A conceptual model to facilitate knowledge sharing in multi-agent systems Valentina Tamma & Trevor Bench-Capon Agent ART group, Department of Computer Science Chadwick Building, Peach Street Liverpool, L69 7ZF, UK {valli, tbc}@csc.liv.ac.uk ABSTRACT ditionally, this paradigm provides robustness and flexibility This paper presents and motivates an extended ontology of the interfaces between both the agents that exist within knowledge model which represents semantic information about the Internet and between agents and software systems, this concepts explicitly. This knowledge model results from en- is essential since the interfaces cannot be anticipated at de- riching the standard conceptual model with semantic infor- sign time. mation which precisely characterises the concept’s proper- Within a multi-agent system, agents are characterised by ties and expected ambiguities, including which properties different ”views of the world” that are explicitly defined by are prototypical of a concept and which are exceptional, the ontologies, that is views of what the agent knows to be the behaviour of properties over time and the degree of applica- concepts describing application domain which is associated bility of properties to subconcepts. This enriched conceptual with the agent together with their relationships and con- model permits a precise characterisation of what is repre- straints [3]. The interoperability typical of multi-agent sys- sented by class membership mechanisms and helps knowl- tems is achieved through the reconciliation of these views of edge engineers to determine, in a straightforward manner, the world by a commitment to common ontologies that per- the meta-properties holding for a concept. Meta-properties mit agents to interoperate and cooperate while maintaining are recognised to be the main tool for a formal ontological their autonomy. analysis that allows building ontologies with a clean and un- In open systems, agents are associated with knowledge sources tangled taxonomic structure. which are diverse in nature and have been developed for dif- This enriched semantics can prove useful to describe what ferent purposes. Knowledge sources embedded in a dynamic is known by agents in a multi-agent systems, as it facilitates environment can join and leave the system at any time. the use of reasoning mechanisms on the knowledge that in- From the ontologies perspective dealing with open systems stantiate the ontology. These mechanisms can be used to implies that ontologies are often the efforts of many domain solve ambiguities that can arise when heterogeneous agents experts and are designed and maintained independently in have to interoperate in order to perform a task. distributed environments. In such a situation interopera- tion between agents is based on the reconciliation of their heterogeneous views, which is accomplished by merging or 1. INTRODUCTION integrating the diverse ontologies associated with the agents Advances in the Internet have made it possible to access composing the system [27]. The merging and integration of huge amounts of diverse information from different places diverse ontologies has to be accomplished bearing in mind all over the world. This possibility has stimulated a grow- that since agents are highly heterogeneous, they are likely to ing demand for understanding how to integrate multiple and be incapable to fully understand each other, therefore both heterogeneous knowledge sources in order to provide added syntactic and semantic inconsistencies can arise and thus value. The complexity of this task is quite high, chiefly be- need to be reconciled. cause of the heterogeneity of the knowledge sources and, to Agent’s ability to represent domain knowledge in a consis- a limited extent, of their size. tent manner has to be complemented by some reasoning One knowledge engineering paradigm that has proved to capability. According to Wooldridge and Jennings, [31] an be useful for dealing with the integration of heterogeneous agent architecture is one that contains an explicitly repre- knowledge is based on a multi-agent system architecture, sented, symbolic model of the world. and in which decisions where human and software agents interoperate and so coop- (for example about what action to perform) are made via log- erate within common application areas. Agents in a multi- ical (or at least pseudo-logical) reasoning, based on pattern agent system are characterised by abstraction, interoperabil- matching and symbolic manipulation. Therefore ontologies ity, modularity and dynamism. These qualities are particu- in multi-agent systems require a high degree of expressive larly useful in that they can help to promote open systems power to support the application of reasoning techniques which are typically dynamic, unpredictable and highly het- that result in sophisticated inferences such as those used erogeneous [14], as is the Internet. In these types of applica- in negotiation, which is motivated by the requirement for tion domains, the interoperability offered by the multi-agent agents to solve problems arising from their interdependence system approach is required because the individual compo- upon one another. [19] nents that interact with agents are not known a priori. Ad- Designing multi-agent systems to deal with the sharing of and which properties change over time. This dynamic be- heterogeneous knowledge sources gives rise to the require- haviour