### 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) |
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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

*Readings in Qualitative Reasoning About Physical Systems*(pp. 422-434). Elsevier Inc.. https://doi.org/10.1016/B978-1-4832-1447-4.50039-0

**Order of Magnitude Reasoning in Qualitative Differential Equations.** / Davis, Ernest.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Readings in Qualitative Reasoning About Physical Systems.*Elsevier Inc., pp. 422-434. https://doi.org/10.1016/B978-1-4832-1447-4.50039-0

}

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

SN - 1558600957

SN - 9781483214474

SP - 422

EP - 434

BT - Readings in Qualitative Reasoning About Physical Systems

PB - Elsevier Inc.

ER -