Abstract
We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.
| Original language | English (US) |
|---|---|
| Title of host publication | Readings in Qualitative Reasoning About Physical Systems |
| Publisher | Elsevier Inc. |
| Pages | 422-434 |
| Number of pages | 13 |
| ISBN (Print) | 1558600957, 9781483214474 |
| DOIs | |
| State | Published - Sep 17 2013 |
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ASJC Scopus subject areas
- Computer Science(all)
Cite this
Order of Magnitude Reasoning in Qualitative Differential Equations. / Davis, Ernest.
Readings in Qualitative Reasoning About Physical Systems. Elsevier Inc., 2013. p. 422-434.Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Order of Magnitude Reasoning in Qualitative Differential Equations
AU - Davis, Ernest
PY - 2013/9/17
Y1 - 2013/9/17
N2 - We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.
AB - We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.
UR - http://www.scopus.com/inward/record.url?scp=84944053429&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84944053429&partnerID=8YFLogxK
U2 - 10.1016/B978-1-4832-1447-4.50039-0
DO - 10.1016/B978-1-4832-1447-4.50039-0
M3 - Chapter
AN - SCOPUS:84944053429
SN - 1558600957
SN - 9781483214474
SP - 422
EP - 434
BT - Readings in Qualitative Reasoning About Physical Systems
PB - Elsevier Inc.
ER -