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. 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