Attribute meta-properties for knowledge sharing Valentina Tamma and Trevor J.M. Bench Capon Abstract. Formal ontological analysis is a methodology that builds to which the agents involved in the interoperation refer to, that is, on some philosophical notions in order to guide the process of build- by building a single ontology that is the merged version of different ing ontologies whose structure is correct and little or no tangled. agent’s ontologies, which often cover similar or overlapping domains This paper presents an ontology model that facilitates formal onto- [8]. logical analysis, by providing a set of metaproperties which char- Ontology merging starts with the attempt to find the places in which acterise the behaviour of concept properties in a concept definition, the source ontologies overlap [24], that is the coalescence of two while providing a richer semantics of the concept. We describe con- semantically identical terms in different ontologies so that they can cepts in terms of their attributes (characterising features) and we also be referred to by the same name in the resulting ontology. This is describe the role played by these features in the concept definition, the only step of the merge process which is relevant to the scope of whether they are prototypical or exceptional, whether they are per- this article. The coalescence of terms in diverse ontologies has to mitted to change over time, and if so, how often this happens, how be accomplished bearing in mind that agent’s ontologies might be likely is a concept to show these features, etc. We show that these heterogeneous, and any kind of heterogeneity has to be reconciled in metaproperties can support a methodology, OntoClean [44] that uses order to share knowledge. Heterogeneity is out of the scope of this formal ontological analysis to build cleaner taxonomies (which are article, however we recognise that it can hinder attempts to coalesce thus more sharable). The set of metaproperties for attributes we pro- terms, especially when it concerns semantics. Ontology or semantic pose can be used to guide in determining which metaproperties for heterogeneity occurs when different ontological assumptions about concepts hold for an ontology and therefore can support the use On- overlapping domains are made [43]. toClean. Any consideration on ontology heterogeneity it is usually done assuming that the ontologies involved in the merging process are either built according to some kind of engineering methodology, 1 Introduction such as Methontology [6], or ontology taxonomic structures are Many current applications such as e-commerce or the semantic web validated according to some methodologies such as OntoClean [44]. rely on the ability of different resources or agents to interoperate Both methodologies are aimed to insure that the ontology obtained with each others and with users. In some cases, interoperation after applying them is correct, that it does not contain cycles or becomes more complex, because agents may have been indepen- recursive definitions, and it has a taxonomic structure that is no or dently developed, therefore the assumption that agents use the same little tangled. communication language and the same terminology in a consistent Methontology and OntoClean are complementary methodolo- way cannot be made. When dealing with independently developed gies in that Methontology provides the guidelines for building agents, their interoperability with humans and others depends on or re engineering ontologies, whereas OntoClean can be used the agents’ ability to understand them, which leads us directly either in the validation step (when ontologies are engineered or to ontologies. Ontologies are an explicit, formal specification of restructured) or simultaneously with the ontology construction a shared conceptualisation, where a ‘conceptualisation’ refers to (when ontologies are built from scratch). These two method- an abstract model of some phenomenon in the world by having ologies are currently undergoing an integration process [5] as identified the relevant concepts of that phenomenon, ‘explicit’ means part of the activities of the OntoWeb special interest group on that the type of concepts used, and the constraints on their use are Enterprise-standards Ontology Environments (SIG’s home page: explicitly defined, ‘formal’ refers to the fact that the ontology should http://delicias.dia.fi.upm.es/ontoweb/sig- be machine-readable, and lastly ‘shared’ reflects the notion that an tools/index.html). ontology captures consensual knowledge, that is it is not private to Methodologies to obtain well-built ontologies, however, are not some individual, but accepted by a group [37]. That is ontologies enough to support the semi-automatic coalescence process. In fact provide a formally defined specification of the meaning of those in order to recognise whether two concepts (that can be affected terms that are used by agents during the interoperation. by heterogeneity) are similar, we cannot only rely on the the Agents can differ in their understanding of the world surrounding terms denoting them, on the relationships with other terms, and on them, in their goals, and their capabilities, but they can still interop- their descriptions, but we need to have a full understanding of the erate in order to perform a task. The interoperation among agents concepts. As noted by McGuinness [23], an explicit representation is the result of reaching an agreement on a shared understanding, of the semantics of terms would be useful to understand whether two mainly obtained by the reconciliation of the differences. This kind concepts are similar. It emerges that the current ontology models are of reconciliation might be accomplished by merging the ontologies not expressive enough to provide such an explicit representation of  Department of Computer Science, University of Liverpool, Chadwick the semantics. Even when heavyweight ontologies are considered Building, Liverpool L69 7ZF, UK, email:  valli, tbc  @csc.liv.ac.uk (that is, concepts described in terms of attributes, linked by relations, organised into an Is-a relationship and constrained by axioms) their people are the same if they have the same fingerprints. Fingerprints expressiveness does not allow a full account of the semantics of the are intrinsic to the individual, they are not assigned by an external concepts described. agent. A re-identification criterion might depend on the role played This paper is organised as follows: Section 2 presents the OntoClean by the object: one can be a student and an employee at the same methodology and the notions of formal ontological analysis, while time, and is re-identified as student by the student id, whereas is Section 3 introduces our proposal for an ontology model encom- re-identified as employee by an employee number. passing a set of metaproperties for attributes which are discussed in Although the problem of identifying what features an entity should the following subsections. This ontology model was also presented have in order to be what it is and recognised as such has been in [39], in this paper we do not discuss any implementation issues central to philosophy, it did not have the same impact in conceptual and we concentrate on the metaproperties, clarifying the relationship modelling and more generally AI. The ability to identify individuals with the concept metaproperties used in OntoClean and the role is central to the modelling process, more precisely, it is not the attribute’s metaproperties play in associating senses to concepts. mere problem of identifying an entity in the world that is central Section 4 discusses the metaproperties and relates them with two to the ontological representation of the world, but the ability to notions (identity and rigidity) of formal ontological analysis and re-identify an entity in all its possible forms, or more formally re- with roles. Then we proceed by presenting in Section 5 and subsec- identification in all possible worlds. 