Rivero L.Encyclopedia of database technologies and applications.2006

Zelasco, J. F., Ennis, K., & Blangino, E. (2001). Quality control in altimetry and planimetry for 3D digital models. Paper presented at the 8th European Congress for Stereology and Image Analysis, Bordeaux, France.

Zelasco, J. F., & Ennis, K. (2000). Solución de un problema en la estimación de variancias en un caso especial en el que no se pueden aplicar estimadores habituales. XXVIII Coloquio Argentino de estadística, Posadas, Misiones, Argentina.

KEY TERMS

Covariance Matrix: The square n x n of which the entries are the pairwise correlations of the variables of a random vector of length n; the (i,j)th entry is the correlation between the ith and the jth variables.

DEM Geometric Quality: Geometric precision measured in terms of the difference between a digital elevation model (DEM) and a reference DEM (R-DEM).

Digital Elevation Model (DEM): The set of points in a three-dimensional coordinate system modeling a real object’s surface.

Geometric Quality in Geographic Information

Geographic Information System (GIS): Tool for processing localized information. A GIS will model and locate the spatial data of a real phenomenon.

Homologous Points: The point in the DEM and the point in the R-DEM modeling the same point in the real surface. Their distance is the error of the DEM point, assuming the points in the R-DEM are without error.

Photogrammetry: Technique permitting the setup of the coordinates of points (DEM) of an object surface by processing stereo images of the object’s surface.

RevolutionEllipsoid:Three-dimensionalsolid obtained from revolving an ellipse about one of its axes.

Spatial Data: Information related to a real system involving geometric (dimension, shape) and topological (relative position) aspects of it.

Stereo Images: Two or more images of a real object’s surface obtained from different points of view.

Variance Estimation: Average of the sum of the squares of the differences of the values attained by a random variable from its mean.

Manjunath R.

Bangalore University, India

INTRODUCTION

Expert systems have been applied to many areas of research to handle problems effectively. Designing and implementing an expert system is a difficult job, and it usually takes experimentation and experience to achieve high performance. The important feature of an expert system is that it should be easy to modify. They evolve gradually. This evolutionary or incremental development technique has to be noticed as the dominant methodology in the expert-system area.

Knowledge acquisition for expert systems poses many problems. Expert systems depend on a human expert to formulate knowledge in symbolic rules. It is almost impossible for an expert to describe knowledge entirely in the form of rules. An expert system may therefore not be able to diagnose a case that the expert is able to. The question is how to extract experience from a set of examples for the use of expert systems. Machine learning algorithms such as “learning from example” claim that they are able to extract knowledge from experience. Symbolic systems as, for example, ID3 (Quinlan, 1983) and version-space (Mitchell, 1982) are capable of learning from examples. Connectionist systems claim to have advantages over these systems in generalization and in handling noisy and incomplete data. For every data set, the rule-based systems have to find a definite diagnosis. Inconsistent data can force symbolic systems into an indefinite state. In connectionist networks, a distributed representation of concepts is used. The interference of different concepts allows networks to generalize

A network computes for every input the best output. Due to this, connectionist networks perform well in handling noisy and incomplete data. They are also able to make a plausible statement about missing components. A system that uses a rule-based expert system with an integrated connectionist network could benefit from the described advantages of connectionist systems.

BACKGROUND

Maintenance of databases in medium-size and largesize organizations is quite involved in terms of dynamic

reconfiguration, security, and the changing demands of its applications. Here, compact architecture making use of expert systems is explored to crisply update the database. An architecture with a unique combination of digital signal processing/information theory and database technology i tried. Neuro-fuzzy systems are introduced to learn “if-then-else” rules of expert systems. Kuo, Wu, and Wang (2000) developed a fuzzy neural network with linguistic teaching signals.

