Month Year Issue

“Peircean” Reorganization in
Conceptual Modeling Terminology
by Esko Marjomaa

The analysis and representation of an object of our interest (the Universe of Discourse, the UoD) often begins by creating a conceptual schema of it. When the UoD is large, the creation demands some reorganization tools. First of all, the terminology should be clear. In the paper, characterizations for relevant terms are given. The over-all process of conceptual modeling is described, and some basic principles are given. Also, a preliminary basis for future work is developed along ”Peircean” lines.

There are various hierarchies of the systems of different terms, concepts, model constructs, and categories in information modeling. One reason for that is that people capture the world differently. Most often the capturing is not based on any clear metaphysics nor on any exact ontology. The situation in any particular case in information systems design is often so complicated that we are forced to ignore some less relevant features of the application area in order to get any results in design. There are plenty of ways to do that, such as, condensation, abstraction, idealization, classification, generalization, axiomatization, formalization, etc. In this paper, we shall discuss such important points in conceptual modeling that should be taken in account when modeling any particular information system.

The paper is structured as follows: In Section 2, we introduce a classification of models. In Section 3, we describe the process of conceptual modeling, and give some basic principles for it. For a future project, in Section 4, we prescribe a new way to approach the problem of ”How to enrich the description of different user schemata?”

It is often not very clear what is meant by “information” or “model”, but here we shall give some hints.

By "information" we may mean any of the following senses of the word:
    - physical, i.e., negative entropy (much order) in physical,
    - syntactic, i.e., a relational property of certain kind of sign(al)s,
    - semantic, i.e., the content of some message that a string of sign(al)s expresses,
    - pragmatic, i.e. psychological, inter-subjective, but, at most, semantic.

In spite of the multiplicity of different kinds of model and ways of classifying them, the basic modeling situation is simple. We can notice, namely, that any particular modeling situation consists (necessarily) of the following four kind of things: 1. the modellum (i.e. the object to be modeled, the entity of interest, the universe of discourse, etc.), 2. the modeler (i.e. the modeling subject, the designer, a student, a group of agents, etc.), 3. the modellens (i.e. the constructed model, which may consist of different kinds of representation, such as, for instance, sentences), and 4. the interactions between these three things.

For a more detailed analysis of the basic modeling situation, see Marjomaa & Palomäki (1992). The main reason for the employment of the terms "modellum", "modeler", and "modellens" is that they are connotation-free. Another motivation is that it is not always clear whether one means by a "model" descriptive or prescriptive model, or both.

There are many different uses of the word model, which are all relevant in information modeling. However, different kinds of "modeler" (such as analysts, designers, constructors, etc.) at different stages of the information systems design have usually not explicitly considered what they mean by "modeling" and "model". The question to be asked is "What kinds of model are there?", or "What is usually meant by a 'model'?". The next classification is meant to be a preliminary review of the topic. However, note that the classes are not logically nor factually independent from each other.

1. Analogy models, which represent a chosen part of the reality by means of an analogy relation. There are three kinds of these models:

(b) comparisons, allegories and metaphors, which relate some definite parts of two different languages - or, rather, of two different "Wittgensteinian language-games"

- definitional conceptual schemata (where we introduce new expressions referring to new concepts)

2. Idealized models, which represent the most relevant features of the entity to be modeled. There are two kinds of these models:

(a) mathematical models, by which we mean simplified and idealized mathematical theories concerning some definite portions of the reality

(b) "caricatures", which tend to represent some of the most effective features of an entity of interest

3. Models in logical semantics - i.e. set-theoretical structures, where the formulas of some formal language are interpreted.

This classification will serve us as a tool to describe different factors (or, ”phases”) of the over-all process of conceptual modeling. Depending on certain background factors (see Marjomaa 1997), our models in (ideal) conceptual modeling cases may be the following kinds:
    - set-theoretical structures (models in logical semantics)
    - conceptual sub-schemata (representational conceptual schemata)
    - global conceptual schemata (definitional conceptual schemata)
    - user screens (”caricatures”)

We shall discuss these models in Sections 3.2 and 3.3, in some detail. But before that, in Section 3, we shall characterize the term ”conceptual modeling”. We shall also give some basic principles for conceptual modeling.

