionforthis
holdstruesothattheconsumerscanvalidateit. Itmayalso
0 tool to compute the inferred triples for the proposed rules.
providetheWebpageorthearticlewherethetriplewasex-
. We evaluate the computation of the proposed rules on a
1 tractedfrom,oranyprovenanceinformationthatallowsfor
large scale using various real-world knowledge bases such
0 tracking the origin of the triples so that the consumers can
as Bio2RDF NCBI Genes and DBpedia. The results show
7 assess the reliability of the triples. Since a fact would not
that the computation of the inferred triples can be highly
1 hold true in every context, the context in which a proposi-
scalable. On average, one billion inferred triples adds 5-6
:
v minutestotheoveralltransformationprocess. NCBIGenes, tionholdstrueneedstobepresentedintheknowledgebases
i with20billiontriplesintotal,tookonly232minutesforthe so that the proposition can be validated and reused.
X
Popular knowledge bases currently represent the contex-
transformationof12billiontriplesandadded42minutesfor
r tualinformationoftheirtriplesintheRDFquadform. For
inferring 8 billion triples to the overall process.
a
example, DBpedia [6], CTD [1], and GO Annotations [2],
NCBI Genes [4], and PharmGKB [5] have the provenance
1. INTRODUCTION
ofeveryRDFtriplerepresentedinthequadform. Sincethe
Semantic Web technologies such as RDF and OWL are fourth element of the RDF quad is not formalized as first-
emergingasstandardlanguagesformachine-understandable class citizen of the current model-theoretic semantics [15],
knowledge representation and reasoning. A Semantic Web itcannotberepresentedintheentailmentrules. Therefore,
to support the inferences involving contextual information
about RDF triples, we believe that the current RDF and
OWL semantics should be expanded to allow for the acco-
modation of contexts of triples as first-class citizens in the
This work is licensed under the Creative Commons Attribution- model-theoretic semantics and entailment rules.
NonCommercial-NoDerivatives4.0InternationalLicense. Toviewacopy
1.1 MotivatingExample
ofthislicense,visithttp://creativecommons.org/licenses/by-nc-nd/4.0/.For
anyusebeyondthosecoveredbythislicense,obtainpermissionbyemailing Givenastatement“BarackObamaismarriedtoMichelle
[email protected].
Obama” (T ), and a sub-property relationship between is-
ProceedingsoftheVLDBEndowment,Vol.10,No.4 1
MarriedToandisSpouseOf (T ),applyingtherulerdfs7[14]
Copyright2016VLDBEndowment2150-8097/16/12. 2
Derivingstatements T : BarackObama isMarriedTo MichelleObama .
1
S1. BarackObamaismarriedtoMichelleObamainIllinois. T4: T1 happenedIn Chicago .
S2. BarackObamaismarriedtoMichelleObamainUSA. T5: Chicago partOf Illinois .
S3. BarackObamabecamespouseofMichelleObamainChicago. T6: Illinois partOf USA .
S4. BarackObamabecamespouseofMichelleObamainIllinois. We call T a primary triple and T a meta triple about
S5. BarackObamabecamespouseofMichelleObamainUSA. location. T1he primary triple T is a4 regular RDF triple,
1
while the meta triple T describes the context in which the
Table 1: Statements inferred from “BarackObama 4
primary triple holds true.
is married to MichelleObama in Chicago”
Considering the original statement represented in T and
1
T , there is no relationship between the triple “Barack-
4
Obama isMarriedTo MichelleObama” and its identifier T .
1
Therefore, there is no relationship between the primary
forrdfs:subPropertyOfonthetwotripleswillentailthenew
triple T and the meta triple T .
triple“BarackObamaisaspouseofMichelleObama”(T ). 1 4
3 Tobridgethisgapandfulfilltherequirementofrepresent-
T1: BarackObama isMarriedTo MichelleObama . ing contextual statements in machine-understandable form
T2: isMarriedTo subPropertyOf isSpouseOf . asdiscussedearlier,severalapproachessuchasnamedgraph
T3: BarackObama isSpouseOf MichelleObama . [9], RDF reification [14], and singleton property [22] can be
Thesetripleswouldprovideenoughknowledgeforanswer- used for representing the relationship between a triple and
ing simple questions. For example, who is Barack Obama itsidentifier. Furthermore,thesemanticsoftherelationship
married to? Or who is spouse of Barack Obama? betweenatripleanditsidentifiermustbecapturedandex-
However,thesetriplesdonotprovidesufficientknowledge pressed as a first-class citizen in the formal semantics. It
to give answers to more complex questions. For example, allows the semantics of the contextual statements to be ex-
whenandwheredidBarackObamamarryMichelleObama? pressed in the formal model as well as in the logical rules.
Was he married to Michelle Obama before 2008? Was he a Among the existing approaches, the singleton property
spouse of Michelle Obama in Harvard, Massachusetts? representation comes with a formal semantics formalizing
To answer these questions, contextual information such the relationship between the singleton property and the
as time and location need to be represented, as in “Barack triple it represents. Meanwhile, although the named graph
Obama is married to Michelle Obama in Chicago in 1992”. couldbeusedasatripleidentifier,itwasnotintendedtobe
Given this contextual statement and the knowledge that used for that purpose. Instead, the named graph is mainly
ChicagoisacityinIllinois,andIllinoisisastateintheUSA, used for representing a set of triples. The RDF reification
weashumanscanquicklyinfermanycontextualstatements does not have a formal semantics for capturing the rela-
which could answer the above questions. Furthermore, we tionshipbetweenastatementinstanceandthetripleitrep-
canalsoinferstatementsthatcouldbemuchdifferentfrom resents. As a result, we choose the singleton property (SP)
the original statement and from each other. For example, representationanduseitssemanticsinourentailmentmech-
the statements S and S in Table 1 only share the subject anism. Correspondingly, all the knowledge bases available
1 5
and the object while their relationships and contextual in- in the form of RDF reification or named graph need to be
formationaretotallydifferent,asshowninTable1withthe transformed into the singleton property representation for
inferred information in bold font. inference purposes.
