=Paper=
{{Paper
|id=Vol-1080/owled2013_15
|storemode=property
|title=Representing Kinship Relations on the Semantic Web
|pdfUrl=https://ceur-ws.org/Vol-1080/owled2013_15.pdf
|volume=Vol-1080
|dblpUrl=https://dblp.org/rec/conf/owled/LongoGC13
}}
==Representing Kinship Relations on the Semantic Web==
https://ceur-ws.org/Vol-1080/owled2013_15.pdf
Representing Kinship Relations on the Semantic
Web
Domenico Cantone1 , Aldo Gangemi2,3 , and Cristiano Longo4
1
Università di Catania, Italy
2
STLab, ISTC-CNR, Rome, Italy
3
LIPN, Université Paris 13-CNRS-Sorbonne Cité, France
4
Network Consulting Engineering (NCE) S.r.l, Valverde (CT), Italy
Abstract. Kinship plays a fundamental role in human communities as
a basic principle for organizing individuals into social groups. Represent-
ing kinship relationships in a formal and precise way is then a crucial
task when modelling many knowledge domains, and it may constitute
a relevant benchmark for the reasoning layer of the Semantic Web. In
this paper we face the problem of representing some basic aspects of
kinship relationships using the fragments of OWL2 corresponding to the
description logics SROIQ and EL++ . As a first step, we provide an in-
tuitive but formal description of some kinship terms, using an expressive
description logic. From this intuitive description, we derive a set of test
cases, indicating the expected inferences that should be drawn from the
candidate ontologies. Finally, three different ontologies (two for SROIQ
and one for EL++ ), whose coherence with the intuitive description of
kinship terms is established, are compared by means of these test cases.
1 Introduction
This paper reports work about representing and reasoning over kinship rela-
tionships when using OWL2. The practical impact of this study is not only in
describing a relevant ontology engineering problem, but also in being able to
make sense of heterogeneous kinship data emerging from the linked open data
cloud.
Kinship relationships are important knowledge crossing the biological, an-
thropological, social, and legal domains. Such knowledge involves non-trivial
reasoning even at a purely cognitive human level. As a matter of fact, much
of the historically evolved knowledge organization systems have been based on
metaphors deriving from kinship knowledge: trees, transitivity, syllogistic rea-
soning, etc. But kinship knowledge goes well beyond purely formal relations:
different conceptual dimensions intersect at the kinship level: “blood” (genetic)
relations, breeding relations, nursing relations, transfer of legal rights and obli-
gations, etc. Those dimensions play complicated roles in the cultural evolution of
practices and laws, so that complicated reasoning tasks emerge, and the typical
reasoning on those data is pretty simple compared to the requirements of tasks
defined for kinship knowledge. The growing amount of kinship knowledge flowing
2 Domenico Cantone, Aldo Gangemi, and Cristiano Longo
from Big Data and especially in Linked Open Data is on one hand quite simple
as compared to actual kinship reasoning needs, but on the other hand it is rather
messy. It is therefore important to establish explicit representation and reason-
ing patterns over kinship (e.g., in order to enhance kinship linked data), and to
exploit them in realistic applications. Kinship seems then a relevant benchmark
for the reasoning layer of the Semantic Web: does OWL2 DL support kinship
reasoning in ways that are nontrivial, e.g., lightweight entailment regimes of
SPARQL? or do we need stronger ones, e.g., RIF?5
The description logic [3] varieties of OWL26 are globally underpinned by the
SROIQ description logic, described in [8]. The first-order direct semantics of
OWL2 enables reasoning on OWL2 knowledge bases, thus allowing one on the
one hand to test whether a knowledge base is incoherent/inconsistent, and on the
other hand to perform inferences, which permit to derive additional information
from the facts explicitly mentioned in the knowledge base.
An example of inference consists in automatically detecting that Alice is the
grandmother of Charlie from the facts that Alice is the mother of Bob and that
Bob is the father of Charlie.
