The Semantic Web is a proposal from the World Wide Web Consortium aimed at solving problems like data integration and application interoperability. To reach these goals several languages for the representation of semantic data have been proposed. One of the essential concepts behind semantic data is that the data is according to a certain ontology. However, the goals of the semantic web seem challenged because it seems essential for its working that ontologies are agreed upon and shared. This work-in-progress paper describes a rst step to solving these problems. When an ontology is missing or only partially known a system might try to make an approximation of the missing part of the ontology. The quality of this estimated ontology will depend on the context of the application. This paper proposes the solving of a dynamic multi-objective and context sensitive optimisation problem as a way to evalute the quality of the ontology.
The World Wide Web Consortium (W3C) regards the Semantic Web as a web
of data. Currently, data is created at extremely high rate and is not available
enough to end users. The Semantic Web aims \To do for machine processable
information (application data) what the World Wide Web has done for
hypertext\ by supporting the creation of interoperable and linked data. [
The paper \Which Semantic Web?" [
In order to address the rst problem, it would be necessary to create a
system which can make use of semantic data without having knowledge about the
ontology used by the system which generated it. Therefore, it would be needed
to derive the meaning from the data which another application generated. The
approach proposed in this paper is that there would be an optimisation
procedure which yields an ontology for an application processing semantic data.
The second problem is that computer systems might not be suitable to describe
human-oriented concepts. This problem has been tackled in the past by using
fuzzy logic. One approach is described in [
One important application of the proposed approach can be found in
selfmanaged systems. The `executable reality' approach as described in [
Optimisation problems are in general statements of problems where a best solution is to be found according to certain criteria and restrictions. The rst paragraphs describe a few classes of global optimisation problems in order to introduce the Context-dependant Dynamic Multi-objective optimisation class in the last paragraph.
Static single-objective optimisation is considered a basic type of optimisation problems. The problem statement consists of a function which will be called f with domain D and range R. The domain of the function can be given explicitly as a set or described using constraints on a set. The set used for the range should have a total order relation 6 de ned on its elements, i.e. there is a transitive, antisymmetric, and total relation on the elements of R. De nition 1. An element d 2 D is optimal for a function f , i.e. d 2 opt (f ) , 8 e 2 D : f (e) 6 f (d)
The class of optimisation problems described in the previous de nition can be extended to a multi-objective variant by allowing the range of the function to be a set of vectors of dimension n. The range of the function f is thus R1 R2 Rn where we require a (strict) total order relation <i to be de ned on each Ri. The domain of the function is a set D. Note that all single objective optimisation problems are multi-objective problems.
De nition 2. An element d 2 D is multi-objective optimal for a function f , i.e. d 2 opt (f ) , 8 e 2 D n fdg : (9 i 2 [1; n] : f (e)i <i f (d)i)
Dynamic optimisation is essentially not di erent from solving a series of (multi-objective) static optimisation problems. The dynamism in the series is to be found in the way the function which is optimised or the constraints on the domain of the function being optimised are changing. The series can be represented by a function F , which maps the natural numbers to a set of pairs of a function and its domain. The functions in the tuples have a domain which is a subset of the total domain D the optimisation problem is working on. One way of solving the dynamic optimisation problem is by nding the optimal value for the functions for all possible values in N and then selecting the maximum value. We denote opt0(F (t)) to be the optimisation problem with function F (t)1 and constraints F (t)2.
De nition 3. An element d 2 D is considered optimal for the dynamic optimisation of the function F : N ! (f unctions; constraints) if 8t 2 N : opt0(F (t)) d.
Another possible de nition follows: De nition 4. A function sol is the solution of the dynamic optimisation problem if sol : N ! D and sol(t) = opt0(F (t)) In other words, a solution is such function which gives the optimal solution for each possible t 2 N.
Context-dependant dynamic multi-objective optimisation problems are an extension of the dynamic optimisation problems de ned in the previous paragraph. In this case the domain of the function F is a series of what will be called `contexts' instead of the natural numbers. The solution of the optimisation problem can be stated in a similar way as the de nitions in the previous paragraphs. A solution of this type of problem indicates (multi-objective) optimal solutions in particular contexts, or analog optimal solutions over the range of all possible contexts. 3
An application needs schemas or ontologies in order to give meaning to the
semantic data it is processing. Di erent de nitions of ontologies have been
proposed. Gruber [
For this article, the concrete syntax of the ontology used is not of mayor
importance. More important is the fact that an ontology has certain features.
Examples of features of an ontology include coverage, cohesion and coupling. [
For the representation of not exactly de ned sets, fuzzy sets as described in
\Fuzzy Sets" [
Calegari and Giucci used the concept of fuzzy sets to describe what they
call `Fuzzy Ontologies', `Fuzzy Description Logics' and `Fuzzy-OWL'. [
In research on databases it has been noticed that the schemas which are used
change over time. Ontologies have similar properties. Changes in the domain, the
conceptualisation and the speci cation are unavoidable and the ontology has to
be changed accordingly. The domain changes because the real world changes, the
conceptualisation because the perspective changes and the speci cation changes
when an ontology is to be represented in a language with di erent semantics
and expressiveness. The whole of these changes is called ontology evolution.