How does a machine become intelligent enough to infer This paper has two contributions:
contextualstatementsashumansdo? Weaddressthisques-
• We developed a new entailment mechanism that al-
tionby(1)developinganinferencingmechanismthatcould
lowscontextualstatements,representedintheformof
entail new contextual statements and (2) demonstrating an
RDF contextual triples about triples, to be the first-
inferencing process that derives the human-inferred contex-
class citizens in model-theoretic semantics as well as
tual statements from the original statement.
in the logical rules. The proposed mechanism is well-
In order for machines to infer contextual statements,
formalizedwithallnewconceptsforRDFtriplesabout
we believe that two requirements need to be fulfilled.
triples(Section2)beingcapturedbyamodel-theoretic
First, these contextual statements must be represented in
semantics (Section 3). The formal semantics also al-
machine-understandable form, with explicitly defined se-
lows us to derive a new set of rules that could entail
mantics for the relationship between the triple and its con-
new contextual statements (Section 4.1). We demon-
textualinformation. Second,weneedanentailmentmecha-
strate how the human-inferred contextual statements
nismthattakesintoaccountthesemanticsofthecontextual
in Table 1 can be entailed using the proposed rules
triples about triples so that it can entail the new ones.
(Section 4.2).
To the best of our knowledge, there is no RDF/RDFS
inferencing rule that involves RDF contextual triples about • Wedemonstratedthattheproposedentailmentmech-
triples. Our paper addresses this missing capability. anismisscalable. Wedevelopedanewtool,calledrdf-
contextualizer, to transform existing knowledge bases
from the named graph form to the singleton property
1.2 Approach
representation. We then provide the option to com-
The contextual statement “Barack Obama is married to puteallinferredtriplesusingtheproposedcontextual
Michelle Obama in Chicago” is used as an illustrative ex- entailment rules in this tool (Section 5). We evalu-
ample throughout the paper. We represent this contextual atedthecomputationalperformanceinverylargereal-
statementandthebackgroundknowledgeofChicagointhe world knowledge bases with billions of triples such as
form of triples as follows: DBpedia and NCBI Genes (Section 6).
This paper presents the foundational capability. While of pairs while the singleton property is mapped to a single
thelocationcontextandsimplequestionansweringareused pair. If a singleton property also plays the role of a generic
as the illustrative examples, discussions of a broad class of property, it will occur as the predicate in multiple triples.
SemanticWebapplicationssuchasqueryingSPARQLwith This contradicts to the definition of the singleton property.
backward-chaining reasoning, streaming reasoning, tempo- Therefore,asingletonpropertyshouldneverbedefinedasa
ralreasoning,trackingcontextofinferredtriples,andques- generic property. In other words, the set of generic proper-
tion answering based on extracted knowledge and logical ties and the set of singleton properties are disjoint. The
inferences, are beyond the scope of the paper. two classes SingletonProperty and GenericProperty do
The remaining sections are as follows. We present the not share common instances.
related work in Section 7. We discuss the future work in EverygenericpropertyisanRDFproperty,butnotevery
Section 8 and conclude with Section 9. RDFpropertyisagenericpropertyas,forexample,itcould
beasingleton. ThatmakesGenericPropertyasub-classof
2. CONCEPTUALMODEL Property.
rdf:GenericProperty rdfs:subClassOf rdf:Property .
2.1 Preliminaries rdf:SingletonProperty rdfs:subClassOf rdf:Property .
Every generic property is an instance of the Property
Herewerecallthesingletonpropertyconceptwithitssyn-
class. However, one Property instance may not belong to
tax and semantics from [22].
anyoftheclassesSingletonPropertyorGenericProperty.
A singleton property is a specific property instance that
We call this a regular property. In the example at hand,
represents a unique relationship under a specific context.
partOf is a regular property.
For the example at hand, the singleton property isMar-
Althougharegularpropertyinsomecasesmaysharethe
riedTo#1 uniquely represents the isMarriedTo relationship
same property extension with a generic property, it is nec-
betweenBarackObamaandMichelleObama. Thissingleton
essary to make the clear distinction between them.
property can be asserted with contextual information “in
Distinguishing property types. Here we distinguish
Chicago” about the relationship as follows:
three types of properties: singleton, generic, and regular.
SP1: BarackObama isMarriedTo#1 MichelleObama. We also call them context-associated, context-dissociated,
SP2: isMarriedTo#1 singletonPropertyOf isMarriedTo. and context-agnostic property, respectively. A singleton
SP3: isMarriedTo#1 happenedIn Chicago. propertysuchasisMarriedTo#1iscalledcontext-associated
Formalsemantics. Herewerecallthemappingfunction
because it can be asserted with contextual information.
I from the current model-theoretic semantics [15].
EXT A generic property, or context-dissociated property such
A property mapping function I is a binary relation
EXT as isMarriedTo, does not have contextual information at-
that maps one property to a set of pairs of resources.
tached. Finally, a regular property such as happenedIn, in-
Formally, let IP be the set of properties, IR be the set of
stance of Property class, is called a context-agnostic prop-
resources. Then I : IP → 2IR×IR.
EXT erty because it is not yet committed to be associated or
AsingletonmappingfunctionI isabinaryrelation
SEXT dissociated with contextual information.
that maps one singleton property to one pair of resources.
Formally, let IR be the set of resources, IPs ⊆ IP be the 2.3 TripleTypes
set of singleton properties. Then I : IPs → IR × IR.
SEXT Similar to the distinction of the property types, here we
For example, I (isMarriedTo#1) = (cid:104)BarackObama,
SEXT canalsodistinguishthetypeofatriplebasedonthetypeof
MichelleObama(cid:105). AsthesingletonpropertyisMarriedTo#1
itsproperty. Thethreetypesofpropertiesformthreetypes
is also a property, its property extension is a singleton set,
of triples: singleton, generic, and regular triple. A single-
which has only one element.
ton triple is the only triple that has its singleton property
I (isMarriedTo#1) = (cid:104)BarackObama, MichelleObama(cid:105).
EXT occurring as a predicate. A generic triple is a triple that
The syntax and the semantics of singleton properties de-
has its predicate asserted as a generic property. A regular
scribed here are sufficient to allow us to attach contextual
tripleisatriplethatdoesnothaveitspredicateassertedas
information for any RDF individual triple.
a generic or singleton property.
Next,wedescribehowsingletonpropertiescanbeutilized
Singleton: BarackObama isMarriedTo#1 MichelleObama.
for developing our inference scheme to infer new triples.
Generic: BarackObama isMarriedTo MichelleObama.
Regular: Chicago partOf Illinois.