To be useful in practice, a description logic must admit automated algorithms
for computing inferences. In other words, reasoning in the considered description
logic must be decidable. As a consequence, the expressivity of currently used
description logics is somehow limited. This is the case for the aforementioned
description logic SROIQ which, among others, imposes some restrictions on
predicates stating transitivity and irreflexivity of roles. Such kind of limitations
may be frustrating when one attempts to describe a knowledge domain using a
specific description logic, and the lower is the expressive power of the logic, the
more pronounced is this issue (see Section 6). Moreover, due to these limitations
one may be forced to provide some counterintuitive constraints at this stage.
For example, in order to increase the inferencing capabilities of the resulting
ontology, in the knowledge base KSq , reported in Section 5, we adopted a recursive
definition for the concept of all persons with an Italian ancestor rather than the
more intuitive definition ItDescendant ≡ ∃descendantOf.Italian.
In this paper, we use a method based on a formal representation of the re-
quirements for an ontology of the kinship knowledge domain. This starts from an
intuitive (but precise) description KL of the knowledge domain we are describ-
ing. This description is intuitive in the sense that the correspondence between
the definitions and the intuitive meaning of concept and roles is immediately
clear, thanks to the shared conceptualization of (basic) kinship relations. The
description is provided by means of a formal language, which is powerful enough
to express suitable limitations on the specifications of conceptualizations and,
therefore, not necessarily decidable. Then, given a candidate set of description
logic constraints K, its coherence with the intuitive description KL must be veri-
fied, in order to guarantee that no unexpected consequence can be deduced from
K. In other words, this verification phase ensures that every fact that can be
5
http://www.w3.org/standards/techs/rif#w3c_all
6
http://www.w3.org/TR/2009/REC-owl2-overview-20091027/
Representing Kinship Relations on the Semantic Web 3
inferred from K must also be inferable from KL as well. On the other hand, due
to the expressive limitations of decidable description logics, the inferences which
can be drawn from K may be a strict subset of those which can be drawn from
KL . Thus, the inferencing capabilities of the candidate constraint set K have to
be tested against a collection of expected inferences (see for example Tables 2
and 3), defined starting from the intuitive description KL . Such test cases, whose
execution can be easily automatized, provide an immediate view of which kinds
of inferences will be drawn from a set of constraints and which will not.
The paper is organized as follows. In Section 2 work related to representing
kinship using Semantic Web languages is briefly reviewed. In Section 3 some
preliminary notions about the description logic framework are recalled. Section
4 provides an intuitive but formal description of kinship using a really expressive
description logic. In Section 5 two different descriptions of kinship in terms
of SROIQ-constraints are provided and compared. The less expressive (but
more efficient) description logic EL++ is used for building a kinship ontology in
Section 6. Finally, in Section 7 we draw our conclusions, and provide some hints
for future work.
2 Related work
In the large area of social relationships, kinship plays a fundamental role, since it
pervades (in different ways) all human communities as a basic principle for orga-
nizing individuals into social groups. In light of this, kinship relationships have
been intensively studied by anthropologists,7 in order to understand how they
influence social organization in human communities. Also population genetics is
heavily involved in studying kinship relations with respect to the dynamics of
genetic inheritance in humans [10]. Sociology [12], law, and jurisprudence [4] as
well have substantially contributed to shape current perception and representa-
tion of kinship in human cultures.
Research focused on kinship and, more in general, on human relationships,
is also active in the field of knowledge representation. The ‘Friend Of A Friend’
(FOAF) vocabulary is a de facto standard for representing social relationships
in the semantic web,8 and it provides a generic human-to-human relation knows.
The RELATIONSHIP vocabulary, presented in [5], contains a basic set of
kinship terms.9 Among other human-to-human relationships, it provides vocab-
ulary terms for representing childhood, parenthood, siblinghood, and a relation
SpouseOf.
A more comprehensive set of kinship terms is provided by the agrelon vo-
cabulary,10 devised in the context of the CONTENTUS Project [6]. One of
the most interesting aspects of this terminology is the distinction between legal
and natural relationships. For example, natural and adoptive children can be
7
E.g., http://anthro.palomar.edu/kinship/kinship_5.htm
8
http://www.foaf-project.org/
9
http://vocab.org/relationship/.html
10
http://www.contentus-projekt.de/fileadmin/download/agrelon.owl
4 Domenico Cantone, Aldo Gangemi, and Cristiano Longo
distinguished by means of the two distinct relations hasBiologicalChild and
hasAdoptiveChild.