2 That is, the problem is related tions a novel approach to knowledge sharing that we are currently to distinguishing a specific instance of a concept from its siblings on investigating and which motivated the ontology model presented in the basis of certain characteristic properties which are unique and Section 3. This approach, called ontology clustering, is thought of intrinsic to that instance in its whole. Intrinsic properties correspond being more suited to open evironments in which agents interoperate to the modelling primitive attributes. Extrinsic properties represent with each others. We Finally, Section 6 draws conclusions and in relations between classes, thus corresponding to the modelling Section 7 we describe future work. primitive relationship. This notion is, of course inherently time dependent, since time gives rise to a particular system of possible worlds where it is highly likely 2 The philosophical notions of Identity, Unity, that the same instance of a concept exhibits different features 3 . Essence, and Dependence This problem is known as identity through change: an instance of a OntoClean [44] is a methodology to perform a formal ontolog- concept may remain the same while exhibiting different properties ical analysis on taxonomies in order to to verify which formal at different instants of time. Therefore it becomes important to metaproperties hold, thus making clear and explicit the modelling understand which features or properties can change and which assumptions made while designing the ontologies. The clarification cannot [44], and also the situations that can trigger such changes. and explication of the modelling assumptions is a necessary step If we reformulate the identity problem as re-identification we to perform in order to evaluate ontologies, it permits knowledge realise that re-identification is also affected by time; how can we engineers to detect and reconcile ontological conflicts that may affect re-identify the same instance at different instant of times? We one or more ontologies. Ontological conflicts may become apparent face the re-identification problem in everyday life; we are able to when two ontologies are compared in order to coalesce term, and recognise the features that permits us to distinguish an instance from they reveal cases of ontological heterogeneity. For example two the others, and when intrinsic features are not available, we ‘attach’ well known ontologies, present the following conflict: one models artificial features, that permit us to establish identity. One example is Physical Object as subconcept of Amount of matter wheres the other the Student ID, which is assigned to university students, in order to models Amount of matter as subconcept of Physical object, this is identify students univocally. a case of ontology heterogeneity due to different modellings of the concepts. Ontologial conflicts need to be detected and resolved if Unity: the notion of unity is often included in a more gener- terms are to be coalesced. alised notion of identity, although these two notions are different. OntoClean is strongly based on the philosophical notions of identity, While identity aims to characterise what is unique for an entity unity, essence (rigidity), and dependence. The attribute metaprop- of the world when considered as a whole, the goal of unity is erties we present in this paper are related to these notions, and we that of distinguishing the parts of an instance from the rest of the discuss them below. world by means of a unifying relation that binds them together (not involving anything else) [44]. For example, the question ‘Is this my Identity: Identity is the logical relation of numerical sameness, car?’ represents a problem of identity, whereas the question ‘Is the in which a thing stands only to itself. Based on the idea that every- steering wheel part of my car?’ is a problem of unity. Also the notion thing is what it is and not anything else, philosophy has tried for a of unity is affected by the notion of time; for example, can the parts long time to identify the criteria which allow a thing to be identified of an instance be different at different instants of time? for what it is even when it is cognised in two different forms, by two different descriptions and/or at two different times [45, 15]. Essence: The notion of essence is strictly related to the notion This comprises both aspects of finding constitutive criteria (which of necessity [16]. An essential property is a property that is neces- features a thing must have in order to be what it is), and of finding sary for an object, that is, a property that is true in every possible re-identification criteria (which feature a thing has to have in order world [22]. Based on the notion of essence, Guarino and colleagues to be recognised as such by a cognitive agent). These are distinct, [14] have introduced the notion of rigidity. A rigid property is a although equally important aspects of identity.In fact, while identity  Some philosophers, e.g. Lewis [21, page 39 ff], hold that there is no such is not affected by the context and is based on the the intrinsic features thing as trans-world identity, although objects in one world can have coun- of an object, whereas re-identification is affected by context and it is based on features that are external to the object. For example, an  Here terparts in other worlds. the counterpart theory does not hold, and so identity through time is identity criterion for people is to have matching fingerprints, so two always accepted. property that is necessary to all instances in any instant of time, that their values can be inherited from multiple parents. The values asso- is a property  such that:    . For ciated with an attribute can be restricted in order to provide a better this formula, and in the remainder of this paper, we use the modal definition of a concept [19]. notions of necessity  and possibility quantified over possible Attributes are described in terms of their structural characteristics, worlds (in Kripke’s semantics [18]), meaning that the extension of such as the concepts that they are defining, their allowed values, the predicates concerns what exists in any possible world. We use these type of the values (string, integer, etc.), and the maximum and mini- operators according to the following meanings: ! means that  mum values (if attributes are numeric). Attributes are also described holds in all possible worlds " means that  is possible, i.e. that  in term of the following metaproperties: holds in at least one possible world. # Attribute’s behaviour over time: The metaproperties Mutability, Rigidity strictly depends on the notions of time and modality [38]; this point is further elaborated in Section 4.2. It is important,however, Mutability Frequency, Event Mutability and Reversible Mutability not to confuse modal necessity with temporal permanence. Modal provide a better description of attributes by characterising their be- necessity means that the property is true in every possible world. haviour over time, that is, whether they are allowed to change their Time is undoubtedly one partition of these worlds, but temporal value during the concept lifetime (Mutability) and how often the permanence means that the property is true in that world (time), with change occurs Mutability Frequency), whether the change is re- no information concerning the other possible worlds, and this might versible (Reversible Mutability), and what triggers change (Event # happen by pure chance. Mutability); Modality: this meta-property is a qualitative description of the de- Dependence: In OntoClean [44], the notion of dependence is # gree of inheritability of a concept property by its subconcepts; Prototypes and Exceptions: the metaproperties Prototypical and considered related to concept properties. In