also forms part of the domain conceptualisation and ment for ontologies that can be easily integrated and pro- can help to identify the meta-properties holding for the con- vide a base for applying reasoning mechanisms, highlighting cept. the importance of suitable conceptual models for ontologies. From the multi-agent system perspective, we wish to pro- Indeed, it has been made a point that the sharing of ontolo- vide a better characterisation, and thus understanding of gies depends heavily on a precise semantic representation of the concepts that are known to an agent. Understanding the concepts and their properties [4, 16, 28]. which concepts are associated with an agent and the prop- This paper presents and motivates a knowledge model for erties holding for each concept becomes extremely impor- ontologies which extends the usual set of facets in the OKBC tant when agents need to agree on one or more common frame-base model [2] to encompass more semantic informa- shared ontologies, where each shared concept is obtained tion concerning the concept, to give of a precise characteri- as reconciliation of the local views. Describing concepts by sation of the concept’s properties and expected ambiguities: characterising the behaviour of their properties allow incon- these include which properties are prototypical of a concept sistencies while integrating and reasoning that have to be and which are exceptional; the behaviour of the property dealt with, as illustrated is the next two subsections. over time and the degree of applicability of properties to subconcepts. This enriched knowledge model aims to pro- vide enough semantic information to deal with problems of 2.2 Integrating diverse ontologies The second argument concerns the integration of the di- semantic inconsistency that arise when reasoning with inte- verse agent views, which is accomplished by integrating the grated ontologies. ontologies associated with the agents. The paper is organised as follows: section 2 presents the Integrating ontologies involves identifying overlapping con- motivations for adding semantics to the conceptual model, cepts and creating a new concept, usually by generalising section 3 presents the enriched knowledge model while in the overlapping ones, that has all the properties of the orig- section 4 the model is discussed with respect to the motiva- inals and so can be easily mapped into each of them. Newly tions. Section 5 discusses the representation of roles using created concepts inherit properties, usually in the form of the knowledge model and section 6 provides an example of attributes, from each of the overlapping ones. That is, let concept description using the knowledge model. Finally, in us suppose that the concept C is present in n ontologies section 7 conclusions are drawn and future research direc- O1 , O2 , · · · , On , although described by different properties. tions are illustrated in section 8. That is each ontology Oi , i = 1, · · · , n defines a concept Ci , i = 1, · · · , n such that C1 ≈ C2 ≈ · · · ≈ Cn (where ≈ 2. ENCOMPASSING SEMANTICS IN THE denotes that the concepts are overlapping). Each concept CONCEPTUAL MODEL Ci , i = 1, · · · , n is described in terms of a set of properties The motivation for enriching semantically the ontology con- PiC , i = 1, · · · , n. The result of the integration of the n on- ceptual model draws on three distinct arguments that are tologies is another ontology defining the concept Cintegrated S n analysed in the reminder of this section. which is defined in terms of PiC , where all the PiC have i=1 to be distinguished. 2.1 Nature of ontologies One of the key points for integrating diverse ontologies is The first argument is based on the nature of ontologies. It providing methodologies for building ontologies whose taxo- has been argued that an ontology is ”an explicit specifica- nomic structure is clean and untangled in order to facilitate tion of a conceptualisation” [8]. In other words an ontology the understanding, comparison and integration of concepts. explicitly defines the type of concepts used to describe the Several efforts are focusing on providing engineering prin- abstract model of a phenomenon and the constraints on their ciples to build ontologies, for example [6, 7]. Another ap- use. [26]. An ontology is an a priori account of the objects proach [11, 12] concentrates on providing means to perform that are in a domain and the relationships modelling the an ontological analysis which gives prospects for better tax- structure of the world seen from a particular perspective. onomies. This analysis is based on on a rigorous analysis of In order to provide such an account one has to understand the ontological meta-properties of taxonomic nodes, which the concepts that are in the domain, and this involves a are based on the philosophical notions of unity, identity, number of things. It involves knowing what can be sensi- rigidity and dependence [13]. bly said of a thing falling under a concept. This can be When the domain knowledge associated with different agents represented by describing concepts in terms of their proper- needs to be integrated, inconsistencies can become evident. ties, and by giving a full characterisation of these properties. Many types of ontological inconsistencies have been defined Thus, when describing the concept Bird it is important to in the literature, for instance in [30] and there are ontol- distinguish