Revising and Managing Multiple Ontology Versions in a Possible Worlds Setting

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1 Revising and Managing Multiple Ontology Versions in a Possible Worlds Setting Pieter De Leenheer Semantics Technology and Applications Research Laboratory Departement Informatica en Toegepaste Informatica Vrije Universiteit Brussel Pleinlaan 2, B-1050 BRUSSEL, Belgium pdeleenh@vub.ac.be Abstract. To date, ontology research seems to have come to an equilibrium: there is a wide variety of theories, methods and tools for extracting, representing, storing and browsing ontologies. Furthermore, ontologies have become an integral part of many academic and industrial applications. There are, however, still deep theoretical problems to be resolved. One fundamental problem is ontology evolution. Essentially, changes occur when new knowledge is agreed on by the (not necessarily human) cognitive agents. Each change engages an evolution process from which a new (possibly inconsistent) ontology version may emerge. How will we manage multiple versions of an ontology in a scalable fashion? How will we represent differences and transformations between ontologies, and moreover, can we solve this question independently from any ontology representation model? This paper describes a research project that will investigate all these critical problems in ontology evolution. 1 Introduction The last ten years ontology research has received a renewed impetus, moreover pushed by the need for taming the wealth of knowledge that is implicitly present on-line on today s web, with the purpose of rendering into a shared resource that allows making more meaningful, and thus more productive use of that knowledge [24]. These knowledge resources are called ontologies. A plethora of research has been spent on how ontologies should be formally defined and represented in a computerisable way [15, 16, 23], and resulted in a wide variety of theories, methods and tools for extracting, representing, storing, browsing and using ontologies [37, 10]. Meanwhile, ontologies have become an integral part of many academic and industrial applications in the domains such as supporting interoperability, database mediation [6, 39], configuration, regulatory compliance [32], semantic-based search [4], Semantic Web [3] applications [11, 25, 8], etc. It seems we have come to an equilibrium in ontology research, though still several deep theoretical problems need to be resolved. Evidently the methodology for manual construction (or

2 should we say growing ) of standardisable, hence reusable computerized ontologies will not be a main feature. At least we can try to enhance this construction by searching for algorithms that help us or perhaps automate this process. Alignment and merging of existing ontologies, ontology learning from incompatible information, and internal reorganisation of ontologies in the light of new information by means of transformations and/or versioning are the three main issues for intelligent ontology construction and evolution. Ontology alignment and merging is not a new problem, and useful results have already been achieved [28, 9]. Two agents having different ontologies merge by negotiating in order to come to an agreement on meaning, being a merged ontology. The success of the merging process depends on an (at least non-zero) initial notion of agreement on some part of the Universe of Discourse (UoD). Two agents align if they define an explicit mapping between their meanings. Ontology learning is extracting semantic knowledge from plain natural text, web documents, dictionaries and so on, which contains (incompatible) redundant mass information. Other important sources are DB schemas, numerous existing thesauri and glossaries, general-purpose lexicons like Wordnet, or possibly even ontologies. One of the principle characteristics of an ontology is that it should define a reusable knowledge component, but in order to create reusable components, evolution is critical, because effective reuse can only be achieved after a component has been evolving over an extended period of time. It is indeed unimaginable to predict all possible uses of an ontology upon its conception. In reality, the UoD will be too complex to enable a complete a priori conceptualisation, that remains valid in the light of new information, or change of pragmatics. Emerging ontologies, domain-specific or general-purpose, will continually re-organise through help of/negotiating with other ontologies (merging and alignment, issue 1), by learning from mining (issue 2) and with or without human support (e.g., change in pragmatics). It is clear that our third issue, re-organisation of ontologies, is an indispensable factor in the issues 1 and 2, and can even be seen as an independent research component. Finally, an intelligent system should be able to accommodate all such issues. In this doctoral research we concentrate on the problem imposed by (issue 3) re-organisation of ontologies: ontology evolution. Note that in this paper we do not consider the distributed character of ontologies. Until now, relevant results of research on the problem of ontology evolution are sparse [27, 18, 20, 35, 36], and there is no consensus about the requirements. However, in currently ongoing EU 6th Framework projects 1 where ontology engineering is being studied, ontology evolution is becoming an ubiquitous part of the work packages. This phenomenon is another indicator for the global interest by the ontology research community and again proves the importance of the subject. This paper is structured as follows: in Sect. 2 we shortly summarise existing approaches and the current knowledge in the field. In Sect. 3 we state the 1 E.g., Data, Information, and Process Integration with Semantic Web Services (DIP) (EU-FP ) and Knowledge Web (EU-FP ).