this context, dependence permits us to distinguish between extrinsic and intrinsic properties Exceptional aim to describe properties that are prototypical for based on whether they depend on objects other than the one they are a concept, that is the properties that obtain for the prototypical ascribed to or not. (from a cognitive viewpoint, according to Rosch [30]) instances of a concept. Exceptions are those properties which can be ascribed In order to establish whether these metaproperties hold, Onto- # to a concept although being highly unusual; Inheritance and Distinction: inherited metaproperties regard those Clean is supported by a description logic based system that can help knowledge engineers to assign the metaproperties to concepts and properties that hold because inherited from an ancestor concept, to verify the taxonomic structure on the grounds of the modelling they may be overruled in the more specific concept in order to ac- methodology. In this paper we focus our attention on the process commodate inheritance with exceptions. Distinguishing are those of assigning the metaproperties. OntoClean guides knowledge properties that permit us to distinguish among siblings of a same engineers in this process by asking them to answer some questions concept. In other words a distinguishing property  is a prop- such as “Does the property carry identity”. Knowledge engineers can erty such that %$%&')(*%$%,+' , that is there is possibly answer yes, no or unsure, in this latter case more specific questions something for which the property  holds, and there is possibly can be asked, such as “Are instances of the property countable?”. something for which the property does not hold, and these are The OntoClean methodology depends on the knowledge engi- neither tautological nor vacuous [44]. Distinguishing properties neers understanding of the ontologies to analyse and can thus be might cause disjoint concepts in the ontology’s taxonomic struc- problematic if used to evaluate independently designed ontologies. ture. Moreover, OntoClean does not take into account the structure of These metaproperties provide means to distinguish between nec- concept definitions, as it does not consider the characteristic features essary and sufficient conditions for class membership. Indeed, the (or attributes) that might have been used to define concepts. modality meta-property and those describing the behaviour over time This work proposes an enriched ontology model whose aim is to permit the identification of essential (or rigid) properties and neces- complement the OntoClean methodology, by providing an additional sary properties are those that are essential to all instances of a con- way to determine metaproperties to concepts. In our proposal cept. Prototypical properties are good candidates to identify suffi- we describe concepts in terms of their characterising properties, cient conditions, as discussed in Section 3.3. which are in turn described not only in terms of their structural Relations between concepts are supported by the model as are in- features (such as range, domain, cardinality etc.), but also in terms stances. Finally, the ontology model supports roles. Concepts are also of their metaproperties, which describe the contribution given by used to represent roles, which can be thought of describing the part these properties to the concept definition. We describe the enriched played by a concept in a context, (a more complete discussion on ontology model and the metaproperties for attributes in the next roles is postponed to Section 4.3). Roles are described in terms of sections. their context, and the formal role relationship holds, that is, roles are related to concepts by a ‘Role-of’ relations. 3 Enriched ontology model This ontology model enriches the traditional model proposed initially by Gruber [12], in that it permits the characterisation of a concept The ontology model we propose comprises concepts, attributes, re- properties. From this viewpoint it should be more expressive. The lations, and instances. We do not consider here axioms. Concepts solution of adding information characterising concept properties is represent the entities of the domain and the tasks we want to model a controversial one. Although we do realise that often it is not true in the ontology. Concepts are described in terms of defining proper- that ‘more is better’, this work claims that an ontology model which ties, which are represented by associating an attribute with either a include this type of property’s characterisation might be helpful to single value or a set of values. Concepts are organised into an Is-a deal with ontology heterogeneity problems in two ways. On the one hierarchy, so that a concept attributes and their values are inherited hand the model complements the set of formal ontological proper- by subconcepts. Multiple inheritance is permitted, so attributes and ties proposed in [44], and can guide in assigning these to concepts in a way which depends on concept definitions in terms of attributes. always thought of as point events, and we consider durational events This might result particularly useful when knowledge engineers need (events which have a duration) as being a collection of point events to assign formal properties to ontologies they have not designed. in which the property whose mutability is modelled by the set of On the other hand, this conceptual model for ontologies facilitates metaproperties hold as long as the event lasts. a better understanding of the concept semantics. Currently ontology merge is performed by hand based on the expertise of the knowledge engineers and on the ontology documentation. Even in this case the 3.2 Modality: Weighing the validity of attributes’ ontology model we propose can prove useful by providing a charac- properties terisation of the properties, which can help to identify semantically The term modality is used to express the way in which a statement is related terms. The following subsections describe all the metaprop- true or false, which is related to establish whether a statement consti- erties for attributes but Inheritance and Distinction (which are trivial) tutes a necessary truth and to distinguish necessity from possibility more in detail: [18]. The term can be extended to qualitatively measure the way in which a statement is true by trying to estimate the number of possible 3.1 Behaviour over time worlds in which such a truth holds. This is the view we take in this work, by denoting the degree of confidence that we can associate The metaproperties which model the behaviour of the attributes over with finding a certain world with the meta-property modality. This time are: notion is analogous to the rankings defined by Goldszmidt and Pearl # Mutability, which models the liability of a concept property to [10]: ‘Each world is ranked by a non-negative integer - representing the degree of surprise associated with finding such a world’. change, a property is mutable if it can change during the concept Here we use the term modality to denote the degree of surprise in # finding a world where the property . holding for a concept / does lifetime; not hold for one of its subconcepts / . The additional semantics Mutability Frequency, which models the frequency with which a # property can change in a concept description; encompassed in this meta-property is important for reasoning with Event Mutability, which models the reasons why a property may statements that have different degrees of credibility. Indeed there is change; Reversible Mutability, which models reversible changes a difference in asserting facts such as ‘Cats are pets’ and ‘All felines of the property. are pets’, the former is generally more believable than the latter, for These metaproperties describe the behaviour of fluents over time, which many more counterexamples can be found. The ability to dis- where the term fluent is