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Über dieses Buch

The book provides a survey about the field of Qualitative Reasoning, it contrasts and classifies its approaches and puts them into a common framework. Qualitative Reasoning represents an approach of Artificial Intelligence to model dynamic systems, about which little information is available, and to derive statements about the potential behavior of these systems, putting emphasis on a causal explanation of the behavior. Both variables and relationships between variables are described by means of qualitative terms such as small and large or positive and negative. Since this approach also takes into consideration the way how humans reason about physical systems, it can be stated that Qualitative Reasoning participates in the creation of a cognitive theory of non-numerical process descriptions which can be mapped onto a digital computer. This approach can be used for simulation, diagnosis, design, structure identification and interpretation. Areas of application are physics, medicine, the field of ecology, process control, etc. In addition to the classification of existing methods, the book presents a new approach based on fuzzy sets. And the work relates Qualitative Reasoning with such fields of Expert Systems, System Theory and Cognitive Science.

Inhaltsverzeichnis

Frontmatter

Part I. Introducing Qualitative Reasoning

Abstract
In the first part we introduce qualitative reasoning in a rather descriptive way. We will show several fields of application, give a short history and present its basic principles.
Hannes Werthner

Part II. The Basics of Qualitative Reasoning

Abstract
This part describes the basic approaches used in qualitative reasoning as well as the underlying qualitative calculus and the different dimensions of mapping a quantitative model onto a qualitative one. Additionally, we provide a first classification of these methods. We separate the description of the modeling perspectives of the respective approaches in the next chapter from the detailed discussion of their specific reasoning techniques in chapter II.4 in order to underline the basic principles and their differences. However, also short descriptions of the reasoning mechanisms are provided in the first chapter. We use the following notation: if x denotes a variable or quantity in a numerical model, [x] or x denotes its qualitative equivalent. The same is true for operations: addition becomes ⨁, multiplication ⨂ and so on.6
Hannes Werthner

Part III. Advanced Topics

Abstract
This part deals with topics such as causality, ambiguity and uncertainty, which were mentioned shortly in the previous chapters. Additionally, several approaches will be discussed which explicitly deal with these topics and, to some extent, manage to avoid the limitation of ambiguity.
Hannes Werthner

Part IV. Qualitative Reasoning and Related Fields

Abstract
In the following we will relate qualitative reasoning to other fields of research such as the area of simulation in system theory or expert systems. Moreover, we will also take a short look at cognitive science. This comparison will uncover several correspondences with these fields and support further distinction between the different approaches in qualitative reasoning. Since we are concentrating on dynamic systems, we will not discuss other related fields such as spatial reasoning.61
Hannes Werthner

Part V. Modeling in Qualitative Reasoning

Abstract
The problem of when and how to use a model (or formula) was one of the main motivations in the first works of qualitative reasoning, i.e. the program NEWTON and its application to the roller coaster problem [de Kleer 77]. Thus, this part leads back to one of the initial objectives, i.e. how to build and how to select a proper model. However, the task of modeling is not specific to qualitative reasoning, it is fundamental in every scientific work. A model of the problem has to exist before we can draw conclusions or derive consequences or answer a specific question. But qualitative reasoning offers a specific approach which has one advantage: since it takes a radical point of view, it is satisfied with very little information. Modeling — as a well-identified task distinguished from behavior generation and explanation — represents a major issue and main challenge of qualitative reasoning.
Hannes Werthner

Part VI. Conclusion and Suggestions for Further Research

Abstract
Our work has clearly revealed the roots of qualitative reasoning in AI in its attempts to formalize and model common-sense physical knowledge as well as human reasoning mechanisms. Since AI — as stated by [Newell 90] — provides a theoretical infrastructure for the study of human cognition, we may also conclude that qualitative reasoning aims at establishing a cognitive theory of “non-numerical” process description and at automating the phase of model building. And AI still constitutes the main background of qualitative reasoning. However, since qualitative reasoning deals with physical systems and their changes in time, basic concepts about dynamic systems such as state diagrams, trajectories, state variables or input — output relations have been introduced. Thus, simulation and system theory constitute a second basis of this approach. This does not seem to be surprising, as they both deal with the modeling of dynamic systems and the generation of their behavior. Nevertheless, although there exists an evident similarity between the semantics of both areas, the structural descriptions as well as the behavior generation mechanisms are derived from AI, based on mathematical concepts. And, as already stated, we can identify cognitive science as a further area close to qualitative reasoning. This is also shown by the discussion about the problem of causality. Because of shortcomings of the early developments — mainly the problem of ambiguity — further knowledge in the form of quantitative information and more elaborated reasoning techniques was integrated. However, these improvements were mainly based on well-known concepts of fields outside AI, as for example the non-crossing rules of trajectories or Markov chains, which we have introduced in this paper. Thus, we can identify qualitative reasoning as an interdisciplinary approach.
Hannes Werthner

Backmatter

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