The novel feature of the expert system is that it makes use of a large number of previous outputs to generate the present output. Such a system is found to be adaptive and reconfigures fast. The expert system makes use of a learning algorithm based on differential feedback. The differentially fed learning algorithm (Manjunath & Gurumurthy, 2002) is introduced for learning. The learning error is found to be minimal with differential feedback. Here, a portion of the output is fed back to the input to improve the performance. The differential feedback technique is tried at the system level, making the system behave with the same set of learning properties. Thus, control of an expert system controls the entire system

KNOWLEDGE EXTRACTION FROM DIFFERENTIALLY FED NEURAL NETWORKS

The expert systems are organized in a hierarchical fashion. Each level controls a unique set of databases. Finally, the different expert systems themselves are controlled by a larger expert system. This ensures security of databases and selective permissions to their access, (i.e., some of the data needs to be public and the rest has to be private and protected; a concept borrowed from object-oriented programming). Thus, the master expert system can have access to public information. The neural networks are integrated with a rule-based expert system. The system realizes the automatic acquisition of knowledge out of a set of examples. It enhances the reasoning capabilities of classical expert systems with the ability to generalize and the handle incomplete cases. It uses neural nets with differential feedback

algorithms to extract regularities out of case data. A symbolic-rule generator transforms these regularities into rules governing the expert system. The generated rules and the trained neural nets are embedded into the expert system as knowledge bases. In the system diagnosis phase it is possible to use these knowledge bases together with human experts’ knowledge bases in order to diagnose an unknown case. Furthermore, the system is able to diagnose and to complete inconsistent data using the trained neural nets exploiting their ability to generalize.

It is required to describe a possible approach for the optimization of the job scheduling in large distributed systems, based on self-organizing neural networks. This dynamic scheduling system should be seen as adaptive middle-layer software, aware of current available resources and making the scheduling decisions using past experience. It aims to optimize job-specific parameters as well as resource utilization. The scheduling system is able to dynamically learn and cluster information in a large dimensional parameter space and at the same time to explore new regions in the parameter’s space. This self-organizing scheduling system may offer a possible solution for providing an effective use of resources for the off-line data-processing jobs.

Finding and optimizing efficient job-scheduling policies in large distributed systems, which evolve dynamically, is a challenging task. It requires the analysis of a large number of parameters describing the jobs and the time-dependent state of the system. In one approach, the job-scheduling task in distributed architectures is based on self-organizing neural networks. The use of these networks enables the scheduling system to dynamically learn and cluster information in a high-dimensional parameter space. This approach may be applied to the problem of distributing off-line data processing. These jobs need random access to very large amounts of data, which are assumed to be organized and managed by distributed federations of OODB (object-oriented database) systems. Such a scheduling system may also help manage the way data are distributed among regional centers as a function of time, making it capable of providing useful information for the establishment and execution of data replication policies. A hybrid combination of neural networks and expert systems was tried by Apolloni, Zamponi, and Zanaboni (2000). Fdez-Riverola and Corchado (2003) used unsupervised learning for prediction of parameters during the learning process.

module encodes such cases in a suitable way to be learned by neuronal networks. This module performs as follows:

First, it transforms or preprocesses the data so that the components with equal scopes or a hierarchy is formed. It has been shown that discretization of data (i.e., preprocessing of data in to several subdivisions) makes the neural network converge faster (Abu Bakar, Jaaman, Majid, Ismail & Shamsuddin, 2003). At the same time, hierarchy in the data can be maintained.

Second, the transformation module encodes the data into a binary input pattern because some neural networks, as, for example, the competitive learning model (Rumelhart & Zipser, 1985) processes only binary inputs. To do this, the intervals of the components are subdivided into different ranges. These ranges are adapted according to the distribution of the components. So, every component of a vector is represented by the range its value belongs to. Depending on the kind of representation, the ranges could be encoded locally.

With the transformed data, different neuronal networks with unsupervised learning algorithms, such as competitive learning (Rumelhart & Zipser, 1985), ART, and Kohonen, are trained. These networks have the ability to adapt their internal structures (i.e., weights) to the structure of the data. In a rule-generation module, the structures learned by the neuronal networks are detected, examined, and transformed into expert systems rules. These rules can be inspected by a human expert and added to an expert system. When a case is presented to the expert system, the system first tries to reason with the rules that have been acquired from the human expert to produce a suitable diagnosis. If this fails to produce a diagnosis, the new rules produced by the process described can be used. If the case can be handled in such a way, all steps of the reasoning process may be inspected by and explained to a user of the system.