borrowed from situation calculus to denote tinguish facts whose truth holds with different degrees of strength is a property of the world that can change over time. Modelling the important in order to find which facts are true in every possible world behaviour of fluents corresponds to modelling the changes in prop- and therefore constitute necessary truth. erties that are permitted in a concept description without changing The ability to evaluate the degree of confidence in a property describ- the essence of the concept. Describing the behaviour over time also ing a concept is also related to the problem of reasoning with ontolo- involves distinguishing properties whose change is reversible from gies obtained by merge. In such a case, mismatches can arise if a those whose change is irreversible. concept inherits conflicting properties. In order to be able to reason Property changes over time are caused either by the natural pas- with these conflicts some assumptions have to be made, concerning sage of time or are triggered by specific event occurrences. We need, on how likely it is that a certain property holds. In case of conflict the therefore, to use a suitable temporal framework that permits us to property’s degree of credibility can be used to apply some forms of reason with time and events. In [39] we chose Event Calculus [17] non monotonic reasoning or belief revision. For example, we could to accommodate the representation of changes. Event calculus deals rank the possible alternatives on the grounds of the degree of credi- with local event and time periods and provides the ability to reason bility following an approach similar to the one presented in [10]. about change in properties caused by a specific event and also the ability to reason with incomplete information. 3.3 Prototypes, exceptions, and concepts Changes of properties can be modelled as processes [35]. Processes can be described in terms of their start and end points and the changes In order to get a full understanding of a concept it is not sufficient that happen in between. We can distinguish between continuous and to list the set of properties generally recognised as describing a typ- discrete changes, the former describing incremental changes that ical instance of the concept but we need to consider the known ex- take place continuously while the latter describe changes occurring ceptions. In this way, we partially take the cognitive view of proto- in discrete steps called events. Analogously we can define continuous types and graded structures, which is also reflected by the informa- properties to be those changing regularly over time, such as the age tion modelled in the meta-property modality. In this view all cogni- of a person, versus discrete properties which are characterised by an tive categories show gradients of membership which describe how event which causes the property to change. If a property’s mutability well a particular subclass fits people’s idea or image of the category frequency is regular (that is it changes regularly), then the process is to which the subclass belong [30]. Prototypes are the subconcepts continuous, if it is volatile the process is discrete, and if it changes which best represent a category, while exceptions are those which once only in the concept lifetime, then the process is considered dis- are considered exceptional although still belonging to the category. crete and the triggering event is set equal to time-point=T. In other words all the sufficient conditions for class membership hold Any regular occurrence over time can be, however, expressed in form for prototypes. For example, let us consider the biological category of an event, since most of the forms of reasoning for continuous mammal: a monotreme (a mammal who does not give birth to live properties require discrete approximations. Therefore in the ontol- young) is an example of an exception with respect to the property of ogy model we present here, continuous properties are thought of as giving birth to live young. Prototypes depend on the context (that is discrete properties where the event triggering the change in property on the specific domain that is conceptualised); there is no universal is the passing of time from the instant  to the instant   . Events are prototype but there are several prototypes depending on the context, therefore a prototype for the category mammal could be cat if the Furthermore, the enriched ontology model we propose forces knowl- context taken is that of animals that can play the role of pets but it is edge engineers to make ontological commitments explicit, that is the lion if the assumed context is animals that can play the role of circus agreement on the meaning of the terms used to describe a domain animals. In the ontology model presented above the context can be [13]. Knowledge sharing is possible only if the ontological com- partially described by the roles applicable to the concept for which mitment of the different agents is made explicit. Real situations are prototypical and exceptional properties are modelled. By providing information-rich events, whose context is so rich that, as it has been this example we do not mean that any member of the category ani- argued by Searle [32], it can never be fully specified. When dealing mals that can play the role of pets could be a prototype, but just that with real situations one makes many assumptions about meaning and prototypes vary if we vary the perspective we are taking on the do- context [31], and these are rarely formalised. But when dealing with main. Therefore there is no unique prototype for the category animal ontologies these assumptions must be formalised since they are part but a number of prototypes, depending on how people conceptualise of the ontological commitments that have to be made explicit. En- the domain, and this implies also contextual information, for exam- riching the semantics of the attribute descriptions with things such as ple what is the role played by animals. the behaviour of attributes over time or how properties are shared by Ontologies typically presuppose context and this feature is a major the subconcepts makes some important assumptions explicit. source of difficulty when merging them, since information about con- The enriched semantics is essential to reconcile cases of ontology text is not always made explicit. heterogeneity. By adding information on the attributes we are also Prototypes are also quite important in that they provide a frame of aiming to measure the similarity between concepts more precisely reference for linguistic quantifiers such as tall, short, old, etc. These and to disambiguate between concepts that seem similar while they quantifiers are usually defined or at least related to the prototypical are not. instance of the concept which is being described, and indeed their A possible drawback of enriching the ontology model is that knowl- definition changes if we change the point of reference. edge engineers are required a deeper analysis of a domain. We re- Therefore including the notions of prototypes and exceptions per- alise that it makes the process of building an ontology even more mits us to provide a frame of reference for defining these qualifiers time consuming but we believe that a more precise ontological char- with respect to a specific concept. For the purpose of building ontolo- acterisation of the domain at least balances the increased complexity gies, distinguishing the prototypical properties from those describing of the task. Indeed, in order to include the attribute’s metaproperties exceptions increases the expressive power of the description. Such to the ontology model, knowledge engineers need to have a full un- distinctions do not aim at establishing default values but rather to derstanding not only of the concept they are describing, but also of guarantee the ability to reason with incomplete or