Some considerations about human relationships are presented in [13], where
the authors point out that every relationship among persons is in some way
caused by one or more specific events, for example childhood is caused by a
birth event.
From a different perspective, in [14] the authors propose an ontology of (com-
plex) Social Relationships, based on the foundational ontology DOLCE (cf. [7]),
extended with the D&S (Descriptions and Situations) framework. The ontology
enables the definition of context-specific relationships, i.e., relationships which
may hold or not depending on the context we are considering. This is possi-
ble because social relations are reified : relation reification design patterns make
relation representation very flexible, but they also prevent full-fledged descrip-
tion logic reasoning on kinship relations, unless appropriate binary projections
of reified relations are provided.
A more reasoning-oriented work is contained in [15], which describes the
Family History Knowledge Base (in short FHKB ). This ontology, which has
been developed as a tutorial example to highlight some features of OWL2, pro-
vides definitions and constraints for a considerable amount of kinship relations.
However, the authors report some issues that prevent applications from using it.
For example, the relation isSiblingOf is explicitly stated to be transitive and
symmetric, and thus it must be necessarily reflexive.
In general, the aforementioned vocabularies do not provide a relevant amount
of intensional knowledge, as they limit themselves to supply a set of names to
denote different human-to-human relationships. By converse, in this paper we
provide reasoning-oriented definitions of some kinship relationships by means
of description logics. We begin with characterizing kinship relationships derived
from common sense, using a very expressive description logic.
3 Description Logics
Description logics (the reader may refer to [3] for a quite complete introduction
to the description logic framework) are a family of logic-based formalisms which
allow one to describe a knowledge domain in terms of individuals, to denote
domain elements, concepts, which denote domain subsets, and roles, which des-
ignate relations among domain items, and to state constraints on the domain
structure.
Basic syntactic building blocks of all languages in this framework are the
three denumerable infinities of concept names, role names, and individual names.
Each description logic is mainly characterized by a set of constructors (see the
first part of Table 1), which allow one to define complex concepts and roles
starting from concept, role, and individual names, and by the types of constraints
(see the second part of Table 1) which can form a knowledge base (namely, a finite
set of description logic constraints). In what follows, we will use the term concepts
to indicate concept names and complex concepts (i.e., concepts constructed from
Representing Kinship Relations on the Semantic Web 5
other concepts by means of concept constructors). Analogously, we will use the
term roles for role names and complex roles.
Description logic semantics is given in terms of interpretations. An interpre-
tation I is a pair (∆I , ·I ), where ∆I is a nonempty set (interpretation domain)
and ·I is an interpretation function which associates domain subsets, relations
on the domain, and domain items to concept names, role names, and individ-
ual names, respectively. The interpretation function extends to complex terms
(concepts and roles) as indicated in the first part of Table 1, where C,D are
concepts, R,S are roles, a is an individual name, and n is a nonnegative integer.
An interpretation I evaluates a constraint γ by assigning a truth value to it.
Evaluation of constraints by a given interpretation I is defined as in the second
part of Table 1, with C,D concepts, R,S roles, and a,b individual names. We
write I |= γ to indicate that the constraint γ is evaluated to true by the in-
terpretation I. Otherwise, we write I 6|= γ. An interpretation I is said to be a
model for a knowledge base K (and we write I |= K) if I |= γ for all γ ∈ K. A
knowledge base K is said to be consistent if K admits a model. Given any two
knowledge bases K and K0 , we say that K entails K0 , and write K =⇒ K0 , if and
only if one has I |= K0 whenever I |= K holds, for all interpretations I.
4 Formalizing requirements for kinship relations
In this section we introduce the basic terminology used to describe kinship re-
lationships. We also describe a set of constraints KL intended to characterize in
a precise and formal way the terms so introduced, according to their intuitive
meaning. We remark that the set of constraints devised in this phase has a purely
descriptive intent, and therefore one should not care about the decidability of
the representation language involved. Let us put:
KL = { dom(relativeOf) v Person, [C1]
Sym(relativeOf), [C2]
relativeOf ≡ relativeOf+ u (¬id(Person)), [C3]
partnerOf v relativeOf, [C4]
Sym(partnerOf), [C5]
childOf v relativeOf, [C6]
parentOf ≡ childOf− , [C7]
descendantOf ≡ childOf+ , [C8]
descendantOf v relativeOf, [C9]
ancestorOf ≡ parentOf+ } . [C10]
The concept Person is intended to denote all human beings, whether alive or
not. Firstly, the generic relation relativeOf over persons (see [C1]) is defined.