If the system, however, is not able to produce a suitable diagnosis in this way, be it, that data is missing, or the input is erroneous or no rule fits the data, since such a case has not been considered while building the knowledge base, the expert system can turn the case over to the networks. The networks, with their ability to associate and generalize, search for a most suiting case that has been learned before. The diagnosis that has been associated with that case is then returned as a possible diagnosis.

SYSTEM DESCRIPTION

Case data that are presented to an expert system are usually stored in a case database. A data-transformation

PROPOSED ARCHITECTURE

In recent years, neural networks have been extensively used to simulate human behavior in areas such as vision, speech, and pattern recognition. In large scales, they

perform the recognition and classification tasks better than human beings. Neural nets can find a relation by making a match between known inputs and outputs in a pool of a large data. The performance of these networks can be improved by providing a differential feedback from the output to the input

Expert systems have been used in conjunction with neural network technology to eliminate the time-con- suming part of constructing and debugging the knowledge base. Neural networks can be used to recognize patterns, such as financial or sensory data, which are then acted on by the rules of an expert system. An expert system trains the neural network that in turn generates rules for an expert system. The use of an artificial neural network greatly simplifies the knowledge-engineering task because it allows the system itself to construct the knowledge base from a set of training examples. Because the correct output of the expert system is known for the given set of inputs, a supervised learning algorithm is used to train the system.

Compared to rule-based expert systems, connectionist expert systems give a better model of reasoning. These models can be applied to any type of decision problems, especially when the creation of ifthen rules is not possible, or the information is contradictory. A connectionist expert system usually contains three major parts: a knowledge base, an inference engine, and the user interface. The knowledge base is a problem-dependent part that contains expert knowledge. The connectionist expert system database is composed of neurons and connections among them. The inference engine is a problem-independent driver program which is responsible for reasoning. The user interface is a link between the inference engine and the external user. The architecture of a connectionist expert system is shown in Figure 1. The weight matrix stores the rules that are translated in to the input–output dependency in the neural network through the dependency matrix and the pattern vector. The differential feedback connects a part of the output to the input and reduces the training period as well as the errors in pattern matching.

Figure 1. An expert system with DANN-based learning

DATA PROCESSING

H

The Kohonen network, consisting of two layers, is used here. The input layer has n units representing the n components of a data vector. The output layer is a twodimensional array of units arranged on a grid. The number of the output units is determined experimentally. Each unit in the input layer is connected to every unit in the output layer, with a weight associated. The weights are initialized randomly, taking the smallest and the greatest value of each component of all vectors as boundaries. They are adjusted according to Kohonen’s learning rule (Kohonen, 1984). The applied rule uses the Euclidean distance and a simulated Mexi- can-hat function to realize lateral inhibition. In the output layer, neighboring units form regions, which correspond to similar input vectors. These neighborhoods form disjoint regions, thus classifying the input vectors.

The automatic detection of this classification is difficult because the Kohonen algorithm converges to an equal distribution of the units in the output layer. Therefore, a special algorithm, the so-called U-matrix method, is used to detect classes that are in the data (Ultsch & Siemon, 1990).

In summary, by using this method, structure in the data can be detected as classes. These classes represent sets of data that have something in common.

RULE EXTRACTION

As a first approach to generate rules from the classified data, a well-known, machine-learning algorithm, ID3, is used (Ultsch & Panda, 1991). Although able to generate rules, this algorithm has a serious problem: It uses a minimization criterion that seems to be unnatural for a human expert. Rules are generated that use only a minimal set of decisions to come to a conclusion

A large number of parameters, most of them time dependent, must be used for the job scheduling in large distributed systems. The problem is even more difficult when not all of these parameters are correctly identified, or when the knowledge about the state of the distributed system is incomplete or is known to have a certain delay in the past.

SCHEDULING DECISION

A “classical” scheme to perform job scheduling is based on a set of rules using part of the parameters and a list of empirical constraints based on experience. It

may be implemented as a long set of hard coded comparisons to achieve a scheduling decision for each job. In general, it can be represented as a function, which may depend on large numbers of parameters describing the state of the systems and the jobs. After a job is executed based on this decision, a performance evaluation can be done to quantify the same.