Conceptual modeling is the description of information systems on the meta-level, where conceptual processes, model constructions and knowledge representations play an essential role. On the other hand, conceptual modeling can be characterized as an activity the goal of which is to develop higher level concepts, tools and techniques for all areas in computer science. In practice, according to Kangassalo (1990), conceptual modeling is a methodology for constructing conceptual schemata. Also - and especially - such an activity as the developing of a scientific theory is essentially conceptual modeling.

Generally, we can say that in information systems design it has shown to be very useful first to construct a conceptual schema, which describes the Universe of Discourse (hereafter the UoD) and contains all relevant concepts and rules of the UoD, before building a knowledge based system. The technical realization of the system will then be based on these concepts and rules.

So, according to Kangassalo (1992: 17), conceptual modeling, in short, is "a process of forming and collecting conceptual knowledge about the Universe of Discourse. and documenting the results in the form of a conceptual schema".

The term "universe of discourse" is widely used also in other research areas such as, for example, social sciences. Here we shall give a technical characterization for the term - compare Griethuysen (1982: Ch. 1.3., with a few changes): The UoD is a collection of all those entities that have been, are, or ever might be in a selected portion of the real world or postulated world. (An entity is here used as a primitive term, but we can characterize it by saying that an entity is any thing, which can be conceived as one and can be named.) However, in most cases the UoD may be regarded as a collection of expressions involved in the whole information modeling process in question.

There is much conceptual unclarity in information modeling terminology. This concerns especially "conceptual schema", the ontological status of which has not been properly explicated by the researchers. In other words, it is often difficult to find out whether one means by a "conceptual schema" a transcendental schema, a mental representation, or a physical representation. In addition, most of the researchers do not discuss the problem whether conceptual schemata (as non-physical entities) can be shared by different individuals. Donald Davidson (1985: 129) expresses the problem as follows:

Conceptual schemes, we are told, are ways of organizing experience; they are systems of categories that give form to the data of sensation; they are points of view from which individuals, cultures, or periods survey the passing scene. There may be no translating from one scheme to another, in which case the beliefs, desires, hopes, and bits of knowledge that characterize one person have no true counterparts for the subscriber to another scheme. Reality itself is relative to a scheme: what counts as real in one system may not in another.

According to Kangassalo (1983: 225) a conceptual schema is "a completely or partially time-independent description of the slice of reality in the sense that a conceptual schema contains the definition of all concepts and all relationships between concepts allowed to be used in the description of that slice of reality." In a broader sense, they are frameworks for dealing with things concerning our object of interest. The term originates from Immanuel Kant, who in his Critique of Pure Reason (1966: 121-125; i.e., A: 134-145; B: 173-185) speaks of transcendental schemata which, however, correspond rather to conceptual models in information modeling terminology. Kangassalo (1983: 238) defines the latter as follows: "A conceptual model M of the universe of discourse W, or of some part of W, is a completely connected and completely consistent set of fact constructs." By a conceptual construct he means "a construct composed of a set of concepts connected with each other with the aid of associations". Kangassalo (1983: 236). Kant's transcendental schemata are, in short, procedures of the imagination by which the categories of the understanding are applied to sensations.

Davidson uses the word scheme, but I shall use the word schema following the common practice in conceptual modelling research. However, I want to stress that I shall use the expression "conceptual schemata" to denote only physical representations. When speaking of non-physical representations I shall use other expressions, such as, "mental models", or "conceptual models”.

(2) The explication of the use of the desired conceptual model and that of the conceptual schema.

(3) The definition (or the description) of the new information concerning the modellum.

(8) The developing 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.

Factor (1), the explication of the tasks of modeling, is the most basic one here, because the other factors are in many ways dependent on it.