2.2 PropertyTypes
Distinguishing triple types based on context. The
A generic property asserts the relationship between the
threetypesofpropertiesformthreetypesoftriples: context-
subject and the object without providing additional con-
associated, context-dissociated, andcontext-agnostictriple.
textual information about the relationship. This property
A context-associated triple is a singleton triple that may
groupsallsingletonpropertiessharingthesamecharacteris-
have contextual information associated with it via its sin-
ticsacrosscontexts,anditisconnectedtoasingletonprop-
gleton property. A context-dissociated triple is a generic
erty via the property singletonPropertyOf.
triple that does not have any contextual information asso-
SP2: isMarriedTo#1 singletonPropertyOf isMarriedTo. ciated with it. A context-agnostic triple is a regular triple
In this example, isMarriedTo is a generic property. that is not committed to be associated or dissociated with
Here we propose to add the new class GenericProperty contextual information.
to represent the set of generic properties, in addition to
2.4 Contextualtripleinstantiation
the class SingletonProperty from [22]. Any property that
is not defined as a singleton property can become generic Back to the motivating example, we have the original
property. Intuitively, a generic property is mapped to a set statement “Barack Obama married to Michelle Obama in
Chicago” represented as follows: Next, we describe model-theoretic semantics using these
T : BarackObama isMarriedTo MichelleObama . mapping functions.
1
T : T happenedIn Chicago . For RDF and RDFS, the entailments are determined by
4 1
themodel-theoreticsemantics. ForanentailmentrelationX
Weutilizethesingletonpropertygraphpatterntobridge
(e.g.,RDFSentailment),anRDFgraphGissaidtoX-entail
the gap between the primary triple T and its identifier as
1 an RDF graph G(cid:48) if each X-interpretation that satisfies G
explained in Section 2.1.
also satisfies G(cid:48). This definition is completed with a math-
SP1: BarackObama isMarriedTo#1 MichelleObama. ematical definition of X-interpretation.
SP2: isMarriedTo#1 singletonPropertyOf isMarriedTo. Wespecifythreeinterpretations: simple,RDFandRDFS
SP3: isMarriedTo#1 happenedIn Chicago. byextendingthemodel-theoreticsemanticsdescribedin[16,
This singleton property graph pattern represents the pri-
22]. For each interpretation, we add additional criteria for
marytripleT anditsmetatripleT bycreatingasingleton
1 4 supportingthesingletonpropertyandthegenericproperty.
property isMarriedTo#1 and using it as triple identifier for
While we explain the new vocabulary elements in detail,
asserting meta triples.
elements without further explanation remain as they are in
From triple SP , isMarriedTo#1 is the singleton prop-
2 theoriginalmodel-theoreticsemanticsdescribedin[16,22].
erty and isMarriedTo is a generic property. According to
the triple type classification in Section 2.3, T is a generic 3.2 SimpleInterpretation
1
triple and SP is a singleton triple. SP can be considered
1 1 Inthesimpleinterpretation,weformalizethethreetypes
as one contextual triple instance of T . We generalize this
1 of properties as described in Section 2. We also use the
relationship between the two triples as follows.
mapping functions described in Section 3.1 to assign each
Definition. Letspbethesingletonpropertyofproperty
property to a semantic construct.
p and (s, sp, o) be the singleton triple, (s, sp, o) is the
GivenavocabularyV,thesimpleinterpretationIconsists
contextual triple instance of the generic triple (s, p, o).
of:
How a generic triple (s, p, o) can be derived from the
singletongraphpatternwillbeformalizedintheRDFformal 1. IR, a non-empty set of resources, alternatively called
semantics described in Section 3.3. domain or universe of discourse of I,
2. IP, the set of properties of I,
3. MODEL-THEORETICSEMANTICS
3. IPs, called the set of singleton properties of I, as a
subset of IP,
3.1 MappingFunctions
Intheformalsemantics,weusetheconceptoffunctionto 4. IPg,calledthesetofgenericpropertiesofI,asasubset
assign the set of URIs and literals into the set of resources of IP, IPs ∩ IPg = ∅,
inamodelinterpretation,andassigneachpropertyasetof
5. IPr, called the set of regular properties,
pairs (subject, object).
IPr = IP \ (IPs ∪ IPg),
Next, we define new mapping functions to be used in the
interpretationsdescribedlaterinthissection. Wereusethe 6. I , a function assigning a generic property to a set of
G
set of singleton properties IPs, the set of properties IP, the its singleton properties,
mappingfunctionI ,andthesingletonmappingfunction
EXT
ISEXT mentioned in Section 2.1. 7. IEXT, a mapping function assigning to each property
Definition. AgenericpropertyinstancefunctionI isa a set of pairs from IR,
G
binary relation that maps a generic property to a set of its I : IP →2IR×IR where I (p) is called the ex-
EXT EXT
singleton properties. tension of property p,
Formally, let IPg ⊆ IP be the set of generic properties.
We define the function 8. ISEXT(ps), the singleton mapping function assigning
I : IPg →2IPs such that a singleton property to a pair of resources.
G
IG(pg)={ps|(cid:104)ps,pg(cid:105)∈IEXT(rdf:singletonPropertyOf)}. ISEXT : IPs →IR×IR.
Forexample,isMarriedToisagenericpropertyandithas
two singleton properties as follows: 9. IGEXT(pg), the generic mapping function assigning
each generic property a set of pairs of resources.
isMarriedTo#1 rdf:singletonPropertyOf isMarriedTo .
isMarriedTo#2 rdf:singletonPropertyOf isMarriedTo . IGEXT : IPg →2IR×IR.
IG(isMarriedTo) = {isMarriedTo#1, isMarriedTo#2}. Note that the mapping function ISEXT is not a one-to-
Definition. A generic mapping function IGEXT is a bi- onemapping;multiplesingletonpropertiesmaybemapped
nary relation that maps a generic property to a set of pairs to the same pair of entities.
of resources.
I : IPg → 2IR×IR such that 3.3 RDFInterpretation
GEXT
IGEXT(pg)={ISEXT (ps)|ps ∈ IG(pg)}. In the RDF interpretation, we formalize the definition of
Since IPg ⊆ IP, we have IGEXT(pg)⊆IEXT(pg). singleton property, generic property, and how to derive the
We also have IEXT(ps) = {(cid:104)s,o(cid:105)|(cid:104)s,o(cid:105)=ISEXT(ps)}. generic triple from a singleton graph pattern.
