Kinship plays a fundamental role in human communities as a basic principle for organizing individuals into social groups. Representing 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 rst step, we provide an intuitive 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 di erent 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.
This paper reports work about representing and reasoning over kinship relationships 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, anthropological, 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 reasoning, etc. But kinship knowledge goes well beyond purely formal relations: di erent conceptual dimensions intersect at the kinship level: \blood" (genetic) relations, breeding relations, nursing relations, transfer of legal rights and obligations, 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 de ned for kinship knowledge. The growing amount of kinship knowledge owing 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 reasoning 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 [
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 irre exivity of roles. Such kind of limitations may be frustrating when one attempts to describe a knowledge domain using a speci c 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 de nition for the concept of all persons with an Italian ancestor rather than the more intuitive de nition ItDescendant 9descendantOf:Italian.
In this paper, we use a method based on a formal representation of the requirements for an ontology of the kinship knowledge domain. This starts from an intuitive (but precise) description KL of the knowledge domain we are describing. This description is intuitive in the sense that the correspondence between the de nitions 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 speci cations 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 veried, in order to guarantee that no unexpected consequence can be deduced from K. In other words, this veri cation phase ensures that every fact that can be
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), de ned 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 brie y 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 di erent descriptions of kinship in terms of SROIQ-constraints are provided and compared. The less expressive (but more e cient ) description logic E L++ 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
In the large area of social relationships, kinship plays a fundamental role, since it
pervades (in di erent ways) all human communities as a basic principle for
organizing individuals into social groups. In light of this, kinship relationships have
been intensively studied by anthropologists,7 in order to understand how they
in uence 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 [
Research focused on kinship and, more in general, on human relationships, is also active in the eld 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 [
A more comprehensive set of kinship terms is provided by the agrelon
vocabulary,10 devised in the context of the CONTENTUS Project [
distinguished by means of the two distinct relations hasBiologicalChild and hasAdoptiveChild.
Some considerations about human relationships are presented in [
From a di erent perspective, in [
A more reasoning-oriented work is contained in [
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 di erent human-to-human relationships. By converse, in this paper we provide reasoning-oriented de nitions 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 (the reader may refer to [
Basic syntactic building blocks of all languages in this framework are the three denumerable in nities of concept names, role names, and individual names. Each description logic is mainly characterized by a set of constructors (see the rst part of Table 1), which allow one to de ne 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 nite 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 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 interpretation 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 individual names, respectively. The interpretation function extends to complex terms (concepts and roles) as indicated in the rst 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 by assigning a truth value to it. Evaluation of constraints by a given interpretation I is de ned as in the second part of Table 1, with C,D concepts, R,S roles, and a,b individual names. We write I j= to indicate that the constraint is evaluated to true by the interpretation I. Otherwise, we write I 6j= . An interpretation I is said to be a model for a knowledge base K (and we write I j= K) if I j= for all 2 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 j= K0 whenever I j= K holds, for all interpretations I. 4
Formalizing requirements for kinship relations In this section we introduce the basic terminology used to describe kinship relationships. 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 = f dom(relativeOf) v Person;
relativeOf relativeOf+ u (:id(Person)); partnerOf v relativeOf; Sym(partnerOf); childOf v relativeOf; parentOf childOf ; descendantOf childOf+; descendantOf v relativeOf; ancestorOf parentOf+ g : The concept Person is intended to denote all human beings, whether alive or not. Firstly, the generic relation relativeOf over persons (see [C1]) is de ned. 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 irre exivity of the relativeOf relation as, for example, one
Term
Semantics ( )I > I ? ; :C I n CI C t D CI [ DI C u D CI \ DI
fag faIg 9R:Self fu 2 I : [u;u] 2 RIg 8R:C fu 2 I : (8[u;v] 2 RI)(v 2 CI)g 9R:C fu 2 I : (9v 2 CI)([u;v] 2 RI)g nR:C fu 2 I : jfv 2 CI : [u;v] 2 RIgj ng nR:C fu 2 I : jfv 2 CI : [u;v] 2 RIgj ng U :R R t S R u S
R id(C)
R+
I I ( ) n RI RI [ SI RI \ SI f[u;v] 2 I I : [v;u] 2 RIg f[u;u] : u 2 CIg (RI)+ Constraint Semantics I j= ( ) i
C v D C D
CI DI
CI = DI R v S RI SI
R S RI = SI dom(R) v C (8[x;y] 2 RI)(x 2 CI) range(R) v C (8[x;y] 2 RI)(y 2 CI) R1 ::: Rn v P R1I ::: RnI PI
Sym(R) (8[x;y] 2 RI)([y;x] 2 RI) Tra(R) (8[x;y];[y;y0] 2 RI)([x;y0] 2 RI) Ref(R) (8x 2 I)([x;x] 2 RI) ASym(R) (8[x;y] 2 RI)([y;x] 2= RI)
Irr(R) (8[x;y] 2 RI)(x 6= x) Dis(R;S) RI \ SI = ;
C(a) aI 2 CI
R(a;b) [aI;bI] 2 RI :(R(a;b)) [aI;bI] 2= RI a = b aI = bI a 6= b aI 6= bI 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 re exivity, 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 di erent notions of kinship in di erent 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 speaking, 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 irre exivity of partnerOf, which ensures that no one is partner with herself, directly descends from the irre exivity 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, respectively 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 descendants 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 disjoint. However, as these relations are transitive and mutually inverses of one another, their asymmetricity and pairwise disjointness directly descends from the irre exivity of the super-relation relativeOf (see [C9]).