Factor (2), the explication of the use of the desired conceptual model and that of the conceptual schema, together with Factor (1), gives us most of the practical constraints concerning the construction of the conceptual model and the conceptual schema.

Factor (3), the definition of the needed new information, is not possible without Factor (1), but the scope of it is restricted, especially, by Factor (2). The definition of the needed new information should be such that the information source (the "expert", or the "final user") is capable of giving relevant information.

Factor (4), the available information concerning the modellum, contains not only the receivable new information, but also the information which we cannot, for one reason or another, admit to our model construction.

Factor (5), the information acquisition, contains all the activities that aim at the admittance of the available information concerning the modellum. Here the methods used to support experts' articulation are of crucial importance.

Factor (6), the analysis of the received new information, should be done in respect to the previous information concerning the modellum, not separate of it. This is because the new and the previous information may contain such interrelated issues that we did not possibly take into account in Factors (1) to (5).

Factor (7), the condensation of the analyzed information, can be done in many different ways, because the amount of information concerning the application area is often very large. However, the basic aim is to find the relevant constituents of the modellum.

Factor (8), the developing of a conceptual model on the basis of those relevant constituents, and Factor (9), the physical representation of it, are, in practice, the two proper components of the construction of the conceptual schema. The process of conceptual modeling often stops here, but in practice it is useful to consider Factor (10), too.

Factor (10), the technical realization of the system, may, but not need to affect Factor (1). If it affects Factor (1), we say that........ (In the next figure it is taken into account when building a user-friendly IS based on a global conc. schema)....

In order to develop the theory of conceptual modeling and especially the methods for constructing conceptual schemata we should follow certain general principles. In the literature it is easy to find two of such principles - see, for instance, Griethuysen (1982) or Kangassalo (1990):

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

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

From these two principles together it follows that all the relevant aspects of the UoD should be conceptual. But the principles do not say anything on how to distinguish between "relevant" and "irrelevant" aspects. We shall return to this problem in the end of this section.

In order to construct good conceptual schemata the following two principles are needed, too.

P3 The formalization principle: Conceptual schemata should be formalizable in order to be implementable.

This is an essential restrictive principle, and it is partly opposite to the following principle:

P4 The semiotic principle: Conceptual schemata should be easily interpretable and understandable.

The motivation for the latter principle is that the language for representing conceptual schemata should (1) form a basis for everyone taking part in the modelling process, and (2) be appropriate for fulfilling the task of modeling. So, one reason why P4 may sometimes be opposite to P3 is that not everyone is familiar with the formalisms used in this area. But it may also be vice versa: Everything cannot be formalized.

In spite of the importance of all these principles, however, one may never know whether one has followed all of them:

(1) It is not always possible to be sure whether all the terms that an expert has introduced belong to the "conceptual realm" of the application area.

(2) It is not always possible to be sure whether an expert has introduced all the relevant concepts.

(3) It may happen that the desired conceptual schema can never be wholly formalized in a way which would not strike against the corresponding conceptual model.

(4) Different persons taking part in the modeling process may interpret the resulting conceptual schema differently. Some may not even understand it at all.

In addition, we may mention also the following three principles (for more principles, See Marjomaa 1997):

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 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.

P7 The sub-schemata principle: In order to construct a good conceptual schema it is important first to construct relevant sub-schemata and then to search for connections between them.

Information modeling is the focus of information systems design. Generally, we can say that any system always functions in some environment. If one is interested in the knowledge bases included in the information management processes within an organization (e.g., an enterprise) formed by some group of agents, one should not only consider the organization in itself, but also its environment (e.g., the society) and the relations between them. In general, we can say that whatever the object of interest is, it should not be considered apart from its environment.

As a matter of fact, within any definite design task, modeling activities are directed at the functioning whole (composed of the object of interest and its environment). Or, to put it in other words, one cannot fully catch an object without catching the functioning whole, a part of which the object is. But, in a sense, also vice versa, one cannot fully catch the functioning whole without first catching all the definite parts of it. This kind of hermeneutic circle concerns every conceptual information modeling situation.

