Month Year Issue

December 2002 Issue: 27

Journal of Conceptual Modeling
www.inconcept.com/jcm

Necessary Conditions for High Quality Conceptual Schemata:
Two Wicked Problems
by Esko Marjomaa

Abstract. 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 the solutions of 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 claim that the answers to these questions in great deal also settle the other ones.

1 Introduction: A Framework for Conceptual Modeling

Conceptual modeling has been characterized in various ways, but the most central feature of it is twofold: We model concepts by concepts, and 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:

P1 The conceptualization principle: Only conceptual aspects of the Universe of Discourse 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 formalization principle: Conceptual schema should be formalizable in order to be implementable.
P4 The semiotic principle: Conceptual schema should be easily interpretable and understandable.
P5 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.
P6 The Sperber-Wilson principle of relevance: Every act of ostensive communication communicates the presumption of its own optimal relevance.
P7 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.
P8 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 sub-schemata.
P9 The principle of partiality: In order to construct a good conceptual schema we should begin by concentration on partial idealization and partial concretization.

1.1 Stages in the Modeling Process

It is useful to consider modeling processes as consisted of successive stages: (1) The explication of the tasks of modeling. (2) The explication of the use of the desired conceptual model and that of the conceptual schema. The group of persons try to build the desired conceptual model (and the conceptual schema) in respect to the use of the model (and that of the conceptual schema). (3) The description of the new information about the modellum. If the modelers 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, etc. However, in order to get useful information, they have to describe the needed information as well as possible. (4) The available information about the modellum. (5) The information acquisition. (6) The analysis of the received information. (7) The condensation of the analyzed information. (8) The development of a conceptual model on the basis of the condensed information. (9) The physical representation of the conceptual model (in a form of a conceptual schema) using a language most appropriate for fulfilling the tasks in question. (10) The technical realization of the conceptual schema and the information base.

1.2 Problems of Quality in Conceptual Modeling Processes

We may now ask: “What is relevant in information modeling processes in order to get high quality technical realizations?” Obviously, each one of the stages (1) to (10) above. But it is also relevant to take into account different kinds of affecting background factors, such as (i) modelers’ profiles - for example, whether there are any multi-media experts among the modelers; (ii) determinator – for example, the experts’ profiles, paradigms, authorities; (iii) practical constraints - for example, environment, time, money, tools; (iv) skills of the users - for example, acquaintance with computers; (v) arbitrary conventions - for example, systems of marking; (vi) empirical facts - for example, particular constraints concerning some definite UoD; (vii) hypotheses - for example, generalization; (viii) the ways of analyzing - for example, classification; (ix) the ways of abstracting - for example, aggregation, axiomatization; (x) considerations of simplicity – for example, is the conceptual structure easily visualizable; (xi) considerations of fruitfulness - for example, is the method applicable elsewhere; (xii) idealizations - for example, estimation; (xiii) metaphysical presuppositions - for example, ontological commitments.
We can notice that, especially, the items from (vii) to (xiii) concern the question “How does the basic ontology affect the form and content of the resulting conceptual model?”, and the items from (i) to (xii) concern the question ”What is the status of formalization in pragmatics?” In the following sections, we shall consider these questions a little bit more in detail.

2 The Impact of the Choose of the Basic Ontology

It seems that the more invariant an entity is the more abstract it is. So, we should try to generalize this notice 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 sub-models are the relation of intentional containment and auxiliary (i.e. factual) relations. This strongly involves the account that there are certain concepts which are more basic than some 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: 246) as a concept the properties of which are defined only partially in the following way: (1) 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 (2) The intension of the concept does not contain any factual concepts or, in addition to the set of non-referential concepts, it contains some concepts which 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, state.
    According to Kangassalo (1983: 248), 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: 248) as “a conceptual construct which contains only absolutely abstract concepts or semantically abstract model concepts”. For brevity, it is usually called a model construct. Kangassalo gives us the following examples of model constructs: system, hierarchy, network, schema, theory, algebra.
    One difficult problem is “How to 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?”. 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, etc. This problem is closely interrelated to the problem of abstraction in conceptual modeling.

2.1 Ontological Correctness in Modeling

There are different conceptions of what an ontology is. In philosophy, a general account of the issue can be stated as Palomaki (1994: 23-24) put it: Ontology aims to answer at least three questions, namely, (1) What there is? (2) What is it that there is? (3) How is that 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?
In information modeling, there is a more specialized meaning of the word, 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, an 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 a basic ontology can be found, for instance, in Sowa (2000) and in http://www.jfsowa.com/ontology/toplevel.htm where Sowa describes top-level categories and relations between them.

2.2 Requirements for an Ontology Language

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 explain 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.”
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.

3 Be Careful with Formalisms!

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

3.1 Formal Operations

In developmental psychology, there is a conception that in the age from 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) notices, Piaget did suggest that beyond formal operations, there are post formal 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.

3.2 The Logic of Evaluation

A crucial question is “What impacts 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, Spring 2002, there was a task to construct a conceptual schema of an ”intelligent refrigerator”, and the resulting plans varied a lot: http://cs.joensuu.fi/ marjomaa/ demobox/pakollinen/
    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 ”preference” involves not only the axiological concept ”betterness” but also the anthropological concept ”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 knife than y, we prefer using x.
    All modes of preference are somehow related to goodness, but we can distinguish between two kinds of preference:
    1. Sometimes something is preferred over something else, because the former is supposed to be ”better” than the latter. A person may, for instance, prefer beer over white wine, because of his/her stomach. In this case the mode of preference is called extrinsic.
    2. There are also people who prefer beer simply because they like it better. This kind of mode of preference is called intrinsic.
    We can also speak about different types of preference and about different classificatory bases. One way is to consider the common features of things (or states of affairs) between which there is a preference relation:
    1. Some instrument (or the use of it) may be preferred over another.
    2. One way of doing something may be preferred over another.
    3. Some state of affairs may be preferred over another.
    But it will be enough to develop a formal theory which handles only with 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 some person for 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).

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Esko Marjomaa is a planning officer with over 10 years experience as a university teacher and researcher in cognitive science. Esko is one of the first teachers at the Virtual University of Finland and is specialised in the study of learning organisations. Esko can be contacted by e-mail at marjomaa@cs.joensuu.fi.