The decision for future jobs should be based on identifying the clusters in the total parameter space, which are close to the hyperplane defined in this space by the subset of parameters describing the job and the state of the system (i.e., parameters known before the job is submitted). In this way, the decision can be made evaluating the typical performances of this list of close clusters and choose a decision set that meets the ex- pected–available performance–resources and cost. However, the self-organizing network has, in the beginning, only a limited “knowledge” in the parameter space, and exploring efficiently other regions is quite a difficult task.

In this approach for scheduling, the difficult part is not learning from previous experience, but making decisions when the system does not know (or never tried) all possible options for a certain state of the system. Even more difficult is to bring the system into a certain load state, which may require a long sequence of successive decisions, such as in a strategic game problem. The result of each decision is seen only after the job is finished, which also adds to the complexity of quantifying the effect of each decision. For this reason, a relatively short history of the previous decisions made by the system is also used in the learning process. A relatively long sequence of the decision (a policy) can be described with a set of a few points of decision history, which partially overlap. This means that a trajectory can be built in the decision space by small segments that partially overlap.

FUTURE TRENDS

The present-day expert systems deal with domains of narrow specialization. For such systems to perform competently over a broad range of tasks, they will have to be given a wealth of knowledge. The next generation expert systems require large knowledge bases. This calls for crisp learning algorithms based on connectionist networks with higher order differential feedback. Improvements in the learning rate and stability of these algorithms to organize large data structures provide a good topic for research.

CONCLUSION

The implementation of the system demonstrates the usefulness of the combination of a rule-based expert system with neural networks (Ultsch & Panda, 1991). Unsupervised-learning neural networks are capable of extracting regularities from data. Due to the distributed subsymbolic representation, neural networks are typically not able to explain inferences. The proposed system avoids this disadvantage by extracting symbolic rules out of the network. The acquired rules can be used like the expert’s rules. In particular, it is therefore possible to explain the inferences of the connectionist system.

Such a system is useful in two ways. First, the system is able to learn from examples with a known diagnosis. With this extracted knowledge it is possible to diagnose new unknown examples. Second, the system has the ability to handle a large data set for which a classification or diagnosis is unknown. For such a data set, classification rules are proposed to an expert. The integration of a connectionist module realizes “learning from examples.” Furthermore, the system is able to handle noisy and incomplete data. First results show that the combination of a rule-based expert system with a connectionist module is not only feasible but also useful. The system considered is one of the possible ways to combine the advantages of the symbolic and subsymbolic paradigms. It is an example to equip a rulebased expert system with the ability to learn from experience using a neural network.

REFERENCES

Abu Bakar, A., Jaaman, S.H., Majid, N., Ismail, N. & Shamsuddin, M. (2003). Rough discretisation approach in probability analysis for neural classifier. ITSIM, 1, 138147.

Apolloni, B., Zamponi, G., & Zanaboni, A. M. (2000). An integrated symbolic/connectionist architecture for parsing italian sentences containing pp-attachment ambiguities, Applied Artificial Intelligence, 14(3), 271-308.

Fdez-Riverola, F., & Corchado, J. M. (2003). Forecasting system for red tides: A hybrid autonomous AI model.

Applied Artificial Intelligence, 17(10), 955-982.

Kohonen, T. (1984). Self-organization and associative memory. Berlin, Germany: Springer-Verlag.

Kuo, R. J., Wu, P. C., & Wang, C. P. (2000). Fuzzy neural networks for learning fuzzy if-then rules. Applied Artificial Intelligence, 14(6), 539-563.

Manjunath, R., & Gurumurthy, K. S. (2002). Information geometry of differentially fed artificial neural networks.

IEEE TENCON’02, Bejing, China.

Mitchell, T. M. (1982). Generalization as search. Artificial Intelligence, 18, 203-226.

Quinlan, J. R. (1983). Learning efficient classification procedures and their application to chess end-games. In R.S. Michalski, J.G. Carbonell, & T.M. Michell (Eds.),

Machine learning: An artificial intelligence approach

(pp. 463-482).