Let us suppose that we are designing an information system that would support the information manipulation within an organization formed by, say, n different working groups. Now, it may be that no one of these has any full understanding of all the functions and information units of the organization. In this context, an "information unit" may be composed of devices, instruments, technologies, knowledge bases, persons, or of combinations of these. However, if we could put all these different perspectives together, then we would have, at least, a chance to catch the functioning of all the information units of the whole organization.

In this case, the aim of conceptual modeling is to get a conceptual schema that would contain the descriptions of all the functions and information units and of all the different perspectives on them. In every particular case the perspective on the UoD is different and the constituents of the user schemata may vary greatly, but there are also many general principles and common factors that concern all the different cases.

According to Batini & Lenzerini (1984: 650), conceptual modeling can be divided into two steps: (1) View modeling, during which the user requirements are formally expressed by means of several user oriented schemata, and (2) Schema integration, a process which merges such schemata into a unique global conceptual schema. Within their framework, "such a global schema is the basis for the design of subschemas, i.e., the portions of the global schema that serve the applications at execution time". (p. 650)

User schemata describe the data of interest for n distinct groups of users of the application.

The design of the n user schemata may be, in general, developed independently, by different analysts and at different times. As a consequence, several complex tasks are to be managed during integration: finding the common factors between the different schemata, finding the different representations chosen by the analysts, in some cases discovering inappropriate or unreliable choices, and finally, discovering inter-schema properties, i.e., properties involving data belonging to different schemata that were hidden to the analysts in former design steps. (p. 650)

The constituents of conceptual sub-models are called model constructs. What kinds of entity these model constructs are is an open question, but they may include such entities as concepts, relations, propositions, and structures.

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.

Using bare model constructs without Peircean categories (see below) when reorganizing a UoD, usually yields us a descriptive conceptual schema.

There are plenty of different methods or techniques to "reorganize" the UoD in order to get the best possible modellens. In different kind of textbooks dealing with "information systems design methodologies", for instance, the following ways to manipulate the information carried by the entities belonging to the UoD can be found: "condensation", "abstraction", "idealization", "classification", "generalization", "axiomatization", and "formalization”.

Because no exact definitions for these notions will be developed in this paper, it is perhaps pertinent to give short characterizations of the notions. Keeping in mind that the aim of conceptual modeling is to construct a representation of the UoD, which is regarded as a system of sign(al)s, to condense the information concerning the UoD is to express as shortly as possible all the relevant information concerning the constituents of the UoD. Most often we use some of the following methods:

classification of the constituents of the UoD; i.e. grouping the constituents into classes on the basis of the discovery of common properties;

generalization is then the process of arriving at some general notion from the individual instances belonging to some class;

axiomatization is a 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;

formalization of an axiom system is a step where 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 is a process of constructing a representation which ignores some less relevant aspects of the UoD; we shall next consider this notion when involved in scientific theory formation;

abstraction is the process of separating some relevant partial aspect of some collection of entities.

All these are generally used and useful methods. However, in order to get more generative conceptual schemata, we may propose a new approach to analyze the over-all process of conceptual modeling.

In this and the following two chapters, we shall develop a basis for future work in order to be able to answer the question ”How can we enrich the description of conceptual sub-schemata in a way that would give us a definitional global conceptual schema?” Our future goal is to further develop a heuristic method of constructing global conceptual schemata. We shall not give any exact nor well-formulated theory based on Peircean semiotics, but just a couple of hints about how to approach the analysis of the over-all conceptual modeling process.

The most important species of concepts are called model concepts (or "categories"), which generate connections between different conceptual sub-models. Model concepts form the kernel of conceptual models consisting of different conceptual sub-models. These model concepts can be used as perspectives on the object of interest to throw light on or to detect various connections to other concepts within different conceptual sub-models.