that some birds fly and others do not. A full un- ogy environments currently available that try to deal with derstanding of a concept involves more than this, however: these inconsistencies, such as smart [4] and Chimaera [17]. it is important to recognise which properties are prototypical Here we broadly classify inconsistencies in ontologies into [20] for the class membership and, more importantly, which two types: structural and semantic. We define structural are the permitted exceptions. There are, however, differ- inconsistencies as those that arise because of differences in ences in how confident we can be that an arbitrary member the properties that describe a concept. Structural incon- of a class conforms to the prototype: it is a very rare mam- sistencies can be detected and resolved automatically with mal that lays eggs, whereas many types of well known birds limited intervention from the domain expert. For example, do not fly. a concept C can be defined in two different ontologies O1 Understanding a concept also involves understanding how and O2 in terms of an attribute A that is specified as tak- ing values in two different domains D1 in O1 and D2 in O2 , - Nixon→ Quaker ; where D1 ⊆ D2 . Structural inconsistencies can be detected and resolved automatically with limited intervention from - Quaker→ Pacifist ; the domain expert. Semantic inconsistencies are caused by the knowledge con- - Republican→ Hawk ; tent of diverse ontologies which differs both in semantics and in level of granularity of the representation. They af- The two concepts Quaker and Republican are described fect those attributes that are actually representing concept by two attributes Pacifist and Hawk that have different features and not relations with other concepts. Semantic names but are semantically related (one is the opposite of inconsistencies require a deeper knowledge on the domain. the other), as they both describe someone’s attitude towards Examples of semantic inconsistencies can be found in [17, going to war. In this case extra semantic information on the 28]. Adding semantics to the concept descriptions can be properties, such as the extent to which the property applies beneficial in solving this latter type of conflict, because a to the members of the class, can be used to derive which richer concept description provides more scope to resolve property is more likely to apply to the situation at hand. possible inconsistencies. Of course, such sophisticated assumptions cannot always be made automatically and might need to be validated by the 2.3 Reasoning with ontologies system user or by some other agent. The last argument to support the addition of semantics to ontology conceptual models turns on the need to reason with the knowledge expressed in the ontologies. 3. EXTENDED KNOWLEDGE MODEL In this section we extend the OKBC knowledge model [?]. We have already mentioned that one of the important prob- This knowledge model is based on classes, slots, and facets. lems to be solved when building agents is the representa- Classes correspond to concepts and are collections of objects tion/reasoning problem, [31] that is: sharing the same properties, hierarchically organised into a multiple inheritance hierarchy, linked by IS-A links. Classes how to symbolically represent information about are described in terms of slots, or attributes, that can either real world entities and processes, and how to get be sets of single values. A slot is described by a name, a agents to reason with this information in time for domain, a value type and by a set of additional constraints, the result to be useful. here called facets. Facets can contain the documentation for a slot, constrain the value type or the cardinality of a slot, From the ontology perspective the reasoning aspect of the and provide further information concerning the slot and the representation/reasoning problem involves the ability of rea- way in which the slot is to be inherited by the subclasses. soning with the knowledge obtained by integrating or merg- In the following small example, that will be used throughout ing diverse ontologies. Indeed, when ontologies are inte- the paper to illustrate the knowledge model here provided, grated, new concepts are created from the definitions of the we start by describing a concept using the basic information existing ones. In such a case conflicts can arise when con- provided by a frame-based knowledge model. The example flicting information is inherited from two or more general is taken from the medical domain and we have chosen to concepts and one tries to reason with these concepts. Inher- model the concept of blood pressure. Blood pressure is rep- iting conflicting properties in ontologies is not as problem- resented here as an ordered pair (s, d) where s is the value atic as inheriting conflicting rules in knowledge bases, since of the systolic pressure while d is the value of the diastolic an ontology is only providing the means for describing explic- pressure. itly the conceptualisation behind the knowledge represented Classes are denoted by the label c, slots by the label s and in a knowledge base [1]. Thus, in a concept description con- facets by the label f. We could describe the concept as: flicting properties can coexist. However, when one needs to reason with the knowledge in the ontology, conflicting prop- c: Circulatorysystem; erties can hinder the reasoning process. Furthermore, if