1991 Fiscal Year Final Research Report Summary
Studies on Development of A Software System for Qualitative Analysis of Dynamical Systems
| Project/Area Number |
02680024
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
NISHIDA Toyoaki Kyoto University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70135531)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAHARA Tatsuya Kyoto University, Faculty of Engineering, Assistant Professor, 工学部, 助手 (00234104)
YAMADA Atsushi Kyoto Uniersity, Faculty of Engineering, Assistant Professor, 工学部, 助手 (20240004)
YAMASAKI Susumu Okayama University, Faculty of Engineering, Professor, 工学部, 教授 (10026354)
DOSHITA Shuji Kyoto University, Faculty of Engineering, Professor, 工学部, 教授 (00025925)
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| Project Period (FY) |
1990 – 1991
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| Keywords | qualitative reasoning / dynamical systems / commonsense reasoning / engineering problem solving / artificial intelligence / differential equations |
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| Research Abstract |
In engineering problem solving, analysis of nonlinear differential equations plays a crucial part. This research aimed at development of a software system which can analyze the qualitative behavior of nonlinear ordinary differential equations with two unknowns, by integrating knowledge-based and numerial methods using qualitative reasoning techniques.
We have achieved the following accomphshments with respect to the above research goal :
1. We have devised flow patterns as a means for representing geometric features of solution curves of ordinary differential equations. In addition, we have formulated a flow grammar which is a grammatical characterization of flow patterns one may observe in phase spaces of ordinary differential equations.
2. We have devised a new method of reasoning about qualitative behaviors which operates in both bottom-up and top-down mode. The bottom-up mode follows a prescribed procedure to collect information to capture the behavior. In contrast. the top-down mode is strongly guided by the domain knowledge, attempting to derive most plausible interpretation from partial information. In normal situations, the bottom-up mode is used, which will be switched to the top-down mode once logical failure is recognized.
3. We have designed and implemented a prototype system called PSX2NL and have tested it against typical. examples to evaluate the method from experimental points of view.
4. We have discussed about technical issues involved in a system which can analyze more complex ordinary differential equations with three unknowns. We have partly implemented the idea.
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