IEXT(pg) = {(cid:104)s,o(cid:105)|(cid:104)s,o(cid:105)∈IGEXT(pg)}. RDF interpretation of a vocabulary V is a simple in-
In the example at hand, we have: terpretation I of the vocabulary V ∪ V that satisfies
RDF
I (isMarriedTo#1)={(cid:104)BarackObama,MichelleObama(cid:105)}, the criteria from the current RDF interpretation [15] and
EXT
IEXT(isMarriedTo)={(cid:104)BarackObama,MichelleObama(cid:105)}. the following criteria:
1. Define a singleton property 2. Class rdf:GenericProperty
xs ∈ IPs iff (cid:104)rdf:GenericPropertyI,rdfs:ClassI(cid:105)∈I (rdf:typeI).
(cid:104)x , rdf:SingletonProperty I(cid:105)∈I (rdf:type I(cid:105). EXT
s EXT
The extension of the rdf:GenericProperty class is the
2. Singleton condition set IPg of all generic properties, or
Ifxs ∈IPsthen∃!(cid:104)u,v(cid:105):(cid:104)u,v(cid:105)=ISEXT(xs),andu,v IPg =ICEXT(rdf:GenericProperty I).
∈IR.Thisenforcesthesingleton-nessfortheproperty
instances. 3. Every singleton property is a resource
(cid:104)rdf:SingletonProperty I, rdfs:Resource I(cid:105)∈
3. Define a generic property
I (rdfs:subClassOf I), this causes IPs ⊆ IR.
x ∈ IPg iff EXT
g
(cid:104)xg, rdf:GenericProperty I(cid:105)∈IEXT (rdf:type I). 4. Every generic property is a resource
Ifx∈/IPs,thenIPg=IPg∪{x}. Anypropertythatis
(cid:104)rdf:GenericProperty I, rdfs:Resource I(cid:105)
notdefinedasasingletonpropertycanbecomegeneric
∈I (rdfs:subClassOf I), this causes IPg ⊆ IR.
property. EXT
5. Domain of singleton property (rule rdfs-sp-1)
4. Infersingletonpropertyandgenericproperty(rulerdf-
sp-1 and rdf-sp-2) (cid:104)xs,x(cid:105) ∈ IEXT(rdf:singletonPropertyOf I), (cid:104)x,y(cid:105) ∈
I (rdfs:domainI),if(cid:104)u,v(cid:105)∈I (x ),thenu∈
x ∈ IPs and x ∈ IPg if EXT SEXT s
s g
(cid:104)x , x (cid:105) ∈I (rdf:singletonPropertyOf I). ICEXT(y). A singleton property shares the domain
s g EXT
with its generic property.
Asingletonpropertyx isconnectedtoagenericprop-
s
erty x via the property rdf:singletonPropertyOf. As 6. Range of singleton property (rule rdfs-sp-2)
g
IG(xg) is the set of singleton properties connected to (cid:104)x ,x(cid:105) ∈ I (rdf:singletonPropertyOf I), (cid:104)x,y(cid:105) ∈
s EXT
the property xg, I (rdfs:range I), if (cid:104)u,v(cid:105) = I (x ), then v ∈
EXT SEXT s
IG(xg)={xs| ICEXT(y). Asingletonpropertyalsosharestherange
(cid:104)xs,xg(cid:105)∈IEXT(rdf:singletonPropertyOfI)}. with its generic property.
5. Generic mapping extension 7. Sub-property condition
If (cid:104)xs, xg(cid:105) ∈ IEXT(rdf:singletonPropertyOf I), then If x,y ∈ IPg, (cid:104)x, y(cid:105) ∈ IEXT(rdfs:subPropertyOf I),
xs ∈ IPs, xg ∈ IPg, and ISEXT(xs) ∈ IGEXT(xg). then IG(x)⊆IG(y), and IGEXT(x)⊆IGEXT(y).
I (x ) is called a generic mapping extension of
GEXT g
the generic property x . 8. Sub-property upper bound condition
g
IGEXT(xg)={ISEXT (xs)|xs ∈ IG(xg)}, and If y ∈ IPs and (cid:104)x, y(cid:105) ∈ IEXT(rdfs:subPropertyOf I),
then x∈ IPs and I (x)=I (y).
I (x )⊆I (x ). SEXT SEXT
GEXT g EXT g
Proof. Since y ∈ IPs, ∃!(cid:104)u,v(cid:105) : (cid:104)u,v(cid:105) = I (y),
SEXT
6. Generic triple derivation (rule rdf-sp-3)
and I (y)={(cid:104)u,v(cid:105)}.
EXT
If (cid:104)u,v(cid:105)=I (x ), and
SEXT s Since (cid:104)x, y(cid:105)∈I (rdfs:subPropertyOf I), by defini-
(cid:104)x , x (cid:105)∈I (rdf:singletonPropertyOf I), EXT
s g EXT tion, I (x)⊆I (y)={(cid:104)u,v(cid:105)}.
then (cid:104)u,v(cid:105)∈I (x ). EXT EXT
GEXT g
Sincexcanbemappedtoatmostonepairofresources,
Proof. (cid:104)x , x (cid:105) ∈ I (rdf:singletonPropertyOf I)
s g EXT x∈ IPs, and I (x)=(cid:104)u,v(cid:105)=I (y).
implies (1): I (x )∈I (x ). SEXT SEXT
SEXT s GEXT g
The combination of (cid:104)u,v(cid:105) = I (x ) and (1) im- 9. Sub-property lower bound condition (rule rdfs-sp-4)
SEXT s
plies (cid:104)u,v(cid:105)∈IGEXT(xg). If x∈ IPg and (cid:104)x, y(cid:105)∈IEXT(rdfs:subPropertyOf I),
Thisshowshowthegenerictriple(cid:104)u,v(cid:105)∈I (x ) then y∈ IPg.
GEXT g
can be derived from its singleton graph pattern. Proof. Assume that y ∈ IPs, then x ∈ IPs (upper
3.4 RDFSInterpretation boundcondition). Wehavebothx∈IPsandx∈IPg.
This contradicts to the condition IPs ∩ IPg = ∅.
Here we formalize the connections from a singleton prop-
Therefore,y∈/ IPs,andaccordingtothecondition(3)
erty to its generic property, as well as to other properties
of RDF interpretation, IPg = IPg ∪ {y}, or y∈ IPg.
such as rdfs:domain, rdfs:range, and rdfs:subPropertyOf.