the s: Bloodpressure ontologies one wants to reason with have been developed f: Domain: [(0,0)-(300,200)]; at different times and for diverse purposes, it is likely that f: Value: [(90,60)-(130,85)]; problem of implicit inconsistencies will arise. This kind of problem is quite similar to the semantic inconsistencies that where, for example, the value [(90,60)-(130,85)] means that have been defined in section 2.2. Such a problem has been usually the minimum systolic pressure is 90 and the min- first identified in the inheritance literature [18] where Mor- imum diastolic pressure is 60 while the maximum systolic genstern distinguishes explicit from the implicit inconsisten- pressure is 130 and the maximum diastolic pressure is 85. cies ones. Explicit inconsistencies arise when two concepts In the extended knowledge model that we propose the set of Ci and Cj are described in terms of explicitly conflicting facets has been extended from that provided by OKBC [2] properties, that is in terms of the same attribute which is in order to encompass descriptions of the attribute and its associated with conflicting values V and ¬V . Implicit incon- behaviour in the concept description and changes over time. sistencies arise when the properties are described by different The facets we use are listed below and discussed in the next attributes but with opposite meanings. Morgenstern [18] has section: modified the (notorious) Touretzky’s Nixon diamond [29] to show an example of implicit inconsistencies. Let us consider: • Value: It associates a value v ∈ Domain with an attribute in order to represent a property. However, - Nixon→ Republican ; when the concept that is defined is very high in the hierarchy (so high that any conclusion as to the at- by the knowledge engineers while filling the slots. It tribute’s value is not possible), then either Value = should give an account of information such as why the Domain or Value = Subdomain⊂ Domain; ranking has been set to a specific value or what is the context associated with a prototype (see below the • Type of value: The possible fillers for this facet are discussion concerning prototypes). It is added to keep Prototypical, Inherited, Distinguishing. An attribute’s track of the process leading to the modelling decisions. value is Prototypical if the value is true for any pro- totypical instance or the concept, but exceptions are permitted with a degree of softness expressed by the 4. RELATING THE EXTENDED KNOWL- facet Ranking. An attribute’s value can be Inherited EDGE MODEL TO THE MOTIVATIONS from some super concept or it can be a Distinguishing The knowledge model presented in the previous section is value, that is a value that differentiates among siblings. motivated by the the problems described in section 3. It is Note that distinguishing values become inherited val- based on an enriched semantics that aims to provide a bet- ues for subclasses of the class; ter understanding of the concepts and their properties by characterising their behaviour. • Exceptions: It can be either a single value or a sub- Concept properties are to be considered on three levels: in- set of the domain. It indicates those values that are stance level, class-membership level and meta level. Proper- permitted in the concept description because in the ties at instance level are those exhibited by all the instances domain, but deemed exceptional from a common sense of a concept. They might specialise properties at class- viewpoint. The exceptional values are not those which membership level, which instead describe properties holding differ from the prototypical ones but any value which for the class. Properties at meta level have been mainly de- is possible but highly unlikely; scribed in philosophy, such as identity, unity, rigidity and • Ranking: An integer describing the degree of con- dependency. The proposed model permits the characterisa- fidence of the fact that the attribute takes the value tion of concepts on the three distinct property levels, thus specified in the facet Value. It describe the class mem- also considering the meta level which is the basis for the on- bership condition. The possible values are 1: All, 2: tological analysis illustrated in [12]. Such an enriched model Almost all, 3: Most, 4: Possible, 5: A Few, 6: Almost helps to characterise and identify the meta properties hold- none, 7: None. For example, in the description of the ing for the concepts, thus providing knowledge engineers concept Bird the slot Ability to Fly takes value Yes developing the ontologies with an aid to perform the onto- with Ranking 3, since there are many types of birds logical analysis which is usually demanding to perform. that do not fly. Associating a degree of confidence with Furthermore, the enriched knowledge model forces knowl- a pair (Attribute, Value) is also an arbitrary process edge engineers to make ontological commitments explicit. that depends on the way in which the knowledge en- Indeed, real situations are information-rich complete events gineers writing the ontology perceive the domain. By whose context is so rich that, as it has been argued by Searle giving 7 possibilities to fill the slot ranking we aim to [22], it can never be fully specified. Many assumptions about provide knowledge engineers with the possibility to ex- meaning and context are usually made when dealing with press with more detail their perception of the domain; real situations [21]. These