Ontologies and database schemas are di erent concepts. Firstly, the ontology
itself can also be part of the data and this way the data becomes self-descriptive.
Secondly, ontologies are explicitly designed for reuse in other context as the initial
context of creation and are, moreover, decentralised by nature. Lastly, ontology
models have, in general, a richer set of properties available for describing the
domain and quite often the border between the schema and instance data is
blurry.[
The same article also describes concrete e ects of ontology evolution on the data set. For instance removal of a class causes instances to have a less speci c type, declaring classes disjoint makes instances that are in both classes invalid and de ning a class as a subclass of another one adds new possible properties on the subclass.
Despite their di erences, a more recent article by Hartung et al. [
In order to talk about the quality of an ontology, one needs to take the context within which it is used into account. This statement can be supported by an example. Imagine for instance that one would say that an ontology which contains more concepts, is better than one with less concepts. This could be true in certain situations. However, if one imagines a system which only uses the concepts which are mentioned in the ontology with less concepts, the smaller ontology might be even better because it uses less memory space.
One way of de ning ontological quality is described in \Data Driven Ontology
Evaluation" [
A recent survey on ontology evaluation tools was performed by Aruna et
al. [
Research on improving the quality of an ontology by transformation
operations on an existing ontology is described in [
One way of measuring the quality of an ontology might be to compare the ontology with one or more sets of data which should be described by the ontology. This comparison can be done using either the open-world assumption which is typically made in the semantic web or a closed-world assumption.
Quality does not have to be a one dimensional property. The quality of an ontology in a context can thus be a multidimensional property. The more complete the context for optimisation is, the fewer dimensions the quality will have. A `complete' context will lead to a one dimensional quality. 7
As argued in the previous section, it is only reasonable to make statements about the quality of an ontology in a given context. If for a certain context the quality for two ontologies is given, then it is possible to make a comparison between the two ontologies in that particular context. However, quality will not always be one-dimensional and hence analog to the multi-objective class of optimisation problems, it is not always possible to say that either the rst or the second ontology is better.
When it is possible to compare the quality of ontologies in a context, then it is also possible to de ne what it means for an ontology to be optimal in a given context. Because of the fact that there is no total order on the quality of an ontology in a context, it will be necessary to consider the search for an optimal ontology for a given context as a multi-objective optimisation problem.
Let C be the set of contexts, O be the set of ontologies and Q be the set of qualities. Now we can de ne the optimisation as: De nition 5. The function sol is the solution of the context-dependant dynamic multi-objective problem of nding an optimal ontology for a given context , sol : C ! O and sol(c) = opt0(F (c)) Where F (C) ! (O ! Q) a function which maps the context c to a function which incorporates the context when evaluating the quality of an ontology and its associated domain.
It makes most sense to use the de nition of context-dependant optimisation with a function since the system will be used in a real life setting and it is impossible to predict the optimal ontology over the whole life-time of the system at any point. It should also be noted that in any real system, the function sol can only be known partially and most likely by approximation. It is only known partially because the context is changing all the time and the future contexts are still unknown. Only an approximation can be found because no real system can react quick enough to all changes in a complex context in order to compute a new optimal ontology.
As said in the previous section, it is important to note that the context of the
system in which the ontology is optimised will change dynamically over time.
One important aspect of the context is the history of the system. The reason is
that taking a new ontology into use causes a certain replacement overhead. A
new ontology causing a big overhead has a lower quality in the context of the
system. Cuenca Grau et al. [
In this article we did not specify any concrete ontology notation to be used for this type of system. There is a need to evaluate the di erent possible classes of ontologies and see which properties of ontologies are a ected in this type of optimisation. Depending on the type of ontology chosen, the system has di erent options for the development of its ontology. If the ontology would be for instance a fuzzy ontology, it might even be feasible to change only membership functions to adapt to changes in the context.
It is an open question how the system should search for an optimal ontology for a given context. Furthermore, this article refrained from de ning a concrete de nition of context and how it should be incorporated in the functions for optimisation. One popular choice for the incorporation of context is the use of weighted sum based methods. More research is needed to link particular features of an ontology to quality aspects, as well as how the context in uences this.
Next, it seems reasonable to look whether it is possible to notice trends in the evolution of the ontology. A system could then take the trends into account when assessing a new ontology or predict resource consumption in the future.
Lastly, it is interesting to consider what would happen when two separate systems have their isolated evolutions of the ontology. Questions in that kind of situation include what should be done to align these ontologies, what to do with discrepancy between the ontologies, whether these systems can interact if they are using di erent ontologies, etc. . . 9
The aim of this article was to show initial ndings to solve the problems of interoperability in the Semantic web in case ontologies are not shared among applications and how to allow these applications to work with more `humanised' concepts. The rst problem was reduced to a formulation of the nding of an optimal ontology in a given context in section 7. This context includes for instance the data processed by the application, the past used ontologies and constraints related to the system. The challenge of allowing humanised concepts is attempted by allowing fuzzy logic to be used in this kind of system.
This article was nancially supported by the `Cloud Software Program' of TiViT Oy. We would like to thank `Intelligent Precision Solutions and Services Oy' and in particular Sami Helin for proposing the initial `Cloud Communication Channel' business case in which this research idea was elaborated.