We will reuse the function (from [15]) 10. Property hierarchy (rule rdfs-sp-3)
I :IR→2IR whereI (y)iscalledaclassextension
CEXT CEXT If (cid:104)x , x(cid:105)∈I (rdf:singletonPropertyOf I), and
of y, I (y)={x|∀x∈IR:(cid:104)x,y(cid:105)∈I (rdf:typeI)}. s EXT
CEXT EXT (cid:104)x, y(cid:105) ∈ I (rdfs:subPropertyOf I), then (cid:104)x , y(cid:105) ∈
RDFS interpretationofavocabularyVisanRDFin- EXT s
I (rdf:singletonPropertyOf I).
terpretation I of the vocabulary V ∪ V that satisfies EXT
RDFS
criteria from the current RDFS interpretation [15] and the Proof. (cid:104)xs, x(cid:105) ∈ IEXT(rdf:singletonPropertyOf I)
following criteria: implies (1): xs ∈IG(x).
(cid:104)x, y(cid:105)∈I (rdfs:subPropertyOf I) implies
1. Class rdf:SingletonProperty EXT
(2): I (x)⊆I (y).
(cid:104)rdf:SingletonPropertyI,rdfs:ClassI(cid:105)∈I (rdf:typeI). G G
EXT
(1) and (2) derive (3): x ∈I (y).
Theextensionofrdf:SingletonPropertyclassistheset s G
IPs of all singleton properties, or Inotherwords,xs isasingletonpropertyofy,or(cid:104)xs,
IPs =ICEXT(rdf:SingletonProperty I). y(cid:105)∈IEXT(rdf:singletonPropertyOf I).
3.5 OWL2RDF-basedSemanticConditions A property p is an instance of the class
From the RDF-based semantics of OWL 2 Full [23], we owl:IrreflexiveProperty iff ∀x:
consider the semantic conditions of the OWL classes and (1) p∈IP,(cid:104)x,x(cid:105)∈/ I (p),
EXT
properties that are relevant to singleton properties. These
(2) p∈IPg,(cid:104)x,x(cid:105)∈/ I (p),
GEXT
semantic conditions belong to the two categories: logical
(3) ∀p ∈I (p),(cid:104)x,x(cid:105)(cid:54)=I (p ).
characteristicsoftheproperties,andrelationstootherprop- s G SEXT s
erties. We tighten the semantic conditions of these OWL
• Symmetric property. If two individuals are re-
classes and properties to make sure they are valid in the
latedbyasymmetricproperty,thenthispropertyalso
extended semantics, by enforcing more constraints on the
relates them reversely.
genericpropertyandsingletonpropertyextensions. These-
A property p is an instance of the class
manticconditionsofthesepropertiesmustbesatisfiedinthe
owl:SymmetricProperty iff ∀x,y:
interpretationsextendedwithsingletonpropertysemantics.
Let Vp be the vocabulary of OWL classes and properties (1) p∈IP,(cid:104)x,y(cid:105)∈IEXT(p) implies (cid:104)y,x(cid:105)∈IEXT(p),
relevanttosingletonproperties: Vp ={FunctionalProperty, (2) p ∈ IPg,(cid:104)x,y(cid:105) ∈ IGEXT(p) implies (cid:104)y,x(cid:105) ∈
InverseFunctionalProperty, ReflexiveProperty, Irreflexive- I (p),
GEXT
Property, SymmetricProperty, AsymmetricProperty, Tran-
(3) ∀p ∈ I (p),(cid:104)x,y(cid:105) = I (p ) implies ∃p(cid:48) ∈
sitiveProperty, inverseOf, equivalentOf}. s G SEXT s s
I (p),(cid:104)y,x(cid:105)=I (p(cid:48)).
Letp ,p(cid:48),andp(cid:48)(cid:48)bethesingletonpropertiesofthegeneric G SEXT s
s s s
property p, then ps ∈ IG(p), p(cid:48)s ∈ IG(p), p(cid:48)s(cid:48) ∈ IG(p). We • Asymmetric property. If two individuals are re-
define the OWL 2 RDF-based interpretation as follows. lated by an asymmetric property, then this property
OWL 2 RDF-based interpretationofavocabularyV never relates them reversely.
is an RDFS interpretation I of the vocabulary V ∪ V
OWL A property p is an instance of the class
that satisfies criteria from the OWL interpretation [23] and
owl:AsymmetricProperty iff ∀x,y:
the following semantic conditions:
(1) p∈IP,(cid:104)x,y(cid:105)∈I (p) implies (cid:104)y,x(cid:105)∈/ I (p),
EXT EXT
• Functional property. If a property is functional,
(2) p ∈ IPg,(cid:104)x,y(cid:105) ∈ I (p) implies (cid:104)y,x(cid:105) ∈/
thenatmostonedistinctvaluecanbeassignedtoany GEXT
I (p),
given individual via this property. GEXT
(3) ∀p ∈ I (p),(cid:104)x,y(cid:105) = I (p ) implies (cid:64)p(cid:48) ∈
Apropertypisaninstanceofowl:FunctionalProperty s G SEXT s s
I (p),(cid:104)y,x(cid:105)=I (p ).
G SEXT s
iff ∀x,y ,y :
1 2
• Transitive property. A transitive property that re-
(1) p ∈ IP,(cid:104)x,y (cid:105) ∈ I (p),(cid:104)x,y (cid:105) ∈ I (p) im-
1 EXT 2 EXT
latesanindividualatoanindividualb,andindividual
plies y =y ,
1 2
b to an individual c, also relates a to c.
(2) p ∈ IPg,(cid:104)x,y (cid:105) ∈ I (p),(cid:104)x,y (cid:105) ∈ I (p)
1 GEXT 2 GEXT A property p is an instance of the class
implies y =y ,
1 2 owl:TransitiveProperty iff ∀x,y,z:
(3) ∀p ∈ I (p),(cid:104)x,y (cid:105) = I (p ),(cid:104)x,y (cid:105) =
s G 1 SEXT s 2 (1) p ∈ IP,(cid:104)x,y(cid:105) ∈ I (p),(cid:104)y,z(cid:105) ∈ I (p) implies
I (p ) implies y =y . EXT EXT
SEXT s 1 2 (cid:104)x,z(cid:105)∈I (p),
EXT
• Inverse functional property. An inverse func- (2) p ∈ IPg,(cid:104)x,y(cid:105) ∈ I (p),(cid:104)y,z(cid:105) ∈ I (p)
GEXT GEXT
tional property can be regarded as a “key” property, implies (cid:104)x,z(cid:105)∈I (p),
GEXT
i.e., no two different individuals can be assigned the (3) ∀p ,p(cid:48) ∈ I (p),(cid:104)x,y(cid:105) = I (p ),(cid:104)y,z(cid:105) =
same value via this property. I s(p(cid:48)s) impliGes ∃p(cid:48)(cid:48) ∈I (p),(cid:104)xS,Ez(cid:105)X=T Is (p(cid:48)(cid:48)).