Rumelhart, D. E., & Zipser, D. (1985). Feature discovery by competitive learning. Cognitve Science, 9, 75-112.

Ultsch, A., & Panda, P. G. (1991). Die Kopplung Konnektionistischer Modelle mit Wissensbasierten Systemen. Tagungsband Experteny stemtage Dortmund

(pp. 74-94). VDI Verlag.

Ultsch, A., & Siemon, H. P. (1990). Kohonen’s self organizing feature maps for exploratory data analysis. Proceedings of International Neural Networks (pp. 305308). Kluwer Academic Press.

KEY TERMS

Artificial Intelligence (AI): A research discipline whose aim is to make computers able to simulate human abilities, especially the ability to learn. AI is separated as neural net theory, expert systems, robotics, fuzzy control systems, game theory, and so forth.

Connectionist Expert System: Expert systems that use artificial neural networks to develop their knowledge bases and to make inferences are called connectionist expert systems. A classical expert system is defined with IF-THEN rules, explicitly. In a connectionist expert system, training examples are used by employing the generalization capability of a neural network, in which the network is coded in the rules of an expert system. The neural network models depend on the processing elements that are connected through weighted connections.

The knowledge in these systems is represented by these weights. The topology of the connections are explicit H representations of the rules.

Expert System: An expert system is a computer program that simulates the judgment and behavior of a human or an organization that has expert knowledge and experience in a particular field. Typically, such a system contains a knowledge base containing accumulated experience and a set of rules for applying the knowledge base to each particular situation that is described to the program.

Kohonen Feature Map: It is basically a feed forward/feedback type neural net. Built of an input layer(i.e., the neuron of one layer is connected with each neuron of another laye), called “feature map.” The feature map can be one or two dimensional, and each of its neurons is connected to all other neurons on the map. It is mainly used for classification.

Neural Network: A member of a class of software that is “trained” by presenting it with examples of input and the corresponding desired output. Training might be conducted using synthetic data, iterating on the examples until satisfactory depth estimates are obtained. Neural networks are general-purpose programs, which have applications outside potential fields, including almost any problem that can be regarded as pattern recognition in some form.

Supervised Learning: This is performed with feed forward nets where training patterns are composed of an input vector and an output vector that are associated with the input and output nodes, respectively. An input vector is presented at the inputs together with a set of desired responses, one for each node. A forward pass is done and the errors or discrepancies, between the desired and actual response for each node in the output layer, are found. These are then used to determine weight changes in the net according to the prevailing learning rule.

Unsupervised Learning: A specific type of a learning algorithm, especially for self-organizing neural nets such as the Kohonen feature map.

Esko Marjomaa

University of Joensuu, Finland

FRAMEWORK FOR CONCEPTUAL MODELING

The questions of quality may be divided into four distinct classes, namely, ontological, epistemological, value-theoretical, and pragmatic. However, there are plenty of important problems to the solutions which have bearings on the different classes. Some of the problems are very tricky, and we shall explore two of them: (1) How does the basic ontology affect the form and content of the resulting conceptual model? and (2) What is the status of formalization in pragmatics? There are good reasons to believe that the answers to these two questions may also answer the other ones.

Conceptual modeling has been characterized in various ways, but the most central feature of it is twofold: (a) We model concepts by concepts, and (b) by “concepts” we mean “entities, the role of which is to carry the sameness of different tokens of definite entity types.” In practice, the following principles serve as general guidance for conceptual modeling (see Table 1).

It is useful to consider modeling processes as consisting of successive stages. The first thing we have to do in any definite modeling process is to explicate the tasks of modeling (i.e., we have to clearly express the goal of our modeling activity in question). In addition, we also have to explicate the use of the desired conceptual model and that of the conceptual schema. One tries to build the desired conceptual model (and the conceptual schema) in respect to the use of the model (and that of the conceptual schema).

Table 1. Principles of conceptual modeling

P1 The conceptualization principle: Only conceptual aspects of the Universe of Discourse (UoD) should be taken into account when constructing a conceptual schema.

P2 The 100 Percent principle: All the relevant aspects of the UoD should be described in the conceptual schema.