It may be noticed that no constraint about its range is present in KL . But [C2]
enforces the symmetricity of the relativeOf relation, in order to guarantee that
everyone is relative of her relatives, and consequently the domain and the range
of relativeOf will coincide. The relativeOf relation must be such that all the
relatives of a person’s relatives are relatives of the person herself. However, we
have to impose the irreflexivity of the relativeOf relation as, for example, one
6 Domenico Cantone, Aldo Gangemi, and Cristiano Longo
Term Semantics (·)I
> ∆I
⊥ ∅
¬C ∆I \ C I
C tD C I ∪ DI
C uD C I ∩ DI
{a} {aI }
∃R.Self {u ∈ ∆I : [u, u] ∈ RI }
∀R.C {u ∈ ∆I : (∀[u, v] ∈ RI )(v ∈ C I )}
∃R.C {u ∈ ∆I : (∃v ∈ C I )([u, v] ∈ RI )}
≤ nR.C {u ∈ ∆I : |{v ∈ C I : [u, v] ∈ RI }| ≤ n}
≥ nR.C {u ∈ ∆I : |{v ∈ C I : [u, v] ∈ RI }| ≥ n}
U ∆I × ∆I
¬R (∆ × ∆) \ RI
RtS RI ∪ S I
RuS RI ∩ S I
R− {[u, v] ∈ ∆I × ∆I : [v, u] ∈ RI }
id(C) {[u, u] : u ∈ C I }
R+ (RI )+
Constraint Semantics I |= (·) iff
CvD C I ⊆ DI
C≡D C I = DI
RvS RI ⊆ S I
R≡S RI = S I
dom(R) v C (∀[x, y] ∈ RI )(x ∈ C I )
range(R) v C (∀[x, y] ∈ RI )(y ∈ C I )
R1 ◦ . . . ◦ Rn v P R1I ◦ . . . ◦ Rn
I
⊆ PI
Sym(R) (∀[x, y] ∈ RI )([y, x] ∈ RI )
Tra(R) (∀[x, y], [y, y 0 ] ∈ RI )([x, y 0 ] ∈ RI )
Ref(R) (∀x ∈ ∆I )([x, x] ∈ RI )
ASym(R) (∀[x, y] ∈ RI )([y, x] ∈ / RI )
I
Irr(R) (∀[x, y] ∈ R )(x 6= x)
Dis(R, S) RI ∩ S I = ∅
C(a) aI ∈ C I
R(a, b) [aI , bI ] ∈ RI
¬(R(a, b)) [aI , bI ] ∈
/ RI
a=b aI = bI
a 6= b aI 6= bI
Table 1. Some common description logic constructs
Representing Kinship Relations on the Semantic Web 7
can’t be the mother of herself. For this reason, we do not require the transitivity
of the relativeOf relation since this, in conjunction with symmetricity, would
imply also reflexivity, but we provide instead the constraint [C3]. Indeed, the
relation relativeOf is intended to be as general as possible in order to subsume
all the kinship relations. It can be specialized to capture different notions of
kinship in different countries and cultures.
As basic kinship relationships, we consider childhood, denoted by childOf
([C6]), and partnerOf (see [C4]), which connects all the persons that are
either member of a married couple, or of an established unmarried couple,
or having sex together. For kinship, in many applications this is the correct
generalization. Several relations like spouseOf, unmarriedPartnerOf, loverOf,
havingSexWith can all be specialization of this general property. Legally speak-
ing, all or only some of them will be considered according to country’s laws.
Plainly, the partnerOf relation must be symmetric, as stated by the constraints
[C5]. In addition, the irreflexivity of partnerOf, which ensures that no one is
partner with herself, directly descends from the irreflexivity of relativeOf.