3 research question central in this Ph.D., and elicit requirements for an evolution framework that is model-independent and manages several ontology versions and their interrelationships concurrently. Finally, we present some possible validation techniques for the proposed hypotheses in Sect Related Work Next to related work in ontology evolution [27, 18, 20, 35, 36], a considerable amount of research has been done in the data and knowledge engineering community [15, 37] that can be fruitful for ontology evolution research. Results of schema integration [2, 29] have been proven relevant in the research into ontology alignment and merging [28, 9], and a more recent trend is that many researchers apply certain principles of data schema evolution [1, 22]and versioning [19, 31] for ontology evolution and versioning respectively. The first methodological step in this Ph.D. research project was to make a comprehensive survey [5, manuscript] of relevant approaches and knowledge so far in the field of ontology evolution and evolution, transformations and versioning of data schemas. We also relate principle ideas of belief revision theory and possible worlds semantics. Ontology Evolution Not much efforts have been spent so far on ontology evolution as the field is rather new. [35] provides different levels of granularity for change operators, resulting in a taxonomy of compound change operators, inspired by those in [22]. She also suggests that different evolution strategies can be defined according to user s demands. Her semantics of change recognises the potential of cascading changes. [20] focuses on ontology evolution on the Semantic Web. They adopt principles of pro- and retrospective use from data schema evolution. Prospective use is the use of a data source conforming to a previous version of the schema, via a newer version of the schema. Other important results are [18], and in medical terminology evolution [27]. Data Schemas versus Ontologies Although the problem issues in schema evolution are not entirely the same as in ontology evolution, the philosophy and results from schema evolution in general 2 are fruitfully reconsidered for the treatment of the ontology evolution problem. The argumentation behind this comparison is that: (i) formally, all such kinds of schemas define sets of predicates (data models); (ii) they describe some UoD by means of a (not necessarily) shared formal language 3. 2 Evolution of object-oriented (OO), relational, entity-relationship (ER), fact-oriented (NIAM [38], ORM [17]) data schemas in particular. 3 E.g., [7] presents a language that is able to represent ER, BRM, or relational schemas. She also defines transformations between these different models.

4 An ontology can be put in this picture by interpreting it roughly as a widely shared conceptual model, although the modeling methodology is different. On the other hand, what really differs is the purpose (pragmatics) of a database model. A relational model on the logical level is normalised such in order to get optimal efficiency, based on user-specific demands. On the conceptual level performance is not the issue, there a model should be constructed as detailed as possible in order to give optimal semantic performance for a given UoD. An ontology has no performance constraints as in logical models or whatsoever, but it should be more generic than the optimally semantically detailed conceptual schemas that are tailored for one system, in order to act as a common agreement between multiple applications. When evolving ontologies it is thus very important to focus more on the semantics than in data schema evolution. Ontologies are (in principle and by definition) as generic and task-independent as possible [34, pp. 13]. The resemblance and differences between ontologies and data models are widely discussed in literature such as [24, 34, 26]. Significant examples of data schema evolution include transformation rules to effect change operators on data schemas and change propagation to the data [1], frameworks for managing multiple versions of data schemas coherently [19, 31] and models for compound change operators 4 [22]. 3 Problem Statement and Requirements Elicitation The central research question of this Ph.D. project is stated as: How can we bootstrap requirements for a model-independent framework that provides methods for changing and managing different ontology versions and their interrelationships? In this section, we will propose some ideas that could feature such a framework. As validation we will implement such system and apply it to large-scale problems. 3.1 A Model-independent Ontology Evolution Framework We present a step-wise procedure for bootstrapping an ontology evolution framework: 1. select a representation model to adopt for evolution; 2. determine the knowledge elements 5 that can evolve according to the adopted model; 3. determine the possible (atomic) change operators that could engage an evolution process or evolution strategy on that particular model. In the simplest case, an evolution process would be the application of a finite sequence of atomic change types; 4 e.g., moving an attribute x from a class A to a class B, means (more than) successively deleting x in A and adding x in B. 5 a knowledge element could be any (set of) elementary ontology building block(s) such as concept, class, type, relation, slot, attribute, rule, and an instance.