assumptions are rarely formalised when real situations are represented in natural language • Change frequency: Its possible values are: Regular, but they have to be formalised in an ontology since they Once only, Volatile, Never. This facet describes how are ontological commitments that have to be made explicit. often an attribute’s value changes. If the information is Enriching the semantics of the attribute descriptions with set equal to Regular it means that the process is contin- things such as the behaviour of attributes over time or how uous (see section below), for instance the age of a per- properties are shared by the subclasses makes some of the son can be modelled as changing regularly; if set equal more important assumptions explicit. to Once only it indicates that only one change is possi- The enriched semantics is essential to solve the inconsisten- ble, for example a person’s date of birth changes only cies that arise either while integrating diverse ontologies or once. If the slot is set equal to Never it means that the while reasoning with the integrated knowledge. By adding value associated with the attribute cannot change, and information on the attributes we are able to better measure finally Volatile indicates that the attribute’s value can the similarity between concepts, to disambiguate between change more than once, for example people a person’s concepts that seem similar while they are not, and we have blood pressure can change several times, both because means to infer which property is likely to hold for a concept of the aging process and because of specific events such that inherits inconsistent properties. The remainder of this as chock or diseases; section describes the additional facets and relates them to the discussion in section 5. • Event: Describes conditions under which the value changes. It is the set {((Ej , Sj , Vj ), Rj )|j = 1, · · · , m} where Ej is an event, Sj is the state of the pair attribute- 4.1 Behaviour over time value associated with a property, Vj defines the event In the knowledge model the facets Change frequency and validity and Rj denotes whether the change is reversible Event describe the behaviour of properties over time, which or not. The semantics of this facet is explained in the models the changes in properties that are permitted in the section below; concept’s description without changing the essence of the concept. The behaviour over time is closely related to estab- • Documentation: This is not strictly speaking a facet, lishing the identity of concept descriptions [12]. Describing but a string that is add to document the choices made the behaviour over time involves also distinguishing proper- ties whose change is reversible from those whose change is a property that is essential to all its instances, irreversible. i.e. ∀xφ(x) → 2φ(x). Property changes over time are caused either by the natural passing of time or are triggered by specific event occurrences. We need, therefore, to use a suitable temporal framework The interpretation that is usually given to rigidity is that if that permits us to reason with time and events. The model x is an instance of a concept C than x has to be an instance chosen to accommodate the representation of the changes of C in every possible world. Time can be seen as one of is the Event Calculus [15]. Event calculus deals with local these systems of possible worlds and characterising a prop- event and time periods and provides the ability to reason erty as rigid in time gives a better angle on the necessary about change in properties caused by a specific event and and sufficient conditions for the class membership. also the ability to reason with incomplete information. Changes of properties can be modelled as processes [24]. 4.2 Ranking Processes can be described in terms of their starting and Rankings are defined as [5]: ending points and of the changes that happen in between. We can distinguish between continuous and discrete changes, the former describing incremental changes that take place Each world is ranked by a non-negative inte- continuously while the latter describe changes occurring in ger representing the degree of surprise associated discrete steps called events. Analogously we can define con- with finding such a world. tinuous properties those changing regularly over time, such as the age of a person, versus discrete properties which We have borrowed the term to denote the degree of sur- are characterised by an event which causes the property prise in finding a world where the property P holding for to change. If the value associated with change frequency a concept C does not hold for one of its subconcepts C 0 . is Regular then the process is continuous, if it is Volatile The additional semantics encompassed in this facet is im- the process is discrete and if it is Once only the process is portant to reason with statements that have different de- considered discrete and the triggering event is set equal to grees of credibility. Indeed there is a difference in asserting time-point=T. facts such as ”Mammals give birth to live young” and ”Bird Any regular occurrence of time can be, however, expressed fly”, the former is generally more believable than the latter, in form of an event, since most of the forms of reasoning for which many more counterexamples can be found. The for continuous properties require discrete approximations. ability to distinguish facts whose