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3.1. WHAT IS CONCEPTUALIZATION?

The importance of conceptualization in any problem-solving activity and particularly in diagnostics is never stressed enough. Indeed, an intelligent being's understanding of reality is determined by two systems, whose interaction is obvious and so requires no further explanation. The first is the sensory system and its amplifications, equipped with systems to collect, directly or indirectly, information from the environment. The second is the conceptual system, which extracts from all the above information the relevant concepts for solving the problem at hand, their internal relations, and necessary or sufficient reasoning to arrive at the right conclusions. So, conceptualization is modeling by the diagnostician. This means that there are many ways of conceptualizing and the items (concepts, relations, and functions) in the different conceptualizations are not necessarily related. For example, if we were to calculate the height of a building using a barometer, the problem could be conceptualized in many different ways, ranging from calculating the pressure on the ground floor and on the roof, through measuring it in barometric units, to dropping the barometer from the roof and measuring how long it takes the noise it makes when it hits the ground to reach the roof, etc., and they are all valid. Alternatively, a particular conceptualization of a problem may make it impossible to express given types of knowledge and, therefore, solve the problems thus conceptualized. This is precisely the case when light is conceptualized as waves to express reflection and as particles to describe refraction. Again, a conceptualization may not prevent given types of knowledge from being expressed, but it may make it more difficult, as is the case of the geocentric conceptualization of solar movement. This ontological promiscuity, making several conceptualizations apt for one and the same problem, means that being human inventions, only the alternative most useful for the purpose at hand is retained. That is, a conceptualization apt for diagnostics must both model the behavior of the diagnostician and meet previously established levels of performance and success.

Conceptualization in computer science generally and in knowledge engineering particularly is located in the problem domain tempered by the demands of the software design process. In this sense, apart from modeling diagnostician behavior, conceptualization provides an orientation on how the software should meet a need and is, therefore, a specification of what an ES is to do. So, conceptualization determines system validity; that is, whether the product is correct and meets user needs. It represents the diagnostician's view of the problem, and is, as a result, declarative or explanatory.

3.2. COMPONENTS OF CONCEPTUALIZATION

More formally, a conceptualization is composed of a threesome: concepts, relations, and functions.

The notion of concept is used in a fairly broad sense. It refers to both concrete (objects, persons, etc.) and abstract things (number 2, set of all integers), elemental concepts (electron) or compounds (atoms), and fictitious (unicorn) or real (detective) entities. In short, a concept is anything about which something is to be said and could, therefore, also be the description of a task, function, action, strategy, reasoning process, etc. When concepts are determined, there is little or no concern for classifications, relations, or details. An expert usually works with approximately 12 concepts. So, if more appear during conceptualization, their number has to be constrained to the above value. Two fairly well-known powerful techniques -- generalization and abstraction -- are used to reduce the number of concepts. Formally, generalization is the move from considering a concept to considering a set containing that concept, or the move from considering a small to a more comprehensive set of concepts containing the smaller one. And abstraction consists, at least theoretically, of removing irrelevant items, as discussed by Lwoff (Lwoff, 1975) and retaining only what is necessary.

A relation is a type of interaction between concepts in a universe of discourse. In a conceptualization of part of the world, some relations are stressed and others are ignored. The set of relations in a conceptualization are called the basic relational set.

A description and example of the most important relations used in knowledge engineering (KE) is given in Table 2. Obviously, not all of these relations have to be used for a particular problem, and there is always the possibility of other relations not contemplated in the table appearing.

Relations or links have the three properties discussed below.

  1. Valence, which describes the quantitative manner in which the elements participate in the relation: one-to-one, many-to-one, etc.
    a. One-One, represented by: A — B
      b. Many-one, represented by: A [pipe minus] B
      c. Injection, represented by: A [greater than minus] B
      d. Surjection, represented by: A [right arrow] B
      e. O-implies, represented by: A [greater than, right arrow] B;that is, many-one and injective
      f. 1-implies, represented by: A [right arrow] B; that is, many-one and surjective
      g. Equivalence, represented by: A [if and only if] B; that is, one-one and surjective
      h. Many-many, represented by: A [pipe minus pipe] B;without constraints
  2. Functionality, which indicates how a relation is implemented: injective or monomorphic and surjective or epimorphic.
  3. Cardinality or "arity," which determines the number of arguments participating in the relation: unary, when composed of a single argument; binary, when the number of arguments is two; ternary, if composed of three, and so on, up to n-ary, when referring to n arguments.


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