SEXT s s G SEXT s
A property p is an instance of
• Inverse property. The inverse of a given property
owl:InverseFunctionalProperty iff ∀x ,x ,y:
1 2
isthecorrespondingpropertywithsubjectandobject
(1) p ∈ IP,(cid:104)x ,y(cid:105) ∈ I (p),(cid:104)x ,y(cid:105) ∈ I (p) im-
1 EXT 2 EXT swapped for each property assertion built from it.
plies x =x ,
1 2 (p ,p )∈I (owl:inverseOf I) iff
1 2 EXT
(2) p ∈ IPg,(cid:104)x ,y(cid:105) ∈ I (p),(cid:104)x ,y(cid:105) ∈ I (p)
1 GEXT 2 GEXT (1) ∀p ,p ∈ IP,I (p ) = {(cid:104)x,y(cid:105)|(cid:104)y,x(cid:105) ∈
implies x =x , 1 2 EXT 1
1 2 I (p )},
EXT 2
(3) ∀p ∈ I (p),(cid:104)x ,y(cid:105) = I (p ),(cid:104)x ,y(cid:105) =
s G 1 SEXT s 2 (2) ∀p ,p ∈ IPg,I (p ) = {(cid:104)x,y(cid:105)|(cid:104)y,x(cid:105) ∈
I (p ) implies x =x . 1 2 GEXT 1
SEXT s 1 2 I (p )},
GEXT 2
• Reflexive property. A reflexive property relates (3) ∀p ∈ I (p ),∀p(cid:48) ∈ I (p ),I (p ) = (cid:104)x,y(cid:105),
s G 1 s G 2 SEXT s
every individual in the universe to itself. I (p(cid:48))=(cid:104)y,x(cid:105).
SEXT s
A property p is an instance of the class
• Equivalent property. Two equivalent properties
owl:ReflexiveProperty iff ∀x:
share the same property extension.
(1) p∈IP,(cid:104)x,x(cid:105)∈IEXT(p), (p ,p )∈I (owl:equivalentOf I) iff
1 2 EXT
(2) p∈IPg,(cid:104)x,x(cid:105)∈IGEXT(p), (1) ∀p1,p2 ∈IP :IEXT(p1)=IEXT(p2),
(3) ∀ps ∈IG(p),(cid:104)x,x(cid:105)=ISEXT(ps). (2) ∀p1,p2 ∈IPg:IGEXT(p1)=IGEXT(p2),
• Irreflexive property. An irreflexive property does (3) ∀ps ∈ IG(p1),∃p(cid:48)s ∈ IG(p2) : ISEXT(ps) =
not relate any individual to itself. ISEXT(p(cid:48)s).
4. CONTEXTUALINFERENCES 4.2 ContextualInferencing
In the RDF, RDFS, and OWL 2 Full interpretations, we Back to the motivating example, from the contextual
have proved several deduction rules in Section 3. Here we statement “BarackObama is married to Michelle Obama in
present a set of these rules in Section 4.1 and demonstrate Chicago”,weashumanscaninferalistofstatements(S to
1
how these rules can be applied to derive the inferred state- S )asshowninTable1. Herewedemonstratestep-by-step
5
ments described in the motivating example in Section 4.2. howtoinferstatementsS toS fromtheoriginalstatement.
1 5
Ourinitialknowledgebaseincludesthesingletonproperty
4.1 ContextualEntailmentRules
graphpatternrepresentingtheoriginalcontextualstatement
Thethreefollowingrdf-sprulesarederivedfromtheRDF and the background knowledge as follows:
interpretation. SP1: BarackObama isMarriedTo#1 MichelleObama.
u rdf:singletonPropertyOf v . SP2: isMarriedTo#1 singletonPropertyOf isMarriedTo.
(rdf-sp-1) SP : isMarriedTo#1 happenedIn Chicago.
u rdf:type rdf:SingletonProperty . 3
T2: isMarriedTo subPropertyOf isSpouseOf.
u rdf:singletonPropertyOf v . T5: Chicago partOf Illinois.
(rdf-sp-2) T6: Illinois partOf USA.
v rdf:type rdf:GenericProperty .
Assume that we also have a partOf-rule that, if x hap-
pened in a place y which is a part of a bigger place z, then
u rdf:singletonPropertyOf v .
x also happened at the place z.
x u y .
(rdf-sp-3)
x v y . x happenedIn y . y partOf z .
(partOf-rule)
The four rdfs-sp rules are derived from the RDFS interpre- x happenedIn z .
tation.
We start by applying the partOf-rule on the triples SP
3
u rdf:singletonPropertyOf v . and T , we obtain the triple SP .
5 4
v rdfs:domain x .
(rdfs-sp-1) SP4: isMarriedTo#1 happenedIn Illinois .
u rdfs:domain x .
ThesingletontriplepatternincludingtriplesSP andSP
1 2
u rdf:singletonPropertyOf v . derivesthestatement“BarackObamaismarriedtoMichelle
v rdfs:range y . Obama”accordingtorulerdf-sp-3. Combiningthreetriples
(rdfs-sp-2)
u rdfs:range y . SP1, SP2, and SP4 will derive the contextual statement S1
“Barack Obama isMarriedTo Michelle Obama in Illinois”.
u rdf:singletonPropertyOf x . Re-applyingthepartOf-ruleonthetriplesSP4andT6,we
x rdfs:subPropertyOf y . obtain the new triple SP5.
(rdfs-sp-3)
u rdf:singletonPropertyOf y . SP : isMarriedTo#1 happenedIn USA .
5
Similar to S , the combination of triples SP , SP , and
x rdf:type rdf:GenericProperty . 1 1 2
SP derives the contextual statement S “Barack Obama
x rdfs:subPropertyOf y . 5 2
(rdfs-sp-4) isMarriedTo Michelle Obama in USA”.
y rdf:type GenericProperty .