5 4. optionally compose compound change operators, comparable to those discussed in Sect. 2; 5. specify requirements for a framework performing and validating the evolution process. This methodological procedure can be found throughout the literature on schema and ontology evolution: e.g., Heflin [18] takes the definition of Guarino [16] as basis for his model, while Klein et al. [20] refer to the definition of Gruber [15]. Heflin s model is formal, but his definition of an ontology (being a logical theory) is very much alike with the formal definition of a data schema as in [7]. On the other hand, Klein et al. are more pragmatical in a way that they take Gruber s definition quite literally, and infer that there are three parts of the ontology (i.e. the model) to consider: the specification, the shared conceptualisation and the domain. In data schema evolution, e.g., [1] chooses the ORION object-oriented model, defers a taxonomy of possible change operators and finally defines an evolution strategy which they call transformation rules. Considering the procedure above it seems inevitable to tackle the evolution problem without considering a particular knowledge representation model. In order to think representation model independent, we must represent ontologies and evolution processes more abstractly. Possible Worlds Semantics For abstraction we choose to adopt Kripke semantics (or should we say Leibniz possible worlds) [21]. Kripke s possible worlds theory consists of a model structure having three components: a set K of possible worlds (of which one is privileged to be the real world), an accessibility relation R(u, v) defined over K and an evaluation function Φ(φ, ) of which the details are omitted for now. A formal ontology can be seen as a mathematical object: a logical theory, a formal language with well-formed constraints a possible world. So using this analogy, one possible ontology 2 is accessible from another possible ontology 1, if there exists an evolution process (sequence of changes) applied to 1, resulting in 2. As it is more appropriate in this context, we will label accessibility relations as transformations. Transformations are defined as finite sequences of atomic or compound change operators that map one possible ontology onto another possible ontology. Transformations can also be the composite of two other transformations. The result of the application of a transformation to a consistent ontology should again be a consistent ontology. We call such a transformation a consistency-preserving transformation. Transformation Types We cannot expect that each transformation is consistency-preserving. This statement is too strong: it would imply that we cannot add new knowledge to the ontology that is conflicting with knowledge previously entered in the ontology. In the field of belief revision a similar problem is tackled. Their quest is: how do you update a knowledge base (belief set) in the light of new information?

6 What if the new information is in conflict with something that was previously held to be true? A belief set resides potential facts and theories about how the world could be, in logical parlance in fact it models a set of possible worlds [14]. We adopt the three different kinds of belief change presented in the AGM theory of [13, pp. 3] for our ontology transformation types: 1. Expansion transformation: a new knowledge element φ is added to ontology together with the logical consequences of the addition (i.e. regardless whether the larger ontology is consistent). 2. Revision transformation: a new knowledge element φ that is inconsistent with an ontology is added, but, in order to maintain consistency in the resulting ontology, some of the old sentences in are deleted. 3. Contraction transformation: some knowledge element φ in is retracted without adding any new knowledge element. RETRACTION 30 EXPANSION 30 EXPANSION kl RETRACTION EQUIVALENCE RETRACTION 10 REVISION RETRACTION ij (A) (B) (C) Fig. 1. Different situations might emerge when changing an ontology: (A) illustrates a revision transformation; (B) illustrates consistency-preserving transformations: a clean expansion and retraction; (C) shows equivalence relation between possible ontologies induced by equivalence transformations. In Fig. 1, we visualise transformations in a possible ontology space, by adopting a Lindenbaum lattice [33, pp. 252]. It is an infinite lattice where the nodes represent possible ontologies, and the edges (or paths) transformations between them. A partial order is defined on the paths, that means that the paths going up lead to more general theories, and the paths going down to more specific theories. The more contractions we do, the more general the ontology becomes; ultimately ending up in the empty or universal ontology. Similarly, multiple expansions would ultimately result into the absurd ontology. The lattice represents multiple coherent ontology versions and their inter-relationships in terms of differences.