Next, the inverse relation parentOf of childOf in [C7], stating that every
person must be child of her parents and parent of her children, is introduced.
Together with the childOf and parentOf relations, their transitive closures, re-
spectively descendantOf ([C8]) and ancestorOf ([C10]), are also introduced.
Notice that since parentOf and childOf are mutually inverses, so must be their
transitive closures. No person can be either a descendant of any of her descen-
dants or the ancestor of any of her ancestors. In addition, no person can be both
ancestor and descendant of another person at the same time. In other words,
the relations descendantOf and ancestorOf are asymmetric and pairwise dis-
joint. However, as these relations are transitive and mutually inverses of one
another, their asymmetricity and pairwise disjointness directly descends from
the irreflexivity of the super-relation relativeOf (see [C9]).
The following knowledge base is trivially entailed by KL :
K
b L = { range(relativeOf) v Person, [C11]
Irr(relativeOf), [C12]
Irr(partnerOf), [C13]
Irr(childOf), [C14]
ASym(childOf), [C15]
parentOf v relativeOf, [C16]
Irr(parentOf), [C17]
ASym(parentOf), [C18]
Irr(descendantOf), [C19]
ASym(descendantOf), [C20]
childOf v descendantOf, [C21]
ancestorOf ≡ descendantOf− , [C22]
ancestorOf v relativeOf, [C23]
Irr(ancestorOf), [C24]
ASym(ancestorOf), [C25]
parentOf v ancestorOf, [C26]
Dis(ancestorOf, descendantOf) } . [C27]
8 Domenico Cantone, Aldo Gangemi, and Cristiano Longo
The expressive definition of the primitive kinship relationships provided by KL
and K b L will be used as requirements to build some kinship ontologies in the
well-known description logics SROIQ (cfr. KS0 and KS00 in Section 5) and EL++
(cfr. KE in Section 6). It will be proved that each of the proposed ontologies is
entailed by KL , in order to verify their coherence with KL itself. In addition,
we derive a collection of test cases (see Table 2) from the constraints in KL and
K
b L , which will be used to compare the inferencing capabilities of the candidate
ontologies. Such test cases consists of a set of assertions (namely constraints
of the forms C(a), R(a, b), and ¬(R(a, a))) called premises, and an expected
consequence, i.e., an assertion which should be inferred from the premises.
Premises Consequence KS KS0 KS00 KE
[C1] Alice relativeOf Bob Alice ∈ Person Y Y Y Y
[C2] Alice relativeOf Bob Bob relativeOf Alice Y Y Y N
[C3] Alice relativeOf Bob Alice relativeOf Charlie N N N N
Bob relativeOf Charlie
Alice 6= Bob 6= Charlie
[C4] Alice partnerOf Bob Alice relativeOf Bob Y Y Y Y
[C5] Alice partnerOf Bob Bob partnerOf Alice Y Y Y N
[C6] Alice childOf Bob Alice relativeOf Bob Y Y Y Y
[C7] Alice parentOf Bob Bob childOf Alice Y Y Y N
[C8] Alice descendantOf Bob Alice descendantOf Charlie N Y N Y
Bob descendantOf Charlie
Alice 6= Bob 6= Charlie
[C9] Alice descendantOf Bob Alice relativeOf Bob Y Y Y Y
[C10] Alice ancestorOf Bob Alice ancestorOf Charlie N Y N Y
Bob ancestorOf Charlie
Alice 6= Bob 6= Charlie
[C11] Alice relativeOf Bob Bob ∈ Person Y Y Y Y
[C12] Alice relativeOf x Alice 6= x N N Y N
[C13] Alice partnerOf x Alice 6= x Y Y Y N
[C14] Alice childOf x Alice 6= x N N Y N
[C15] Alice childOf Bob ¬(Bob childOf Alice) N N Y N
[C16] Alice parentOf Bob Alice relativeOf Bob Y Y Y Y
[C17] Alice parentOf x Alice 6= x N N Y N
[C18] Alice parentOf Bob ¬(Bob parentOf Alice) N N Y N
[C19] Alice descendantOf x Alice 6= x N N Y N
[C20] Alice descendantOf Bob ¬(Bob descendantOf Alice) N N Y N
[C21] Alice childOf Bob Alice descendantOf Bob Y Y Y Y
[C22] Alice ancestorOf, Bob Bob descendantOf Alice Y Y Y N
[C23] Alice ancestorOf Bob Alice relativeOf Bob Y Y Y Y
[C24] Alice ancestorOf x Alice 6= x N N Y N
[C25] Alice ancestorOf Bob ¬(Bob ancestorOf Alice) N N Y N
[C26] Alice parentOf, Bob Alice ancestorOf Bob Y Y Y Y
[C27] Alice ancestorOf Bob ¬(Alice descendantOf Bob) N N Y N
Table 2. Test results
Representing Kinship Relations on the Semantic Web 9
5 Defining kinship in SROIQ
SROIQ is a very expressive description logic introduced in [8]. In this section
two different SROIQ-knowledge bases for kinship are presented and compared.
