A Geometric Approach to Total Envisioning

Conventional envisioners proposed in qualitative physics have two difficulties in common: ambiguities in prediction and inability of reasoning about global behaviors. We take a geometric approach to overcome these difficulties and have implemented a program PSX2NL which can reason about global behaviors by analyzing geometry and topology of solution curves of ordinary differential equations in the phase space. In this paper, we highlight a flow grammar which specifies possible patterns of solution curves one may see in the phase space. The role of a flow grammar in PSX2NL is twofold: firstly, it allows PSX2NL to reason about complex patterns in a uniform manner; secondly, it allows PSX2NL to switch to an approximate, top-down algorithm when complete geometric clues are not available due to the difficulty of mathematical problems encountered.

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