credibility holds with dif- Therefore in the knowledge model presented in previous sec- ferent degrees of strength is related to finding facts that are tion, continuous properties are modelled as discrete proper- true in every possible world and therefore constitute neces- ties where the event triggering the change in property is sary truth. The concept of necessary truth brings us back the passing of time from the instant t to the instant t0 . to establishing whether a property is rigid or not. In fact it Each change of property is represented by a set of quadru- can be assumed that the value associated with the Ranking ples {((Ej , Sj , Vj ), Rj )|j = 1, · · · , m} where Ej is an event, facet together with the temporal information on the changes Sj is the state of the pair attribute-value associated with permitted for the property lead us to determine whether the a property, Vj defines the event validity while Rj indicates property described by the slot is a rigid one. Rigid proper- whether the change in properties triggered by the event Ej ties have often been interpreted as essential properties (i.e., is reversible or not. The model used to accommodate this a property holding for an individual in every possible cir- representation of the changes adds reversibility to Event Cal- cumstance in which the individual exists), but, we note that culus, where each triple (Ej , Sj , Vj ) is interpreted either as a property might be essential to a member of a class without the concept is in the state Sj before the event Ej happens or being essential for membership in that class. For example, the concept is in the state Sj after the event Ej happens de- being odd is an essential property of the number 5, but it is pending on the value associated with Vj . The interpretation not essential for membership in the class of prime numbers. is obtained from the semantics of the event calculus, where The ability to evaluate the degree of credibility of a property the former expression is represented as Hold(before(Ej , Sj )) in a concept description is also related to the problem of en- while the latter as Hold(after(Ej , Sj )). abling agents to reasoning with ontologies obtained through The idea of modelling the permitted changes for a property integration. In such a case, as mentioned in section 2.3, is strictly related to the philosophical notion of identity. In inconsistencies can arise if a concepts inherits conflicting particular, the knowledge model addresses the problem of properties. In order to be able to reason with these conflicts modelling identity when time is involved, namely identity some assumptions have to be made, concerning on how likely through changes, which is based on the common sense no- it is that a certain property holds; the facet Ranking mod- tion that an individual may remain the same while show- els this information by modelling a qualitative evaluation of ing different properties at different times [11]. The knowl- how subclasses inherit the property. This estimate repre- edge model we propose explicitly distinguishes the proper- sents the common sense knowledge expressed by linguistic ties that can change from those which cannot, and describes quantifiers such as All, Almost all, Few, etc.. the changes in properties that an individual can be sub- In case of conflicts the property’s degree of credibility can be jected to, while still being recognised as an instance of a used to rank the possible alternatives following an approach certain concept. similar to the non-monotonic reasoning one developed by [5]: The notion of changes through time is also important to in case of more conflicting properties holding for a concept establish whether a property is rigid. A rigid property is description, properties are ordered according to the degree defined in [10] as: of credibility, that is according to the the filler associated with the Ranking facet weighted by the Degree of strength. Therefore, a property holding for all the subclasses is con- mally thought to be a feature of the cognitive category and sidered to have a higher rank than one holding for few of not only what differs from the prototype. the concept subclasses, but this ordering is adjusted by the Also the information on prototype and exceptions can prove relevance, as perceived by the knowledge engineer, of the useful in dealing with inconsistencies arising from ontology property in the concept’s description (Degree of strength). integration. When no specific information is made available For example, to reason about birds ability to fly, the at- on a concept and it inherits conflicting properties, then we tribute species is more relevant than the attribute feather can assume that the prototypical properties hold for it. colour. When reasoning with diverse ontologies, the Degree The inclusion of prototypes in the knowledge model provides of strength represents the weight associated with the inher- the grounds for the semi-automatic maintenance and evolu- itance rule corresponding to the attribute. tion of ontologies by applying techniques developed in other Although this ordering of the conflicting properties needs to fields such as machine learning. be validated by the user, it reflects the common sense as- sumption that, when no specific information is known, peo- 5. PROSPECTS FOR SUPPORTING ROLES ple assume that the most likely property holds for a concept. The notion of role is central to any modelling activities