They are constructed starting from the intuitive description of the knowledge
domain provided by KL , but having to deal with the limitations imposed by
SROIQ. Two limitations are relevant in our context: (a) Boolean operators
on roles, used in [C3], are not allowed; (b) irreflexivity and asymmetry cannot
be stated for transitive roles, or for subroles of transitive ones. Due to these
limitations, the whole set of constraints in KL is not expressible in SROIQ, at
least in an intuitive way. In fact, for example, the irreflexivity of descendantOf,
used in conjunction with transitivity, guarantees the acyclicity of the childOf
and parentOf roles. There is no optimal solution for this issue. Instead, an
ontology designer has to make some design choices in terms of constraints which
are to be excluded and, consequently, inferences which will not be performed by
the system. Hence, we provide a basic set of SROIQ-constraints KS and two
extensions of it, KS0 and KS00 , which guarantee different inferencing capabilities:
KS = { ∃relativeOf.> v Person, Sym(relativeOf),
partnerOf v relativeOf, Sym(partnerOf), Irr(partnerOf),
descendantOf v relativeOf, ancestorOf ≡ descendantOf− ,
childOf v descendantOf, parentOf ≡ childOf− }
KS0 = KS ∪ {Tra(descendantOf)}
KS00 = KS ∪ {Irr(relativeOf), ASym(descendantOf)} .
Notice that the two constrains ancestorOf ≡ descendantOf− and parentOf ≡
childOf− violate the definition of SROIQ syntax reported in [8], which does
not report role equivalences as allowed constrains for SROIQ knowledge bases.
However, this issue can be easily circumvented by the technique reported in
[8, Footnote 2]. For instance, the axiom ancestorOf ≡ descendantOf− can
be regarded just as a macro which introduces a new name ancestorOf for
descendantOf− , so that any ontology extending KS may be rewritten with-
out this axiom (without affecting reasoning) just by replacing every occurrence
of ancestorOf with descendantOf− .
A comparison of the three sets of constrains in terms of types of inferences
they enable is provided in Table 2. It can be easily verified that KL entails KS ,
KS0 , and KS00 , and the test results reported in Table 2 confirm that the converse
entailments do not hold. The amount of inference types guaranteed by KS00 over-
takes that of KS0 , considering the inference types considered in Table 2. On the
other hand, KS0 enforces transitivity of the descendantOf and ancestorOf rela-
tions. This feature may be crucial in some application domains (for example, to
model genealogical trees). In order to evaluate the effective impact of this feature
to real-world applications, let us consider a use case in which a user needs to
retrieve all those persons with an ancestor of a specified nationality, e.g., Italian.
To this purpose, let us introduce the concepts Italian and ItDescendant, de-
noting respectively Italians and people with an Italian ancestor, and define their
intuitive meaning as follows:
q
KL = { Italian v Person, ItDescendant ≡ ∃descendantOf.Italian } .
10 Domenico Cantone, Aldo Gangemi, and Cristiano Longo
Preliminarily, we observe that both KS0 and KS00 can be extended with the con-
q
straints in KL without violating the syntactical limitations imposed by SROIQ.