Next,ifweapplytherulerdfs-sp-3onthetriplesSP and
2
T , we obtain the new triple SP .
u rdf:singletonPropertyOf x . 2 6
x rdfs:subPropertyOf y . SP6: isMarriedTo#1 singletonPropertyOf isSpouseOf.
(rdfs-sp-5)
y rdf:type GenericProperty . Applying the rule rdf-sp-3 on the triples SP1 and SP6
derives the statement “Barack Obama isSpouseOf Michelle
The rule rdfs-sp-5 can easily be drived by combining the
Obama”.
two rules rdfs-sp-3 and rdf-sp-2. Similar to the property
The combination of the triples SP , SP , and SP will
rdfs:subPropertyOf, here we also provide the rules for the 1 6 3
derive the contextual statement S “Barack Obama is-
owl:equivalentOf. 3
SpouseOf Michelle Obama in Chicago”.
u rdf:singletonPropertyOf x . Similarly, combining the triples SP , SP , and SP will
1 6 4
x owl:equivalentOf y . derive the contextual statement S “Barack Obama is-
(owl-sp-1) 4
u rdf:singletonPropertyOf y . SpouseOf Michelle Obama in Illinois”.
The combination of SP , SP , and SP derives the con-
1 6 5
x rdf:type GenericProperty . textual statement S “Barack Obama isSpouseOf Michelle
5
x owl:equivalentOf y . Obama in USA”.
(owl-sp-2)
y rdf:type GenericProperty . Therefore, we have shownhow thecontextual statements
S to S can be inferred in our approach.
1 5
u rdf:singletonPropertyOf x .
x owl:equivalentOf y . 5. IMPLEMENTATION
(owl-sp-3)
y rdf:type GenericProperty .
Hereweexplainhowwecomputeallinferredtriplesusing
If x owl:equivalentOf y then the proposed entailment rules for existing knowledge bases
(1) x rdfs:subPropertyOf y and intwosteps. Firstwedescribehowwetransformtheexisting
(2) y rdfs:subPropertyOf x. knowledge bases into the singleton property representation
The above three owl-sp rules can be derived easily by in Section 5.1. Then Section 5.2 describes how all the pro-
combingthisruleandtherulesrdfs-sp-3,rdfs-sp-4,andrdfs- posed rules are computed for every triple in the resulting
sp-5, respectively. knowledge bases.
5.1 TransformingRepresentation 6. EVALUATION
AswediscussedearlierinSection1,knowledgebaseslike Weevaluatetheperformanceofcomputinginferredtriples
DBpediaandBio2RDFrepresentthecontextualinformation from the proposed rules on a large scale by using the tool
suchasprovenanceintheformofaquad. Beforecomputing rdf-contextualizer on real-world knowledge bases.
the inferred triples for these datasets, we need to prepare
6.1 ExperimentSetup
the knowledge bases by transforming them to the singleton
property representation. WeuseasingleserverinstalledwithUbuntu12.04. Ithas
Given any quad in the form of (s, p, o, g), we trans- 24cores,eachcoreisIntelXeonCPU2.60GHz. Weusetwo
formittothesingletonpropertyrepresentationbycreating disks, one SSD 220GB for storing input datasets, and one
a singleton property (sp , singletonPropertyOf, p) and as- HDdisk2.7Tforwritingtheoutput. Thisserverhas256GB
i
serting the singleton triple (s, sp , o). We use the property of RAM, however, we limit 60GB for each Java program.
i
wasDerivedFrom from the PROV ontology [19] to represent
6.2 Datasets
theprovenanceofthetriple(sp ,prov:wasDerivedFrom,g).
i
The singleton property URIs are constructed by appending We downloaded and used the ontologies and RDF quad
a unique string to the generic property URI, with an incre- datasets from DBpedia [6] and four Bio2RDF datasets in-
mentalcounterfortheuniquenumberinthewholedataset. cluding NCBI Genes [4], PharmGKB [5], CTD [1], and GO
We developed a Java 8 tool, called rdf-contextualizer, to Annotations [2] in our evaluation. We chose these quad
transform any RDF datasets from the quad representation datasets because they are large and widely-used with high
to the singleton property. We took advantages of the Jena impact in the community. For Bio2RDF datasets, we also
RIOT API [7] with high throughput parsers for parsing an downloaded the Bio2RDF mapping files [3].
inputfilefromanyRDFformatandgeneratingastreamof
RDF quads. For each quad stream, we created a pipeline
of streams for converting each quad to the singleton prop- Table 2: Number of RDF quads in the original
ertyrepresentation,shorteningtriplestoTurtleformat,and datasets and number of unique RDF quads in the
writing them to gzip files though buffer writers. As each duplicate-removed datasets
stream is handled by a separate thread, we can utilize the Dataset # of Quads # of Unique Quads
CPU resources, especially the ones with multiple cores, by NCB-NG 4,043,516,408 2,010,283,374
creating multiple threads for parsing multiple files concur- DBP-NG 1,039,275,891 784,508,538
rently. CTD-NG 644,147,853 327,648,659
Wevalidatedthesyntaxoftheoutputdatasetsbywriting
PHA-NG 462,682,871 339,058,720
an analyzer to parse the output files and also generate the
GOA-NG 159,255,577 97,522,988
statistics reported in Section 6.3.
WereportedthenumberofRDFquadsperdatasetinthe
5.2 ComputingInferredTriples first and second columns of Table 2. The dataset identifier
is taken from the first 3 letters of its name.