as Here we assume that the agents reflect the common sense much as those of objects and relations. A thorough discus- reasoning that is typically human. sion of roles goes beyond the scope of this paper, and roles are not supported yet in the knowledge model introduced in 4.3 Prototypes and exceptions section 3. However, the extended semantics provided by the In order to get a full understanding of a concept it is not knowledge model presented above gives good prospects for sufficient to list the set of properties generally recognised as supporting roles. In this section we provide some prelimi- describing a typical instance of the concept but we need to nary consideration and relate the additional facets with the consider the expected exceptions. Here we partially take the main features of the role notion. cognitive view of prototypes and graded structures, which is Despite its importance, highlighted in the literature [9, 23], also reflected by the information modelled in the facet Rank- few modelling languages permit the distinction between a ing. In this view all cognitive categories show gradients of concept and the roles it can play in the knowledge model. membership which describe how well a particular subclass This difficulty is partially due to the lack of a single defini- fits the standard idea or image of the category to which tion for role. the subclass belongs [20]. Prototypes are the subconcepts A definition of role that makes use of the formal meta- which best represent a category, while exceptions are those properties and includes also the definition given by Sowa which are considered exceptional although still belonging to [23] is provided by Guarino and Welty. In [11] they define a the category. In other words all the sufficient conditions for role as: class membership hold for prototypes. For example, let us consider the biological category mammal : a monotreme (a properties expressing the part played by one en- mammal who does not give birth to live young) is an ex- tity in an event, often exemplifying a particular ample of an exception with respect to this attribute. Proto- relationship between two or more entities. All types depend on the context; there is no universal prototype roles are anti-rigid and dependent... A property but there are several prototypes depending on the context, φ is said to be anti-rigid if it is not essential to therefore a prototype for the category mammal could be cat all its instances, i.e. ∀xφ(x) → ¬2φ(x)... A if the context taken is that of pets but it is lion if the as- property φ is (externally) dependent on a prop- sumed context is circus animal. Ontologies typically presup- erty ψ if, for all its instances x, necessarily some pose context and this feature is a major source of difficulty instance of ψ must exist, which is not a part nor when merging them. a constituent of x, i.e. ∀x2(φ(x) → ∃yψ(y) ∧ For the purpose of building ontologies for multi-agent sys- ¬P (y, x) ∧ ¬C(y, x)). tems, distinguishing the prototypical properties from those describing exceptions increases the expressive power of the description. Such distinctions do not aim at establishing In other words a concept is a role if its individuals stand in default values but rather to guarantee the ability to reason relation to other individuals, and they can enter or leave the with incomplete or conflicting concept descriptions. extent of the concept without losing their identity. From this The ability to distinguish between prototypes and excep- definition it emerges that the ability of recognising whether tions helps to determine which properties are necessary and rigidity holds for some property φ is essential in order to sufficient conditions for concept membership. In fact a prop- distinguish whether φ is a role. erty which is prototypical and that is also inherited by all In [25] Steimann presents a list of the features that have the subconcepts (that is it has the facet Ranking set to been associated in the literature with roles. Some of these All ) becomes a natural candidate for a necessary condition. features are conflicting and, as pointed out, no integrating Prototypes, therefore, describe the subconcepts that best definition has been made available. However, from the differ- fit the cognitive category represented by the concept in the ent definitions available, it can be derived that the notion of specific context given by the ontology. On the other hand, role is inherently temporal, indeed roles are acquired and re- by describing which properties are exceptional, we provide a linquished in dependence either of time or of a specific event. better description of the class membership criteria in that it For example the object person acquires the role teenager if permits to determine what are the properties that, although the person is between 11 and 19 years old, whereas a person rarely hold for that concept, are still possible properties de- becomes student when they enroll for a degree course. More- scribing the cognitive category. Here, the term exceptional over, from the list of features in [25] it emerges that many of is used to indicate something that differs from what is nor- the characteristics of roles are time or event related, such as: an object may acquire and abandon roles dynamically, may itly representing additional information on the slot proper- play different roles simultaneously, or may play the same ties. This knowledge model results