Then, we provide some test cases (see the two leftmost columns of Table 3) which
q
are consequences of KL ∪ KL , and test the two SROIQ constraint sets KS0 and
00
KS against them.
q q
Premises Consequence KS0 ∪ KL KS00 ∪ KL q
KS00 ∪ KSq KE ∪ KL
Alice descendantOf Bob Alice ∈ ItDescendant Y Y Y Y
Bob ∈ Italian
Alice descendantOf Bob Alice ∈ ItDescendant Y N Y Y
Bob descendantOf Charlie
Charlie ∈ Italian
Alice childOf Bob Alice ∈ ItDescendant Y Y Y Y
Bob ∈ Italian
Bob ancestorOf Alice Alice ∈ ItDescendant Y Y Y N
Bob ∈ Italian
Bob ancestorOf Alice Alice ∈ ItDescendant Y N Y N
Charlie ancestorOf Bob
Charlie ∈ Italian
Bob parentOf Alice Alice ∈ ItDescendant Y Y Y N
Bob ∈ Italian
Table 3. Test results
As expected, KS0 outperforms KS00 with respect to the use case under consid-
eration, as KS0 enforces transitivity of descendantOf. However, transitivity can
be emulated by extending KS00 with the following constraints:
KSq = { Italian v Person,
ItDescendant ≡ ∃descendantOf.Italian t ∃descendantOf.ItDescendant } .
The constraint set obtained in this way passes all the test cases reported in
Table 3. In addition, having declared the transitivity of descendantOf in KL ,
q
KL ∪ KL entails {∃descendantOf.ItDescendant v ∃descendantOf.Italian},
and thus the coherence of KSq with the intuitive description KL ∪ KL q
can be
easily verified. Then, we can conclude that KS00 serve our purposes better than
KS0 does. Of course, our investigation considered just a single use case relative to
a specific application scenarios. In fact, different use cases have to be developed
and studied for different application scenarios, and it cannot be excluded that
KS0 , or another constraints set coherent with KL , performs better than KS00 when
employed in a different context. For example, when the amount of available com-
putational resources (time, space, CPU, etc.) is limited, using a not-so-expressive
description logic, but which admits efficient reasoning algorithms, may be more
appropriate.
Representing Kinship Relations on the Semantic Web 11
6 Defining kinship in EL++
EL++ (presented in [1, 2]) is a description logic which admits polynomial-time
decision procedures, in contrast with the N2ExpTime worst case for SROIQ
knowledge bases (cf. [11]). This make EL++ suitable for applications when the
amount of available resources is limited, but at the cost of a quite restricted
expressivity. In particular, some key features for representing kinship relation-
ships such as inversion, symmetry, and irreflexivity on roles are not available in
EL++ . The following is a set of EL++ -constrains which aims to capture, as much
as allowed by the language, the intuitive meaning of the kinship relationships
reported in Section 4:
KE = { dom(relativeOf) v Person, range(relativeOf) v Person,
partnerOf v relativeOf, descendantOf v relativeOf,
Tra(descendantOf), childOf v descendantOf,
ancestorOf v relativeOf, Tra(ancestorOf),
parentOf v ancestorOf } .
This set of constraints mainly defines the hierarchy of the considered kinship
relations, and enforces the transitivity of ancestorOf and descendantOf. It is
easily verifiable that all the constrains in KE are entailed by KL . On the other
hand, the test results reported in Table 2 show that, as expected, the inferencing
capability of KE is substantially lower than that of the SROIQ-constraint sets
reported in Section 5. In addition, as two relations cannot be forced to be inverse
of one another, also the use case developed to test the impact of transitivity
declarations (see Table 3) is just partially fulfilled.
7 Conclusions and future work
We provided a full characterization of some basic kinship relationships using an
ad-hoc description logic with the aim of encoding the intuitive meaning of these
relationships in a precise and formal way. Then, we derived some test cases that
can be used to measure the inferencing capability of a candidate kinship ontology.
Finally, we devised two SROIQ ontologies and an EL++ ontology, verified their
coherence with the intuitive meaning of the defined kinship relationships, and
compared their inferencing capabilities. In addition, the three ontologies were
tested against a real-world use case.