conflicting con- the context in which the concept is used. Arguably, they need such cept descriptions. knowledge if they are to perform the modelling task thoroughly. The ability to distinguish between prototypes and exceptions helps The evaluation of the cost to pay for this enriched expressiveness to determine which properties are necessary and sufficient conditions and of the kind of reasoning inferences permitted by this model are for concept membership. In fact a property which is prototypical and strictly dependent on the domain and the task at hand. We can imag- that is also inherited by all the subconcepts becomes a natural candi- ine that the automatic coalescence of terms might require more so- date for a necessary condition. Prototypes, therefore, permit the iden- phisticated inferences whose cost we cannot evaluate a priori. In tification of the subconcepts that best fit the cognitive category rep- some other cases, the simple matching between properties’ charac- resented by the concept in the specific context given by the ontology. tersiations might help in establishing or ruling out the possiblity of On the other hand, by describing which properties are exceptional, semantic relatedness. For example, two concepts are described by we provide a better description of the membership criteria in that it the same properties but with different characterisations, this might permits us to determine what are the properties that, although rarely indicate that the concepts have been conceptualised differently. holding for that concept, are still possible properties describing the cognitive category. Prototypes and exceptions can prove useful in dealing with con- 4.1 Identity flicts arising from ontology merging. When no specific information is The idea of modelling the permitted changes for a property is strictly made available about a concept and it inherits conflicting properties, related to the philosophical notion of identity. The metaproperties then we can assume that the prototypical properties hold for it. modelling the behaviour over time are, thus, relevant for establishing the identity of concept descriptions [44], since the proposed ontol- 4 Discussion ogy model addresses the problem of modelling identity when time is involved, namely identity through change, which is based on the The ontology model presented in previous section could be imple- common sense notion that an individual may remain the same while mented in any kind of ontology representation formalisms. In [39] showing different properties at different times [16]. The knowledge we presented an implementation of the ontology model above in a model we propose explicitly distinguishes the properties that can frame-based representation formalism, therefore attributes were de- change from those which cannot, and describes the changes in prop- scribed by associating values to slots, and their structural description erties that an individual can be subjected to, while still being recog- and metaproperties were modelled by the slot’s facets. nised as an instance of a certain concept. By adding the metaproperties to the ontology model, we provide an Prototypical and exceptional properties and the modality metaprop- explicit representation of the attributes’ behaviour over time, their erties describing how the property is inherited in the hierarchy can all prototypicality and exceptionality, and their degree of applicability contribute to determine what are the necessary and sufficient condi- to subconcepts. This explicit representation may be used to support tions for class membership. Necessary and sufficient conditions are and complement the OntoClean methodology [44], in that they can ultimately the conditions that permit us to define the properties con- help in determining which metaproperties hold for concepts, as we stitutive of identity and to distinguish them from those that permit will illustrate in remainder of this section. re-identification. In order to find suitable identity criteria (which permit to identify a +.@<44(A+?/B<44 ’, where .@<4' denotes that < is a part of concept), knowledge engineer should look at essential property, that while /B<4' denotes that < is a constituent of . In other words a is those properties which hold for an individual in every possible cir- concept is a role if its individuals stand in relation to other individ- cumstance in which the individual exists. It is important to note that uals, and they can enter or leave the extent of the concept without essential properties should also be intrinsic if they have to be used to losing their identity. From this definition it emerges that the ability determine identity. of recognising whether rigidity holds for some property  is essential Also inheritance and distinction contribute to identify identity condi- in order to distinguish whether  is a role. tions, in that identity conditions have to be looked for among distin- Roles may be ‘naturally’ determined when social context is taken guishing properties. into account, and the social context determines the way in which a role is acquired and relinquished. For example, the role of Pres- ident of the country is relinquished differently depending 4.2 Rigidity on the context provided by the country. So, for example, in Italy the Identity through change is also relevant to determine rigidity. In Sec- role may be acquired and relinquished only once in the lifetime of tion 2 a rigid property is defined as a property that is essential to all an individual, whereas if the country is the United Sates, the role its instances. can be acquired and relinquished twice, because a president can be In [38] we have related the notion of rigidity to those of time and re-elected. Social conventions may also determine that once a role modality; and, by including in our ontology model a meta-property is acquired it cannot be relinquished at all. For example, the role modality and that concerning the behaviour over time, we can pre- Priest in a catholic context is relinquished only with the death of cisely identify rigidity in the subset of the set of possible worlds. the person playing the role. The ability to distinguish roles gives also Indeed, since an ontology defines a vocabulary, we can restrict our- a deeper understanding of the possible contexts in which a concept selves to the set of possible worlds which is defined as the set of can be used. Recognising a role can be equivalent to defining a con- maximal descriptions obtainable using the vocabulary defined by the text, and the notion of context is the basis on which prototypes and ontology [26]. By characterising the rigidity of a property in this sub- exceptions are defined. set of possible worlds we aim to provide knowledge engineers the In [36] Steimann compares the different characteristics that have means to reach a better understanding of the necessary and sufficient been associated in the literature with roles. From this comparison conditions for the class membership. However, this does not mean it emerges that the notion of role is inherently temporal, indeed roles that the rigidity of a property depends on any account of whether are acquired and relinquished dependent on either time or a specific the property is used to determine class membership or not. That is, event. For example the object person acquires the role teenager if the final aim is to try to separate the properties constitutive of iden- the person is between 13 and 19 years old, whereas a person be- tity from those that permit re-identification. Under the assumption of comes student when they enroll for a degree course. Moreover, from restricting the discourse to this set of possible worlds, rigid proper- the list of features in [36] it derives that many of the characteristics ties are those properties which are inherited by all subconcepts, and of roles are time or event related, such as: an object may acquire thus which have a