P3 The correspondence condition for knowledge representation: The modellens should be such that the recognizable constituents of it have a one-to-one correspondence to the relevant constituents of the modellum.

P4 The invariance principle: Conceptual schema should be constructed on the basis of such entities found in the UoD that are invariant during certain time periods within the application area.

P5 The principle of contextuality: Conceptual schema should be constructed on the basis of contextually relevant entities belonging to the UoD. This construction should be made according to some of the principles of abstraction levels using appropriate model constructs in order to uncover mutual relevance between different conceptual subschemata.

After the explication phase, we need to describe the new information about the modellum. If the modellers need more information than just their perceptions concerning the modellum, they can get it, for instance, from the people living in the house, from libraries, and so forth. However, in order to get useful information, they have to describe the needed information as accurately as possible.

In addition to the description of the new information, we also need to get all the available information about the modellum. This is the proper information acquisition phase, after which we shall analyze the received information; it is essential here that we speak of received information, because we cannot be sure if we have all the information sent to us.

In order to construct a conceptual model of the application area, we often need to condense the infor- mation—not all the information—only the analyzed information. Then, the construction and the development of the conceptual model will be based only on that condensed information. After we have developed a conceptual model, we have to construct a physical representation of the conceptual model (in a form of a conceptual schema) using a language most appropriate for fulfilling the tasks in question. The technical realization of the conceptual schema and the information base will then be based on this physical representation.

However, there are other more basic prerequisites for the construction of the conceptual schemata (and hence for the technical realization of it), namely, the background factors that almost in any case affect the modeling process. They are presented in Table 2.

We may now ask, “What is relevant in information modeling processes to get high-quality technical realizations?” Obviously, each of the aforementioned stages

(i) through (x). But it is also relevant to take into account different kinds of affecting background factors, such as those presented in Table 2.

Items (vii) to (xiii), especially, concern the question, “How does the basic ontology affect the form and content of the resulting conceptual model?” and items

(i) to (xii) concern the question, “What is the status of formalization in pragmatics?” In the following sections, we shall consider these questions in a bit more detail.

CONSEQUENCES OF THE BASIC ONTOLOGY CHOICE

It seems that the more invariant an entity is, the more abstract it is. So, we should try to generalize this by examining whether there are some very basic (i.e., abstract) concepts that can be used to construct some general frames for considering different conceptual schemata.

According to Kangassalo (1983), the basic connections between different concepts and conceptual submodels are the relation of intentional containment and auxiliary (i.e., factual) relations. This strongly involves the account that there are certain concepts that are more basic than others. In other words, structuring conceptual schemata calls for some set of the so-called model constructs.

A semantically abstract model concept is characterized by Kangassalo (1983) as a concept the properties of which are defined only partially in the following way:

(a) The extension of the concept is undefined or its definition specifies only the type of the elements of the reference class on a high level of abstraction (i.e., only some of the properties of the elements of the reference class are specified); and (b) the intension of the concept does not contain any factual concepts or, in addition to the set of nonreferential concepts, it contains some concepts that refer to an abstract model object. In other words, the intension of the concept does not contain any completely defined factual concepts. Some examples of such model concepts are type, entity, flow, process, event, and state.

According to Kangassalo (1983), model concepts can be regarded as primitive structuring elements the

use of which direct the modeling process by forcing the designer to complete the semantics of model concepts in order to get a completely defined conceptual model. In other words, if the designer wants to use the model concepts “entity,” “process,” and “event” as building blocks for a conceptual model, then he has to add factual semantics to all instances of these model concepts in the conceptual model.

A semantically abstract model, construct is characterized by Kangassalo (1983) as “a conceptual construct which contains only absolutely abstract concepts or semantically abstract model concepts” (p. 248). For brevity, it is usually called a model construct. Kangassalo gives the following examples of model constructs: system, hierarchy, network, schema, theory, and algebra.

“How to do we construct the set of model concepts?” or, to put it differently, “What is the basis on which we choose the model concepts out of the model constructs?” is a difficult problem. The set of model constructs, namely, may be extremely large, including an arbitrary collection of general nouns, such as entity, process, event, state, flow, system, hierarchy, network, schema, theory, frame, object, substance, property, relation, act, disposition, ability, regularity, cause, explanation, function, and so forth. This problem is closely interrelated to the problem of abstraction in conceptual modeling.