The following knowledge base is trivially entailed by KL:
KbL = f range(relativeOf) v Person;
parentOf v relativeOf;
childOf v descendantOf; ancestorOf descendantOf ; ancestorOf v relativeOf;
parentOf v ancestorOf; Dis(ancestorOf; descendantOf) g : The expressive de nition of the primitive kinship relationships provided by KL and KbL 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 KbL, 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 [C1] Alice relativeOf Bob [C2] Alice relativeOf Bob [C3] Alice relativeOf Bob
Alice 6= Bob 6= Charlie [C4] Alice partnerOf Bob [C5] Alice partnerOf Bob [C6] Alice childOf Bob [C7] Alice parentOf Bob [C8] Alice descendantOf Bob
Alice 6= Bob 6= Charlie [C9] Alice descendantOf Bob [C10] Alice ancestorOf Bob
Alice 6= Bob 6= Charlie [C11] Alice relativeOf Bob [C12] Alice relativeOf x [C13] Alice partnerOf x [C14] Alice childOf x [C15] Alice childOf Bob [C16] Alice parentOf Bob [C17] Alice parentOf x [C18] Alice parentOf Bob [C19] Alice descendantOf x [C20] Alice descendantOf Bob [C21] Alice childOf Bob [C22] Alice ancestorOf; Bob [C23] Alice ancestorOf Bob [C24] Alice ancestorOf x [C25] Alice ancestorOf Bob [C26] Alice parentOf; Bob [C27] Alice ancestorOf Bob Consequence Alice 2 Person
Alice relativeOf Charlie KS KS0 KS00 KE Y Y Y Y Y Y Y N N N N N
Bob childOf Alice Y Y Y N
Alice ancestorOf Charlie
Y Y Y Y
N Y N Y
De ning kinship in SROI Q
SROIQ is a very expressive description logic introduced in [
0 and KS00 , which guarantee di erent inferencing capabilities: KS = f 9relativeOf:> v Person; Sym(relativeOf); partnerOf v relativeOf; Sym(partnerOf); Irr(partnerOf); descendantOf v relativeOf; ancestorOf descendantOf ; childOf v descendantOf; parentOf childOf g KS0 = KS [ fTra(descendantOf)g
KS00 = KS [ fIrr(relativeOf); ASym(descendantOf)g :
Notice that the two constrains ancestorOf descendantOf and parentOf
childOf violate the de nition of SROIQ syntax reported in [
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 veri ed that KL entails KS , en0t,aialmndenKtsS00 ,doanndotthheoltde.stTrheesualmtsoruenptoorfteidnfienreTnacebltey2pecsognuarmranttheaetd tbhye KcoS00nvoevresreKS takes that of KS0 , considering the inference types considered in Table 2. On the other hand, KS
0 enforces transitivity of the descendantOf and ancestorOf relations. This feature may be crucial in some application domains (for example, to model genealogical trees). In order to evaluate the e ective 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 speci ed nationality, e.g., Italian. To this purpose, let us introduce the concepts Italian and ItDescendant, denoting respectively Italians and people with an Italian ancestor, and de ne their intuitive meaning as follows:
KLq = f Italian v Person; ItDescendant Preliminarily, we observe that both KS
0 and KS00 can be extended with the conq without violating the syntactical limitations imposed by SROIQ. straints in KL Then, we provide some test cases (see the two leftmost columns of Table 3) which q 0 and are consequences of KL [ KL, and test the two SROIQ constraint sets KS KS00 against them.
Premises
Bob 2 Italian
Charlie 2 Italian Alice childOf Bob Bob 2 Italian
Bob 2 Italian
Charlie 2 Italian
Bob 2 Italian
Consequence Alice 2 ItDescendant Alice 2 ItDescendant Alice 2 ItDescendant Alice 2 ItDescendant Alice 2 ItDescendant Alice 2 ItDescendant
Y Y Y Y
Y As expected, KS
0 outperforms KS00 with respect to the use case under considebreateimonu,laatsedKbSy extending KS00 with the following constraints:
0 enforces transitivity of descendantOf. However, transitivity can KSq = f Italian v Person;
ItDescendant 9descendantOf:Italian t 9descendantOf:ItDescendant g : 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 entails f9descendantOf:ItDescendant v 9descendantOf:Italiang, KL [ KL and thus the coherence of KS q can be q with the intuitive description KL [ KL easily veri ed. Then, we can conclude that KS00 serve our purposes better than 0 does. Of course, our investigation considered just a single use case relative to KS a speci c application scenarios. In fact, di erent use cases have to be developed and studied for di erent application scenarios, and it cannot be excluded that KS0 , or another constraints set coherent with KL, performs better than KS00 when employed in a di erent context. For example, when the amount of available computational resources (time, space, CPU, etc.) is limited, using a not-so-expressive description logic, but which admits e cient reasoning algorithms, may be more appropriate.
De ning kinship in E L++
E L++ (presented in [
KE = f 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 g : This set of constraints mainly de nes the hierarchy of the considered kinship relations, and enforces the transitivity of ancestorOf and descendantOf. It is easily veri able 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 ful lled. 7
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 E L++ ontology, veri ed their coherence with the intuitive meaning of the de ned 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-speci c relations like isFatherOf, or the
distinction between legal and biological relations. Also, further knowledge
representation paradigms should be considered for kinship, in particular those based
on rules (e.g. [