It is obvious that every particular discipline has its own basic concepts. But there are also concepts that apply to most of the modeling cases, e.g. "entity", "relation", "process", etc. The most general concepts are called philosophical (or metaphysical) categories, such as Peircean Firstness ("in-itselfness"), Secondness ("over-againstness"), and Thirdness ("in-betweenness").

Philosophical categories are applicable to every modeling case. Besides that, they can also be used as tools to make important classifications and to find new connections between the entities belonging to some UoD. For example, one of the central functions of the Peircean categories is to guide and stimulate inquiry. They are heuristic.

Example. When we apply Peircean categories, for instance, in Argument, we get abductions (Firstness), inductions (Secondness), and deductions (Thirdness):

In the same way as in the example, applying Peircean categories to any concept whatsoever we may get new concepts that will reorganize the UoD in the manner that yields us a definitional conceptual schema.

Information consists of (uninterpreted or interpreted) signs. So. when we are modeling some object of our interest (the UoD) we are interpreting and representing signs belonging to the UoD. For a detailed analysis of the modeling process, it may be worthy to try somehow to classify the signs. One brilliant way has been introduced by Charles S. Peirce over one hundred years ago in semiotics.

On the basis of his trinitarian metaphysics Peirce introduces three categories that are the basis for his general theory of signs (i.e. semiotics). According to him, in defining a sign we need three aspects: an external world (object) to which the sign refers, the sign itself (representamen), and one kind of second order sign (interpretant) which appears in the receiver's mind because of the first sign. But we can analyze these aspects further. We can namely speak about signs in relation to objects, signs in themselves, and signs in relation to interpretants. This means that when defining a sign we always need to consider three aspects of it: (1) The sign in itself, (2) the sign in respect to its object, and (3) the sign in respect to its interpretant. These aspects can be further considered from a phenomenological point of view which means that we apply the categories Firstness, Secondness, and Thirdness. Doing this yields the following three trichotomies.

(1)       If the sign in itself is
           -   a mere quality, the sign is a                                               Qualisign.
           -   an actual existent, the sign is a                                          Sinsign.
           -   a general law, the sign is a                                                 Legisign.
(2)       If the relation of the sign to its
           object consists of
           -   the sign having some character
               in itself, the sign is an                                                        Icon.
           -   some existential relation
               to its object, the sign is an                                                 Index.
           -   its relation to an interpretant,
               the sign is a                                                                      Symbol.
(3)       If the sign's interpretant represents
           it as a sign of
           -   possibility, the sign is a                                                     Rheme.
           -   fact, the sign is a Dicent Sign.
           -   reason, the sign is an                                                        Argument.

Peircean categories Firstness ("in-itselfness"), Secondness ("over-againstness"), and Thirdness ("in-betweenness") have not been studied properly, but here we can give short characterizations of them.

They describe the relation between man and reality so that Firstness means the unanalysable, immediate and momentary feeling. Firstness is experienced for instance in an acute feeling of pain, in physical pleasure, in sensation of redness or blackness, or in any impression which thrusts into one's mind and claims full attention. Firstness represents the timeless present as an experienced whole. So, this First cannot be a thought. But Secondness contains a thought of something Second, other, and it is based on the dynamics of action and re-action. Where a First is just potential, a Second is a hard fact. It represents something real because it demands the recognition of itself as something else than just a composition of one's mind. Hence it is the Secondness through which we interact with reality. All practical knowledge involving everyday life, such as opening the door, calling the telephone, kicking the football, represent Secondness. While Firstness concerns something here and now Secondness is based on the past from which we are willing to learn something. Thirdness, on the other hand, is a regular rule for feeling and acting: It represents intellectual acting and logical reasoning, which creates order, laws and habits in chaos and arbitrariness. Also the 'noble' emotions, such as love, hope, pity and religious devotion are Thirds.

On the basis of the above three trichotomies we may consider 3x3x3=27 different combinations. But just the following ten classes of signs are possible. For the reasons for this, see Peirce (1931-60 2.228-276).

