Concept Mapping

Abstract

The task of knowledge representation has two parts: the first is to analyze some body of knowledge and identify the relevant concepts, relations, and assumptions; the second is to translate the result of the analysis into some notation that can be processed by computer. Neither part is easy, but the first is far more difficult. Natural languages are capable of expressing anything that can be stated in any artificial language with the same level of detail and precision, but they can tolerate any degree of vagueness during the process of analysis. Artificial languages, such as the many variants of symbolic logic, are valuable because they do not tolerate vagueness, but what they say so precisely may have no relationship to what the author intended. The various notations for logic are designed to represent the final precise stage, but they provide no intermediate forms that can bridge the gap between an initial vague idea and its ultimate formalization. Natural languages can represent every stage from the most vague to the most precise, but no version of fuzzy logic or related variants can come close to the flexibility of natural languages. The vagueness is not caused by natural language, but by the fact that people seldom have a clear idea of what they want to say before the analysis has been completed. Engineers have a pithy characterization of the phenomenon: “Customers never know what they want until they see what they get.” Plato's dialogs illustrate the kind of analysis that is required. Similar dialogs are necessary when programmers or engineers analyze a vague wish list (also called a requirements document) in order to generate a formal specification. Those dialogs always take place in natural languages, often supplemented with hastily scribbled diagrams, but not in any version of logic, fuzzy or precise. This talk discusses a range of representations from informal to formal and compares four notations that are being used in various stages of knowledge acquisition, analysis, and representation: the informal Concept Maps, the semiformalized Topic Maps, the formal Conceptual Graphs, and the formal, but highly readable Common Logic Controlled English (CLCE). These and other similar notations have found useful niches in the process of analysis and representation, but it is important to recognize their different characteristics and areas of applicability. The following slides were presented in the track on Technology, Instruction, Cognition and Learning (TICL) at the AERA Conference, San Francisco, 10 April 2006. The Problem of Knowledge Representation As stated by the logician Alfred North Whitehead: Human knowledge is a process of approximation. In the focus of experience, there is comparative clarity. But the discrimination of this clarity leads into the penumbral background. There are always questions left over. The problem is to discriminate exactly what we know vaguely. And by the poet Robert Frost: I've often said that every poem solves something for me in life. I go so far as to say that every poem is a momentary stay against the confusion of the world.... We rise out of disorder into order. And the poems I make are little bits of order. Poetry and logic are complementary approaches to a common problem: developing patterns of symbols that capture important aspects of life in a memorable form.