A Set-Theoretic Foundation of Qualitative Reasoning and its Application to the Modeling of Economics and Business Management Problems

Information Systems Frontiers, Vol. 5, No. 4, pp. 379-399, 2003

21 Pages Posted: 12 Dec 2007

See all articles by Karl Reiner Lang

Karl Reiner Lang

City University of New York (CUNY) - Paul H. Chook Department of Information Systems & Statistics

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management

Aimo Hinkkanen

University of Illinois at Urbana-Champaign

Abstract

The qualitative reasoning (QR) field has developed various representation and reasoning methods for the modeling with incomplete information or incomplete knowledge. While most uncertain reasoning approaches describe uncertain or imprecisely known information as probability distribution functions, qualitative reasoning bases its model specification on qualitative descriptions that are derived from known qualitative system properties. Problems are formulated as sets of qualitative constraints and their analysis is performed by applying a qualitative calculus. This paper presents a general, unifying theory of the various existing qualitative reasoning systems that includes, as special cases, reasoning methods that use representations of qualitative differential equations and qualitative difference equations. Based on set theory, our QR framework describes fundamental concepts such as qualitative models and solutions, and relates them to the quantitative analogues of its underlying quantitative reference system. Our motivation arises from the types of models found in the management sciences. Thus we emphasize the significance of discrete, dynamic models and optimization models in the business management and economics fields, both of which have received less attention in current QR research. Finally, we extend our theoretical framework to include an approach to qualitative optimization.

Keywords: qualitative reasoning, qualitative modeling, incomplete information, simulation, epistemology

Suggested Citation

Lang, Karl Reiner and Whinston, Andrew B. and Hinkkanen, Aimo, A Set-Theoretic Foundation of Qualitative Reasoning and its Application to the Modeling of Economics and Business Management Problems. Information Systems Frontiers, Vol. 5, No. 4, pp. 379-399, 2003, Available at SSRN: https://ssrn.com/abstract=1070182

Karl Reiner Lang (Contact Author)

City University of New York (CUNY) - Paul H. Chook Department of Information Systems & Statistics ( email )

17 Lexington Avenue
New York, NY 10010
United States
646-312-3370 (Phone)
646-312-3351 (Fax)

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management ( email )

CBA 5.202
Austin, TX 78712
United States
512-471-8879 (Phone)

Aimo Hinkkanen

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL Champaign 61820
United States

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