### 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 |

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

Davis, E. (2013). Order of Magnitude Reasoning in Qualitative Differential Equations. In

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