7 In order to revise the ontology with new knowledge, one must first retract all knowledge that is inconsistent with this new knowledge, and consequently expand the latter with the new knowledge (Fig. 1.A). It is possible that an expansion or a contraction can be performed without a revision. In that case, the transformations are consistency-preserving (Fig. 1.B). [33, pp. 252] notices that in fact each step through the lattice is simple, but that due to infinity of the number of steps it is almost impossible for humans and even computers to find the best theory for a particular problem. But even if we think we have found the optimal theory, it is possible that there exist other equivalent optimal theories. To represent semantic equivalence we introduce another type of transformation. Equivalence-preserving Transformations We introduce a fourth type of transformation: the equivalence-preserving transformation. The accessibility relation R defined by this transformation is reflexive, symmetrical and transitive. This makes R an equivalence relation, causing the set of all possible ontologies to be partitioned into disjoint equivalence classes (see Fig. 1.C and 2). Under this interpretation we can argue that an ontology is not one theory or, more appropriate, conceptualisation, but in fact is the set of all equivalent representations for that conceptualisation. In [7, 30, 17], comparable data schema transformations and semantic equivalence where defined: a transformation is lossless if there is no loss of information in the underlying population during the transfomation. In the case of losslessness there is a bijective mapping between the two data schemas Fig. 2. This figure illustrates an arbitrary set of possible ontologies i,j. The nondirected solid arrows between the ontologies reflect the symmetrical (and transitive) accessibility; each ontology is trivially accessible from itself so reflexive arrows are left implicit. Considering only the regular arrows illustrates three equivalence classes labelled i. The dashed arrows illustrate some possible accessibility between ontologies of different equivalence classes, which happens if we give up the symmetry.

8 Whether two ontological construct are semantically equivalent has to be decided by agreement between human agents. If the ontology is graphically representable, we could formally define graph morphisms that can be used to compare ontological constructs on the semantic level 6. E.g., consider an arbitrary ontology holding the fact Person has Name. An equivalent could be the union of the two facts: Person has First-name and Person has Last-name. Cascading Changes If it is allowed that ontologies include (parts of) other ontologies, a new problem rises. Consider Fig. 3, is defined by including another ontology 1. Scenario (i) illustrates a transformation T 1 from 1 to 1, that initiates a cascade on all the ontologies that include 1 such as. T 1 thus implies a transformation T from to. Scenario (i) can lead to a chain reaction if is also included in another ontology 2, and 2 is on its turn included in 3, etc. In Scenario (ii), transformation T from to will not cause a cascade on all the ontologies that are included in, such as 1. * 1 T IS INCLUDED IN IS INCLUDED IN * T * T IS INCLUDED IN IS INCLUDED IN * 2 2 T 2 * 2 T 2 2 scenario (i) scenario (ii) Fig. 3. Cascading changes Possibility and Necessity Reconsider the evaluation function Φ(φ, ) {T, F } 7, that was omitted earlier: a knowledge element φ is semantically en- 6 Comparing ontologies on the syntactical level is too naive, because more than one representation can exist for one particular ontology. 7 Symbols T and F denote the boolean values true and false respectively.