certain degree of belief associated with the meta- and abandon roles dynamically, may play different roles simultane- property modality and that cannot change in time. ously, or may play the same role several time, simultaneously, and It is important to note that, although in [39] we have modelled this the sequence in which roles may be acquired and relinquished can information as a facet which can take value in the set 0 All, Almost all, be subjected to restrictions. Indeed, what distinguishes a role from a Most, Possible, A Few, Almost none, None 1 , the choice of such a set is concept, in the modelling process, is that a role holds during a spe- totally arbitrary, and it was meant to be such. Knowledge engineers cific span of time in which some property holds. For example, the should be able to associate with this meta-property either a proba- role ‘Student’ is applicable only if the property of being registered bility value, if they know the probability with which the property is to a university holds. Therefore, the metaproperties that model the inherited by subconcepts, or a degree of belief (such as a - -value, as behaviour over time permits the representation of the acquisition and in [10], which depends on a 2 whose value can be changed according relinquishment of a role. to the knowledge available, thus causing the - function to change), For the aforementioned reasons, ways of representing roles must be if the probability function is not available. supported by some kind of explicit representation of time and events. Indeed the proposed model provides a way to model roles as fluents; moreover, by modelling the reason for which a property change, we 4.3 Roles dependence on identity and rigidity provide knowledge engineers the ability to model the events that con- Rigidity is not only central in order to distinguish necessary truth but strain the acquisition or the relinquishment of a role. also to recognise roles from concepts. The notion of role is as central to any modelling activity as those of objects and relations. 5 A novel proposal to knowledge sharing A definition of role that makes use of the formal metaproperties and includes also the definition given by Sowa [34] is provided by We have illustrated and discussed a ontology model which is en- Guarino and Welty. In [44] they define a role as: ‘ the properties riched with metaproperties providing a better characterisation of at- expressing the part played by one entity in an event, often exem- tribute. This characterisation is meant to help in disambiguating het- plifying a particular relationship between two or more entities. All erogeneous concepts when merging ontologies, since we assume that roles are anti-rigid and dependent... A property  is said to be anti- two concepts can be matched if : rigid if it is not essential to all its instances, i.e. 3 4556 %$7%+ ... # their description comprises attributes with matching names (syn- A property  is (externally) dependent on a property 8 if, for all its instances , necessarily some instance of 8 must exist, which # onyms, the name of an attribute is included into the other, etc.); candidate matching attributes are described by matching structural is not a part nor a constituent of , i.e. 39:4,;$%<=87<>?( definitions (range of the attribute, cardinality, etc.); # candidate C matching attributes show the same behaviour in mod- # Lack of tools that can support the building of the ontology clusters. elling the concept, that is, the same metaproperties hold for the attributes. 5.1 Ontology clusters Matching similar concepts plays a pivotal role in those approaches to knowledge sharing which rely on shared ontologies in order to Ontology clustering is based on the similarities between the con- perform the translation between concepts in heterogeneous ontolo- cepts known to different resources, where each resource represents gies. Usually, knowledge sharing is obtained by creating one shared a different aspect of the domain knowledge. We assume that the ontologies to which all the agents commit. However, such an ap- ontologies modelling the resources are consistent, non-redundant, proach has been compared to imposing a standard and suffers from and well structured. We also assume that the ontologies have been the same drawbacks [42]. In this paper we propose a novel archi- built with a methodology including a formal evaluation step, such as tecture to knowledge sharing, which is thought to be more scalable Methontology [11]. We also assume that the ontologies are specified and maintainable, and thus offers more support to the Semantic Web by using a language that conforms to the ontology model described paradigm we have discussed in the Section 1. above. In contrast to an approach in which all resources share one body Since our resources need to communicate in a sensible fashion they of knowledge here we propose to locate shared knowledge in mul- are all supposed to be familiar with some high level concepts. We tiple but smaller shared ontologies. This approach is referred to as group these concepts in an ontology rooted at the top of the hierar- ontology-based resource clustering, or shortly, ontology clustering chy of ontologies. As it describes concepts that are specific to the [33]. Resources no longer commit to one comprehensive ontology domain and tasks at hand we refer to this ontology as the application but they are clustered together on the basis of the similarities they ontology (following Van Heijst and colleagues, [41]. These concepts show in the way they conceptualise the common domain. Thus, we are reusable within the application but not necessarily outside the have not one, but multiple shared ontologies aggregated into clus- application. The concept definitions in the application ontology are ters. chosen from an existing top-level ontology, which in our case is Each cluster can be thought of as a micro-theory shared by all the WordNet [25]. The application ontology thus contains a relevant agents that conform to that cluster. Each micro-theory is in turn gen- subset of WordNet concepts. For each concept one or more senses eralised and they are all eventually generalised by the top-level ontol- are selected, depending on the domain. If some resources share ogy which is a standard upper ontology like the Upper-Cyc [20], so concepts that are not shared by other resources then this leads to as to obtain a structure that is able to reconcile different types of het- the creation of two (or more) sibling ontologies. Each sibling is a erogeneity. We discuss here the feasibility of building such a struc- consistent extension of its parent ontology, but heterogeneous with ture, and in particular, we have investigated the different similarity respect to its peers. We do not pose any restriction to the types of measures that can be used in order to build clusters of ontologies. heterogeneity that can affect the ontologies. This approach is analogous to modularisation in software engineer- A cluster is referred to as a group of consistent ontologies (possibly ing and is thought of having the same advantages, which are: one) in our structure and is described by an ontology which is # Modularity/separability: Each cluster is like a module in soft- shared by those composing the cluster. Both ontology clusters and ontologies within each cluster are organised in a hierarchical fashion # Composability: ware engineering and represents a specific aspect of the domain; Different clusters are composed by generalising where each sibling cluster specialises the concepts that are in its parent cluster. However, while multiple inheritance is permitted the concepts that are common to them. This is the first step to within the ontologies, it is not permitted between ontologies, # permit heterogeneous resources to communicate; Scalability: The addition of a new resource to the architecture therefore the structure of clusters is a tree. In this