I     Rhematic Iconic Qualisign
II    Rhematic Iconic Sinsign
III    Rhematic Indexical Sinsign
IV   Dicent Indexical Sinsign
V    Rhematic Iconic Legisign
VI   Rhematic Indexical Legisign
VII Dicent Indexical Legisign
VIII Rhematic Symbolic Legisign
IX   Dicent Symbolic Legisign
X    Argument Symbolic Legisign

Peirce also gives us the following examples of signs belonging to different classes. (I) A feeling of "red" is a Rhematic Iconic Qualisign. (II) An individual diagram is a Rhematic Iconic Sinsign. It will embody a Qualisign. (III) A spontaneous cry is a Rhematic Indexical Sinsign. It necessarily involves an Iconic Sinsign. (IV) A weathercock is a Dicent Indexical Sinsign. It must involve an Iconic Sinsign to embody information and a Rhematic Indexical Sinsign to indicate the object to which the information refers. (V) A diagram, apart from its factual individuality, is a Rhematic Iconic Legisign. Each of its occurrences will be an Iconic Sinsign. (VI) A demonstrative pronoun is a Rhematic Indexical Legisign. Each occurrence of it will be a Rhematic Indexical Legisign. The interpretant of a Rhematic Indexical Legisign represents it as an Iconic Legisign. (VII) A street cry is a Dicent Indexical Legisign. It must involve an Iconic Legisign to signify the information concerning the object and a Rhematic Indexical Legisign to denote the subject of the information. Each occurrence of it will be a Dicent Sinsign. (VIII) A common noun is a Rhematic Symbolic Legisign. (IX) A proposition is a Dicent Symbolic Legisign. (X) An Argument is a Symbolic Legisign. Each of its occurrences will be a Dicent Sinsign.

On the basis of the hypothesis that concepts are Thirds, we may conclude that there are at most six classes of concepts, namely the classes V to X, above.

Time will show what else can be derived from Peircean semiotics to the analysis of conceptual modeling processes. One possible way to handle the situation is (1) to consider the UoD as Firstness, the user screen as Secondness, and the conceptual model (represented by a global conceptual schema) as Thirdness, and (2) to try to find the kinds of analogy as in the ”Argument”-example, above.

We focused to some important points in conceptual modeling. We gave characterizations for some central terms (and concepts), such as, ”information”, ”modeling”, ”sign”, ”concept”, ”condensation”, "abstraction", "idealization", "classification", "generalization", "axiomatization", "formalization”, etc. The most important point, however, was in considering different factors (or, ”phases”) in conceptual modeling processes. Also, the basic modeling principles introduced above are central. In the end of the paper, we introduced a ”Peircean” way to handle with signs. Much work should still be done before the tool, i.e., ”Peircean splitter” can be applied to any arbitrary UoD.

References

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Brodie, M. L., Mylopoulos, J., and Schmidt, J. W., (eds.), 1984: On Conceptual Modelling. Perspectives from Artificial Intelligence, Databases, and Programming Languages. Springer-Verlag, New York.

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Marjomaa, E., 1997: Aspects of Relevance in Information Modelling: Methodological Principles and Conceptual Problems. Doctoral Dissertation. Fitty 63, Tampere 1997. (Parts of the text may be found at http://www.geocities.com/Athens/Olympus/3404/vaikkari.doc).

Marjomaa, E. and Palomäki, J., 1992: "On the Structure of the BMS. A Proposal for a General Frame for Modelling". Tekoälyn uudet suunnat - New Directions in Artificial Intelligence. Suomen Tekoälytutkimuksen päivät STeP-92. Edited by Hyvönen, E., et al. Espoo.

Peirce, Ch., 1931-60: The Collected Papers of Charles Sanders Peirce, vols 1 &, 11. Edited by Hartshorne, Ch., & Weiss, P. The Belknap Press of Harvard University Press, Cambridge, Mass., 1931, 1932, 1959, 1960.

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.