from a conceptual model role several time, simultaneously, and the sequence in which which encompasses semantic information aiming to charac- roles may be acquired and relinquished can be subjected to terise the behaviour of properties in the concept descrip- restrictions. tion. We have motivated this enriched conceptual model by For the aforementioned reasons ways of representing roles identifying three main categories of problems that can arise must be supported by some kind of time and event explicit in heterogeneous multi-agent systems and that can hinder representation. We believe that the knowledge model we the communication between agents and we have shown that have presented, although it does not encompass roles yet, these problems require additional semantics in order to be provides sufficient semantics to model the dynamic features dealt with. of roles, thanks to the explicit representation of time inter- The novelty of this extended knowledge model is that it vals which is used to model the attributes behaviour over explicitly represents the behaviour of attributes over time time. Furthermore, the ability of modelling events, used to by describing the permitted changes in a property that are describe the possible causes in the state of an attribute, can permitted for members of the concept. It also explicitly rep- be used to model the events that constrain the acquisition resents the class membership mechanism by associating with or the relinquishment of a role. each slot a qualitative quantifier representing how proper- ties are inherited by subconcepts. Finally, the model does 6. A MODELLING EXAMPLE not only describe the prototypical properties holding for a We are now ready to complete the example by modelling the concept but also the exceptional ones. concept blood pressure with the enriched knowledge model We have also related the extended knowledge model to the presented above. In modelling the concept of blood pressure formal ontological analysis by Guarino and Welty [12] which we take into account that both the systolic and diastolic permits to build ontologies that have a cleaner taxonomic pressure can range between a minimum and a maximum structure and so gives better prospects for maintenance and value but that some values are more likely to be registered integration. Such a formal ontological analysis is usually dif- than others. Within the likely values we then distinguish the ficult to perform and we believe our knowledge model can prototypical values, which are those registered for a healthy help knowledge engineers to determine the meta-properties individual whose age is over 18, and the exceptional ones, holding for the concept by forcing them to make the onto- which are those registered for people with pathologies such logical commitments explicit. as hypertension or hypotension. The prototypical values A possible drawback of this approach is the high number of are those considered normal, but they can change and we facets that need to filled when building ontology. We realise describe also the permitted changes and what events can that this can make building an ontology from scratch even trigger such changes. Prototypical pressure values usually more time consuming but we believe that the outcomes in change with age, but they can be altered depending on some terms of better understanding of the concept and the role specific events such as shock and haemorrhage (causing hy- it plays in a context together with the guidance in deter- potension) or thrombosis and embolism (causing hyperten- mining the meta-properties at least balances the increased sion). Also conditions such as pregnancy can alter the nor- complexity of the task. mal readings. Classes are denoted by the label c, slots by the label s and 8. FUTURE WORK facets by the label f. Irreversible changes are denoted by I The extension of the knowledge model with with additional while reversible property changes are denoted by R. semantics opens several new research directions. Firstly, the role representation needs to be formalised in the knowledge c: Circulatorysystem; model in order to represent also the roles hierarchical organ- s: Bloodpressure isation [25]. f: Domain: [(0,0)-(300,200)]; We also plan to use the semantics encompassed in the knowl- f: Value: [(90,60)-(130,85)]; edge model to assist knowledge engineers in the tasks of f: Typeofvalue: prototypical; merging and reasoning with diverse ontologies. To reach f: Exceptions: [(0,0)-(89,59)] ∪ [(131,86)-(300,200)]; this goal we intent to introduce some form of temporal rea- f: Ranking: 3; soning based on the event logics that is used extend the f: Changefrequency: Volatile; facets. f: Event: (Age=60,[(0,0)-(89,59)] ∪ The description of attributes in terms of prototypical values ∪ [(131,86)-(300,200)],after, I); gives us the possibility of exploring the application of ma- f: Event: (haemorrhage,[(0,0)-(89,59)],after, R); chine learning techniques to dynamically extend ontologies. f: Event: (shock,[(0,0)-(89,59)],after, R); f: Event: (thrombosis,[(131,86)-(300,200)],after,R); Acknowledgement f: Event: (embolism,[(131,86)-(300,200)],after,R); The PhD research presented in this paper was funded by BT f: Event: (pregnancy,[(0,0)-(89,59)] ∪ plc. The authors are grateful to Ray Paton for providing the ∪ [(131,86)-(300,200)],after,R); example. This paper is supported by HP. 7. CONCLUSIONS 9. 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