structure, the lower level clusters have more precise concept definitions than the higher requires only the production of the mapping rules between the on- levels, making the latter more abstract. tology associated to the new resource and the cluster to which this Clusters are linked by restriction or overriding relations, that is # resource belongs; Impact of change minimisation: If a concept description needs concepts in one parent ontology are inherited by its children cluster, but overriding is permitted [42]. The link between the resources to be changed only the mapping rules between the updated on- and the local ontologies, on the other hand, is different, and is a tology and the cluster to which this ontology belongs need to be mapping relation as defined in [42], that is a function preserving the # rewritten; semantics. Division of ontology authoring efforts: Ontologies composing a Figure 1 illustrates an example of this structure, where Local Ont. cluster do not need to be authored by the same people as long as are the local ontologies. # their concepts can be mapped into the concepts of the cluster. Since different siblings can extend their parent cluster concepts Accommodation of diverse formalisations: A cluster can be in different ways the cluster hierarchy permits the co-existence of comprised of ontologies representing different formalisations of heterogeneous (sibling) ontologies. Figure 1 illustrates this particular the same domain, such as different temporal ontologies. structure, where D:EGFIH>J7KML'IN  , D?EOFPH%JQKML4PN  , D:EOFPH%JQKML4PN  , and D:EOFPH%JRKML'IN S are the local ontologies, TUH=VXWZY  is the ontology shared by the local ontologies 1 and 2. Analogously TUH=VXWZY  S is This approach has not been tested yet, therefore we can only foresee the ontology shared by the local ontologies 3 and 4. TUH=VGWZY  S some disadvantages: # There is no methodology which permit to build the structure of indicates the ontology shared by the two below that is TUH=VGW[Y  and TUH=VGWZY  S , and in this example is the application ontology # Complexity ontology clusters; of the first order clustering problem from the machine itself, here denoted by Application Ontology. If some ontologies # Lack learning viewpoint; of semantic-sensitive similarity measure to use to assess the share concepts that are not shared by other ontologies then there is a reason to create a new cluster. A new ontology cluster here is a similarity among concepts; child ontology that defines certain new concepts using the concepts which have a common ancestor, and thus it is not suitable for as- sessing the similarity of heterogeneous local ontologies that have to be clustered. Moreover, this method does not fully exploit the struc- ture of the concept representation, since it does not take into account the concept description in terms of attributes, relationships, etc. thus making it more sensitive to synonym and homonym heterogeneity. In fact, only few efforts are addressing the problem of facilitating the (semi) automatic reconciliation of different ontologies, and they have been mainly developed for merging different ontologies. Rec- onciling different ontologies involves finding all the concepts in the ontologies which are similar to one another, determine what the sim- ilarities are, and either change the source ontologies to remove the overlaps or record a mapping between the sources for future ref- erence [9]. Similarity in these efforts is mainly lexical and not se- Figure 1. The hierarchy of multiple shared ontologies mantic. Most systems for ontology merging rely on dictionaries to determine synonyms, common substrings in the concept names, and concepts whose documentation share many unusual words. They do already contained in its parent ontology. Ultimately, ontologies are not take into account the internal structure of concept representation likely to have concepts that are not shared with any other ontology. and the structure of the ontology. In our ontology structure, we then create a separate, domain-specific The ontology merging environment Chimaera [24] partially consid- ontology as sub ontology of the cluster in which the ontology ers the ontology structure in that it assess similarity between con- resides. We refer to these ontologies as local ontologies. The local cepts also on the grounds of the subclass-superclass relationship and ontologies are the leaf nodes of our ontology hierarchy. In each the attributes attached to the concept. Anchor-PROMPT [9] reconciles of the ontologies in the structure, concepts are described in terms ontologies by finding matching terms, that is, terms from different of attributes and inheritance relations holding in the ontology’s source ontologies that represent similar concepts. Anchor-PROMPT structure. Concepts are hierarchically organised and the inheritance assess both lexical and semantic matches exploiting the content and (with exceptions) allows the passing down of information through structure of the source ontologies (names of classes and slots, sub- the hierarchy. Multiple inheritance is only permitted within the classes, superclasses domains and ranges of slot values, etc.), and the ontologies. user’s actions in merging the ontologies. However, the method used Concepts are expressed in terms of inherited and distinguishing in Anchor-PROMPT is based on the assumption that if the ontolo- attributes. To the set of inherited attributes other attributes are added gies to be merged cover the same domain, the terms with the same to distinguish the specific concept from the more general one. These name are likely to represent the same concepts. Such an assump- attributes describe the characteristic differences between a concept tion is a good rule of thumb, but does not take into account cases of and its siblings. The distinguishing attributes are used to map heterogeneity among the source ontologies. In fact, similar concepts concepts from a source ontology into a target ontology preserving might have different names, and be described by attributes with dif- the meaning of the concept. ferent names. Moreover, the hierarchical structure of the source on- tologies might be different, thus a certain subclass-superclass rela- tionship holding in one source ontology might not hold in the others. The ontology model we have presented has been inspired by a par- 5.2 Towards the semi-automatic construction of ticular approach to assess semantic similarity [29], where the authors ontology clusters propose a method for assessing semantic similarity which takes into The structure of ontology clusters introduced in Section 5.1 builds account the differences in the level of explicitness and formalisation on the ability of identifying similar concepts in different ontologies. of the source ontologies specifications. This method does not require Identifying which concepts are similar and assessing the degree of an a priori shared ontology, and thus makes it suitable for building semantic similarity between them are, thus, two essential steps in the the ontology clusters. The similarity between concepts in different process of building ontology clusters. However, assessing the sim- sources ontologies is assessed by a matching process over synonym ilarity between concepts in diverse ontologies is not a trivial task sets (thus accounting for lexical similarity), semantic neighborhood, because of the heterogeneity that can affect concepts and their de- and distinguishing features. The use of distinguishing features to as- scriptions. sess similarity enables the authors not only to handle binary similar- The problem of assessing semantic similarity has received much at- ity measures, typical of lexical similarity (two terms are either similar tention in the artificial intelligence field [27], [3]. In these efforts, or not), but also to consider gradients of similarity. This is based on ‘semantic similarity’ refers to