There are different conceptions of what ontology is. In philosophy, a general account of the issue can be stated thus: “Ontology aims to answer at least three questions, namely, (1) What there is? (2) What is it that there is? (3) How is that there is? These general ontological questions can be rephrased to apply to concepts: (1’) What are concepts? (2’) What stuff are they made of? (3’) How can they exist?” (Palomaki, 1994, pp. 23-24).

In information modeling, there is a more specialized meaning of the word ontology, such as, especially, in Gruber (1993):

“An ontology is a formal, explicit specification of a shared conceptualization. “Conceptualization” refers to an abstract model of phenomena in the world by having identified the relevant concepts of those phenomena. Explicit means that the type of concepts used, and the constraints on their use are explicitly defined. Formal refers to the fact that the ontology should be machine readable. Shared reflects that ontology should capture consensual knowledge accepted by the communities.”

Although, according to Gruber (1993), ontology is a specification of a conceptualization, we may say, in general, that conceptualizations are not possible without a correct basic ontology. So, Gruberian ontologies are specifications of conceptualizations, which, in turn, should be built on correct, basic ontology. One good example of basic ontology can be found, for instance, in Sowa (2000) and at http://www.jfsowa.com/ontology/ toplevel.htm where Sowa describes top-level categories and relations between them.

The World Wide Web Consortium has published a document (W3C, 2002) dealing with the requirements for a Web ontology language. The considerations are applicable also to conceptual modeling languages. In the document, the design goals describe general motivations for the language that do not necessarily result from any single use case. First, there is a description of eight design goals for an ontology language. For each goal, there is also a description of the tasks it supports and explains the rationale for the goal. One central goal is shared ontologies: “Ontologies should be publicly available and different data sources should be able to commit to the same ontology for shared meaning. Also, ontologies should be able to extend other ontologies in order to provide additional definitions” (Berners-Lee, Calilliay, & Groff, 2002).

The use cases and design goals in W3C (2002) motivate a number of requirements for a Web ontology language. The requirements, however, described in the document also seem to be essential to any ontologically correct language. Each requirement includes a short description and is motivated by one or more use cases or design goals.

However, before choosing any ontology, it is common to choose some suitable ontology language(s). But before that, we have to evaluate different needs in knowledge representation, reasoning, and exchange of information (Corcho & Gomez-Perez, 2000).

High Quality Conceptual Scheme

BE CAREFUL WITH FORMALISMS!

Most people cannot think formally. This fact yields some restrictions, or, at least, some requirements concerning desired conceptual schemata.

In developmental psychology, there is a conception that from age 14 to 16, people reach the stage of so-called formal operations. In this stage, intelligence is demonstrated through the logical use of symbols related to abstract concepts. Surprisingly, it has been shown that only one third of high school graduates in industrialized countries obtain formal operations.

We may talk about formal thinking which can be marked by the ability to systematically generate and work with larger spaces of possibilities, including possibilities that are quite abstract. Inhelder and Piaget tested for formal thinking by asking children and adolescents to design and conduct scientific experiments—for instance, experiments to determine what determines the period of a pendulum, or what factors affect the bending of rods that vary in shape, length, size, material, and so on. But thinking explicitly about your values and your course in life, and comparing them with other possible values and other possible courses in life, also qualifies as formal thinking (see Campbell, 2002.)

As Campbell (2002) noticed, Piaget did suggest that beyond formal operations, there are postformal operations, or “operations to the nth power.” Inevitably these would be of a highly specialized nature, and might be found in the thinking of professional mathematicians or experts in some other fields. An early example of “operations to the nth power” is Piaget’s statement that constructing axiomatic systems in geometry requires a level of thinking that is a stage beyond formal operations “one could say that axiomatic schemas are to formal schemes what the latter are to concrete operations” (Piaget, 1950, p. 226).

It would be an interesting research project to study whether the nature of expertise is due to the possession of schemas that guide perception and problem solving and how these schemas are dependent on the ability to use formal operations.