Runningallcontextualentailmentrulesoneverysingleton
We observed that there were too many duplicate quads
triple produces at least two more triples (rdf-sp-1 and rdf-
among the files within each dataset. We also believe that
sp-3). Thenumberofinferredtriplesgoesuptomulti-billion
the duplicates may be created on purpose. Each of these
with datasets like DBpedia and Bio2RDF. That amount of
datasetshasanumberoffilesandeachfilecontainsanum-
inferred triples cannot fit an in-memory reasoner such as
ber of RDF quads for a topic. For example, NCBI Genes
Jena [10]. The proposed entailment rules can also be com-
dataset has one file for all genes belonging to one species.
putedinthereasonerswiththesupportforuser-definedrules
Therefore,wekeepthesedatasetsintheoriginalversionand
suchasOracle[25]. However,fortherulesgeneratingalarge
createdanewversionforeachdatasetwithallduplicatesbe-
number of inferred triples, optimization is necessary as Or-
ing removed. We removed the duplicates by 1) concatenat-
acle has optimized the computation of large number of in-
ingallfilesintoasinglefile,2)splittingthisfileintomultiple
ferredtriplesforowl:sameAs[18]. Withouttakingsuchopti-
smaller files, 3) sorting each small file, and 4) merging all
mizationstepintheexistingengines,itistime-consumingto
the sorted files into a single file. The third column of Ta-
querytherulepatternsandinserttheinferredtriplestothe
ble 2 shows the number of unique quads per dataset after
store because the insert query is always expensive. There-
removing the duplicates.
fore, the proposed contextual entailment rules may not be
Wethengeneratedthesingletonpropertyversionofeach
best computed in the existing engines without taking the
dataset by running the tool rdf-contextualizer with and
optimization step.
without the -infer option. We ran each dataset version at
To demonstrate that the computation of the proposed
least3timesandreportedtheaverageresultsinSection6.3.
rules can be scalable with proper optimization, we imple-
The tool rdf-contextualizer and the materials used in
mented our engine in the tool rdf-contextualizer. Since the
this paper are publicly available for reproducing the exper-
proposed rules can be applied to each triple independently,
iments1.
we can pass the triples to concurrent tasks. While trans-
forming the RDF quads to the singleton property represen- 6.3 Results
tation, we added an optional inferring task in the stream
We consider four dimensions in our evaluation: number
pipelinestocomputetheproposedrulesforeverytriple. The
of triples, number of singleton triples, run time, and disk
timedifferencebetweentherunswithandwithoutthe-infer
option would be the run time for inferring triples added to 1https://archive.org/services/purl/
the overall process. rdf-contextualizer
Figure 1: Total number of triples for each dataset in all four cases: with vs. without reasoning and with vs.
without removing duplicates.
Figure 2: Total number of singleton triples for each dataset in all four cases: with vs. without reasoning and
with vs. without removing duplicates.
space. In all figures, the series Reasoning stands for run- NCBI genes, the largest dataset, contains about 8 billion
ning the tool with -infer option and No-Reasoning stands inferred triples (66.67%) more than the NoReasoning-Dup
for running the tool without -infer option. Running the version. Similarly, the Reasoning-Unique version of NCBI
NoReasoningoptionprovidestheresultsasthebaselinecost. genes contains about 4 billion inferred triples more than
ThedifferencesintheresultsbetweentheNoReasoningand theNoReasoning-Uniqueversion. Someotherdatasetshave
Reasoningversionsaretheextracostestimatedforthecom- their number of inferred triples higher than 66.67%. For
putationoftheinferredtriples. Werunthetoolontwover- example, the Reasoning-Unique version of CTD contains
sions of datasets. The series with Dup denotes the datasets about 950 million inferred triples (96.67%) more than the
withduplicatequadsandtheserieswithUniquedenotesthe NoReasoning-Unique version.
datasets with all duplicates being removed. BetweentheDupandUniqueversions,theReasoning-Dup
Combining the two options: with vs. without -infer and versions contain 50% (NCBI Genes), 32% ( DBpedia), 86%
with vs. without removing duplicates, each evaluating di- (CTD), 35% (PharmGKB) and 63% (GOA) more triples
mensionhasfourcases: Reasoning-Dup,Reasoning-Unique, than the corresponding Reasoning-Unique versions.
NoReasoning-Dup, and NoReasoning-Unique.
6.3.2 NumberofInferredSingletonTriples
6.3.1 NumberofInferredTriples
Resulted from the inference rules involving property hi-
Figure1showsthetotalnumberoftriplesofeachdataset erarchy in the schema, the number of inferred singleton
in four cases. triples varies across datasets as shown in Figure 2 since
In general, the Reasoning cases contain larger num- theyhavedifferentschema. Forexample,sinceNCBIGenes
ber of triples than the NoReasoning cases, from 66.7% datasetdoesnothavepropertyhierarchy,thenumberofsin-
to 96.67%. For example, the Reasoning-Dup version of gleton triples remains the same in both version Reasoning
Figure 3: Disk space (zipped) for each dataset in all four cases: with vs. without reasoning and with vs.
without removing duplicates.
Figure 4: Run time (in minutes) for each dataset in all four cases: with vs. without reasoning and with vs.
without removing duplicates.
and NoReasoning. Meanwhile, CTD dataset inferred 194 form, we chose the Turtle format to serialize the triples to
million singleton triples (30%) for the Reasoning-Dup ver- files. It allows us to arrange the triple order so that we
sion and 148 million singleton properties (45%) for the canshortenthestringsoftriplessharingsubject,orsubject
Reasoning-Unique version. and predicate. For shortening the URIs in the Turtle for-
mat, we compiled a list of prefixes used in these datasets.
6.3.3 DiskSpace Thanks to this compact representation, comparing to the
NoReasoning-Dup version, the Reasoning-Dup version only
Generally speaking, for every RDF quad, we generated 3
adds 15-25% more space for 66.7-96.97% more number of
triplesforNoReasoningversionandatleast5triplesforthe
triples (Figure 3).
Reasoningversion. Thatmakestheoverallnumberoftriples
ofeachSPdatasetincreaseupto3-5timescomparedtothe
6.3.4 RunTime
numberofquadsofthecorrespondingnamedgraphdataset.
Consequently, the disk size of one SP dataset could be 3-5 Figure 4 shows the run time execution for all four cases
times more than the disk size of its corresponding named of each dataset. GO Annotations dataset, took 11 minutes
graph dataset. This is the case in which the triples of SP for 480 million triples of NoReasoning-Dup version and 13
datasets being serialized into the N-Triple format. For very minutesfor796milliontriplesofReasoning-Dupversion. In
large datasets like DBpedia and NCBI Genes, we do not otherwords,itadded2minutestotheoverallprocesstoinfer
recommend this N-Triple serialization since the unzipped 316 million triples. NCBI Genes, the largest dataset, took
files may require disks with tetrabyte capacity. 232minutesfor12billiontriplesofNoReasoning-Dupversion
RDF Turtle format is more compact than the N-Triple and274minutesfor20billiontriplesofReasoning-Dupver-
format, especially with very large datasets. Since our ap- sion. Intermsofpercentage,theReasoning-Dupversionsof
proach enables data to be represented in the RDF triple thesedatasetsadd14-19%runtimeforinferring66.7-96.67%