9 tailed 8 by if Φ(φ, ) has value T. We can now determine whether φ is necessary or possible by considering the truth of φ in the ontologies that are accessible from the current ontology 0 via a consistency-preserving transformation [21]: φ is possible in the current ontology 0 if φ is true in some ontology accessible from 0 via a consistency-preserving transformation; φ is necessary in the current ontology 0 if φ is true in every ontology accessible from 0 via a consistency-preserving transformation. So when a knowledge element is possible in an ontology, then we can simply add it to the ontology without losing consistency. 3.2 Requirements for a Model-independent Evolution Framework As part of the project, an ontology versioning system will be implemented on top of our existing ontology server. On the client side, it will provide 2 components: 1. a graphical ontology version browser that is inspired on the lattices in Fig This lattice of ontologies browser provides basically an hyperbolic view with as first-class citizens all the ontologies and their inter-relationships stored in the server. Further, a zoom feature on all first class-citizens enabling: zooming on an ontology label in the lattice returns the representation of the ontology in an appropriate representation; zooming on an inter-relationship provides detailled information on the associated transformation and meta-information, such as the transformation type, etc. 2. an editor where the engineer can define transformations. Assuming the ontology is representable by a graph, he defines the mapping by selecting a subgraph as source of the revision, and defines a new subgraph as target of the revision. Further, he determines the type of the transformation. Research in graph morphisms can be useful here to ensure well-defined transformations. If the transformation is a revision he has to define a retraction followed by an expansion in order to express the change. 3. A notification agent that notifies the engineer when his change has cascading effects elsewhere in the lattice. The system should accommodate and control the chain reactions mentioned in previous subsection. 4 Validation Once a prototype of the proposed framework is implemented, we will validate it by applying it to some case studies. We will validate each of its components 8 E.g., suppose the facts Person is-referred-by Name and Employee is-a Person are elements of, then trivially they are semantically entailed; further due to the specialisation link between Employee and Person: Employee is-referred-by Name is semantically entailed by.

10 (as specified in the requirements elicitation) separately in order to be able to finetune locally. The first case study tests the effectiveness of the proposed framework to manage and perform sequential transformations on an emerging ontology versions set. The ideal case study would be a distributed ontology modelling environment where a large corpus of knowledge is conceptualised by a distributed team of engineers. The second case study must verify the preciseness of the transformation editor. The third case study will test whether the lattice browser is scalable up to very large versions sets. 5 Discussion and Conclusion In this paper we presented a model-independent framework for the management and revision of multiple ontology versions. In related work, basically a particular ontology representation model is chosen, and consequently, based on the evolvable knowledge elements in that model, the possible change operators that could engage an evolution process are determined. In order to remain representation model independent, we have chosen to represent ontologies and evolution processes more abstractly. By adopting possible worlds semantics, a formal ontology can be seen as a logical theory with wellformed constraints or a possible world. A possible ontology 2 is accessible from another possible ontology 1 if there exists a transformation, that is a finite sequence of changes, from 1 to 2. Further, inspired by belief revision, we have distinguished different types of transformations: revision, expansion, contraction and equivalence-preserving transformations. The possible ontology space and the different types of transformations are visualised by a Lindenbaum lattice. Finally, we present requirements for our ontology evolution framework, where the ideas above are central: a Lindenbaum lattice inspired ontology versions browser and an editor where the knowledge engineer can define transformations of any type. We also suggest a methodology for validating our ideas in the implementation. References 1. Banerjee, J. and Kim, W. (1987) Semantics and Implementation of Schema Evolution in Object-oriented Databases. In ACM SIGMOD Conf., SIGMOD Record 16(3): Batini, C., Lenzerini, M. and Navathe, S. (1986) A Comparative Analysis of Methodologies for Database Schema Integration. ACM Computing Surveys, 18(2): , ACM Press. 3. Berners-Lee, T., Fischetti, M. and Dertouzos, M. (1999) Weaving the Web The Original Design and Ultimate Destiny of the World Wide Web, Harper Collins. 4. Chiang, R., Eng Huang Chua, C. and Storey, V. (2001) A Smart Web Query Method for Semantic Retrieval of Web Data. Data and Knowledge Engineering 38:63 84.

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