We considered just basic kinship relationships. Other aspects of kinship have
to be explored, for example gender-specific relations like isFatherOf, or the
distinction between legal and biological relations. Also, further knowledge repre-
sentation paradigms should be considered for kinship, in particular those based
on rules (e.g. [9]). In our opinion, devising a standard format for test cases and
test results for inferencing capabilities of ontologies may be useful, possibly ex-
tending the W3C standard Evaluation And Reporting Language (EARL).11 As
mentioned in Section 4, the first step of our design methodology may involve
11
http://www.w3.org/standards/techs/earl#w3c_all
12 Domenico Cantone, Aldo Gangemi, and Cristiano Longo
an undecidable formal language. In this case, coherence checking of candidate
ontologies with the provided intuitive description of the knowledge domain un-
der consideration cannot be automatized, but must be performed by a human
agent. However, proofs of this kind may be encoded in the language of some
proof-verification tool, in order to be automatically verified by third-parties.
References
1. Franz Baader, Sebastian Brandt, and Carsten Lutz. Pushing the EL envelope.
In Leslie Pack Kaelbling and Alessandro Saffiotti, editors, IJCAI, pages 364–369.
Professional Book Center, 2005.
2. Franz Baader, Sebastian Brandt, and Carsten Lutz. Pushing the EL envelope
further. In Kendall Clark and Peter F. Patel-Schneider, editors, Proceedings of the
OWLED 2008 DC Workshop on OWL: Experiences and Directions, 2008.
3. Franz Baader, Diego Calvanese, Deborah L. McGuinness, Daniele Nardi, and Pe-
ter F. Patel-Schneider, editors. The Description Logic Handbook: Theory, Imple-
mentation, and Applications. Cambridge University Press, 2003.
4. Lloyd Bonfield. Seeking connections between kinship and the law in early modern
england. Continuity and Change, 25(01), 2010.
5. Eric Vitiello Jr Ian Davis. Relationship: A vocabulary for describing relationships
between people, 2004. http://purl.org/vocab/relationship.
6. Nicholas Flores-Herr, Stephan Eickeler, Jan Nandzik, Stefan Paal, I. Konya, and
Harald Sack. Contentus – Next Generation Multimedia Library,, pages 67–88.
Springer Verlag, Heidelberg, 2011.
7. Aldo Gangemi, Nicola Guarino, Claudio Masolo, Alessandro Oltramari, and Luc
Schneider. Sweetening Ontologies with Dolce. In EKAW 2002, LNCS. Springer,
2002.
8. Ian Horrocks, Oliver Kutz, and Ulrike Sattler. The Even More Irresistible SROIQ.
In Proc. of the 10th Int. Conf. on Principles of Knowledge Representation and
Reasoning (KR2006). AAAI Press, 2006.
9. Ian Horrocks and Peter F. Patel-Schneider. A proposal for an OWL rules language.
In Stuart I. Feldman, Mike Uretsky, Marc Najork, and Craig E. Wills, editors,
WWW, pages 723–731. ACM, 2004.
10. A.L. Hughes. Evolution and human kinship. Oxford University Press, 1988.
11. Yevgeny Kazakov. Sriq and sroiq are harder than shoiq. In Franz Baader, Carsten
Lutz, and Boris Motik, editors, Proceedings of the 21st International Workshop on
Description Logics (DL2008), Dresden, Germany, May 13-16, 2008, volume 353
of CEUR Workshop Proceedings. CEUR-WS.org, 2008.
12. Mary Ann Lamanna and Agnes Riedmann. Marriages & Families: Making Choices
in a Diverse Society. Thomson/Wadsworth, 2006.
13. Yutaka Matsuo, Masahiro Hamasaki, Junichiro Mori, Hideaki Takeda, and Koiti
Hasida. Ontological consideration on human relationship vocabulary for foaf. In
1st Workshop on Friend of a Friend, Social Networking and Semantic Web, 2004.
14. Peter Mika and Aldo Gangemi. Descriptions of social relations. In 1st Workshop on
Friend of a Friend, Social Networking and the (Semantic) Web, September 2004.
15. Robert Stevens and Margaret Stevens. A family history knowledge base using owl
2. In Catherine Dolbear, Alan Ruttenberg, and Ulrike Sattler, editors, Proceedings
of the Fifth OWLED Workshop on OWL: Experiences and Directions, volume 432
of CEUR Workshop Proceedings. CEUR-WS.org, 2009.