a form of semantic relatedness using a the assumption that, in order for concepts to be considered similar, network representation. In particular, Rada and colleagues [28] sug- they should present some common features. By assessing similar- gest that similarity in semantic networks can be assessed solely on ity on the grounds of the distinguishing and common features, this the basis of the IS-A taxonomy, without considering other types of method accounts for those problem of synonym terms heterogeneity links. One of the easiest way to evaluate semantic similarity in tax- that can affect both concepts and attributes. onomies is to measure the distance between the nodes corresponding In [29] the authors argue that from an analysis of different feature- to the items being compared, that is the shorter the path between the based models for semantic similarity has emerged the necessity to nodes, the more similar they are. This way of assessing semantic sim- account for the context dependence of the relative importance of dis- ilarity might be useful for semantic networks, however has the ma- tinguishing features and asymmetric characteristic of similarity as- jor drawback of computing the semantic distance between concepts sessments. The method proposed by Rodríguez and Egenhofer is based on Tver- that describe a concept. It also explicitly represents the class member- sky [40] matching process, which produces a similarity value that de- ship mechanism by associating with each attribute (represented in a pends on both common and different characteristic. In order to take slot) a qualitative quantifier representing how properties are inherited into account common and distinguishing features into the matching by subconcepts. Finally, the model does not only describe the proto- process, the usual ontology model is extended to include also an ex- typical properties holding for a concept but also the exceptional ones. plicit specification of the features. By features the authors collec- By providing this explicit characterisation, we are asking knowledge tively mean the set of functions, parts and attributes. Functions rep- engineers to make more hidden assumptions explicit, thus providing resent the intended purpose of the instances of the concept they de- a better understanding not only of the domain in general, but also of scribe. For example the function of a university is to educate. Parts the role a concept plays in describing a specific domain. are the structural element of a concept, and they do not necessar- This paper has also presented a structure of multiple shared ontolo- ily coincide with those expressing the part-of relationship, while at- gies for knowledge sharing. Although this is still on going research, tributes correspond to additional characteristics of a concept that are we believe that such a structure has advantages over the others espe- not considered to be neither parts nor functions. cially if considered in the context of an open environment such as the It could be argued that enriching the concept structure by distinguish- Internet. We believe that this kind of modularisation is the key to ap- ing between parts, functions and attributes can give rise to the articu- plications where intelligent agents (whose knowledge is represented lation of new types of mismatches associated with the classifications by ontologies) interoperate dynamically, by agreeing on the vocabu- of features. However, the authors claim that the advantages of enrich- lary (and shared knowledge) which is closer to the conceptualisations ing the concept structure, namely a matching process that compares of only those agents which are involved in the interoparation and corresponding characteristics of concepts, and the ability to distin- not of all agents that can be potentially involved. We realise that we guish different aspects of the context, modelled by the features, over- have not investigated in sufficient detail the issues related to build- weights the possible disadvantages deriving from a higher number of ing such structure in an efficient and cost effective manner, and the mismatches. relationships existing within and between the ontologies composing We believe that Rodríguez and Egenhofer approach to assess seman- the structure (both topics are future research directions that we will tic similarity rises an important issue, which is that, in order to be consider, see next section); but we think that we have laid the basis able to have a better assessment of semantic similarity (that gives for future research. also gradients of similarity and not only a binary function) it is nec- essary to provide a richer description of the structure of the concepts 7 Future work in the source ontologies. However, we believe that the distinguishing features proposed in [29] overlap with the semantics already mod- Future research on ontology clusters concerns the relationships be- elled by some relationships, such as part-of. tween and within ontologies, which need to be clarified with respect to previous work presented in the literature. Two candidate sets of relations have been identified, these are Borst’s ontology projections: 6 Conclusions include and extend, include and specialise, include and map [2]; and Sharing ontologies independently developed is a burning issue that Visser and Cui’s ontology relations: subset/superset, extension, re- needs to be solved. This paper presents a set of metaproperties de- striction, mapping [42]. Another issue emerging from this research is scribing concept characteristic features (attributes) that can be used how knowledge sources (or agents), reach consensus on which clus- to support both the process of building correct ontologies (by com- ter in the structure of multiple shared ontologies they have to join plementing and supporting the formal ontological analysis performed in order to achieve interoperation. This kind of consensus should be by the OntoClean methodology [44]) and the disambiguation of cases based on suitable similarity measure, that take into account the se- of ontology heterogeneity. Formal ontological analysis is usually de- mantics of the concepts involved, and the semantics of their proper- manding to perform and we believe that the set of metaproperties for ties. There are no similarity functions of this type, that we are aware attributes we propose can support knowledge engineers in determin- of, and it would be interesting to investigate complex similarity mea- ing the metaproperties holding for the concepts by forcing them to sures, such as those for symbolic objects [4]. We are particularly make the ontological commitments explicit. interested in investigating similarity functions that make use of the The metaproperties we propose, namely Mutability, Mutability Fre- extra semantics provided by the conceptual metamodel, in a way quency, Reversible Mutability, Event Mutability, Modality, Proto- analogous to the similarity measure presented in [29]. These kind typicality, Exceptionality, Inheritance and Distinction encompass se- of similarity functions usually provide a measure of the degree of mantic information aiming to characterise the behaviour of properties similarity among different concepts, and not just a binary measure in the concept description. We have argued that such a precise char- that indicates whether two concepts are similar or not. acterisation might help to disambiguate among concepts that only From the viewpoint of the ontology conceptual metamodel, future seem similar, and in turn can support mappings across the structure work include understanding the kind of inferences and the reasoning of multiple shared ontologies that we have devised as alternative to mechanisms that are supported by the additional semantics included the current approaches to knowledge sharing. We claim that this char- in the ontology metamodel. 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