A crucial question is, What impact does the ability (or the lack of it) to use formal operations have on the creation or interpretation of conceptual structures? For instance, it has been proven quite clear that there are real differences between different students in constructing and interpreting conceptual schemata. Even among the students of computer science, the differences between the quality of constructed conceptual schemata are substantial: During a course on conceptual modeling, at the Department of Computer Science, University of Joensuu, in the spring of 2002, there was a

High Quality Conceptual Schemes

task to construct a conceptual schema of an intelligent refrigerator, and the resulting plans varied greatly.

One way to handle with the issue is to develop a logic of evaluation, or, perhaps rather, a logic of preference. First of all, it should be noted that preference is always related to a subject. It is always somebody’s preference. Preference is also always related to a certain instant or situation.

The first purely logical attempts to handle the problem of preference or betterness were made by Hallden (1957) and von Wright (1963a). But the notion of preference is central also in economics, and especially in econometrics, where it is investigated usually together with the notions of utility and probability. In philosophy these concepts are in the realm of value theory. Generally we can say that such concepts as, for instance, right and duty are deontological, while such concepts as good, bad, and better are axiological. To anthropological concepts belong such concepts as need, desire, decision, and motive.

The borders between these different disciplines are not altogether clear, but the study of deontological and axiological concepts should be based on the study of anthropological concepts. One essential difference between deontological and axiological concepts seems to be that axiological concepts are often comparative (we can speak about their “degrees”), while deontological concepts are not.

It is important to note that the concept of preference involves not only the axiological concept of betterness but also the anthropological concept of selection. The notion of betterness (or goodness) has different modes which are not all intrinsically related to preference. This concerns especially technical goodness. For example, if x is better than y, there seems to be no direct connection to the notion of preference. However, technical goodness may sometimes have a close relation to instrumental goodness. For example, if x is better than y, we prefer using x.

Table 3. Two kinds of preference

1.Sometimes one thing is preferred over another because the former is supposed to be “better” than the latter. For instance, a person may prefer beer to white wine because of his or her appetite. In this case, the mode of preference is called extrinsic.

2.There are also people who prefer beer simply because they like it better than wine. This kind of mode of preference is called intrinsic.

There are also different types of preference and different classificatory bases. Consider the common features of things (or states of affairs) between which is a preference relation:

2.1.Some instrument (or the use of it) may be preferred over another.

2.2.One way of doing something may be preferred over another.

2.3.Some state of affairs may be preferred over another.

All modes of preference are somehow related to good-

ness, but we can distinguish between two kinds of pref- H erence (see Table 3).

But it will be enough to develop a formal theory that handles only states of affairs, because all the other types of preference can be expressed in terms of states of affairs.

In information modeling, both modes of preference are employed. Some kind of logic of “extrinsic preference” is used especially when choosing methods and tools for representing information. But first we should introduce a logic of “intrinsic preference,” because the motives or reasons of someone preferring one state of affairs over another are not always known. One such a logic is von Wright’s Logic of Preference (1963a), and a good starting point to develop a real system of evaluation is his book,

Varieties of Goodness (1963b).

CONCLUSION

Keeping in mind that the aim of conceptual modeling is to construct a representation of the UoD (which is regarded as a system of signs or signals). To condense the information concerning the UoD is to express as briefly as possible all relevant information concerning the constituents of the UoD. Most often we use some of the methods shown in Table 4.

Table 4. Methods of information condensation

Axiomatization

Process of representing the UoD by giving just a few sentences (axioms, or basic truths) from which we can deduce other truths of the system (theorems); this representation is called an axiom system

Classification [of the UoD’s constituents] Grouping the constituents into classes on the basis of the discovery of common properties

Generalization

Process of arriving at a general notion from the individual instances belonging to a class

Formalization [of an axiom system]

Step by which we add to the system such rules that are needed in proving the theorems of the system; formalized axiom systems can be regarded as the ideal cases of condensation

Idealization

Process of constructing a representation that ignores some less relevant aspects of the UoD

Abstraction

Process of separating a relevant partial aspect of a collection of entities