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Philip Schaefer

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AAAI Conference 1991 Conference Paper

Analytic Solution of Qualitative Differential Equations

Philip Schaefer

Numerical simulation, phase-space analysis, and analytic techniques are three methods used to solve quantitative differential equations. Most work in Qualitative Reasoning has dealt with analogs of the first two techniques, producing capabilities applicable to a wide range of systems. Although potentially of benefit, little has been done to provide closed-form, analytic solution techniques for qualitative differential equations (QDEs). This paper presents one such technique for the solution of a class of ordinary linear and nonlinear differential equations. The technique is capable of deriving closedform descriptions of the qualitative temporal behavior represented by such equations. A language QFL for describing qualitative temporal behaviors is presented, and procedures and an implementation QDIFF that solves equations in this form are demonstrated.

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IJCAI Conference 1987 Conference Paper

Belief Functions for Real-Time Script Processing

Philip Schaefer

Real-time situation understanding is a difficult problem, in that decisions must be made on a continuous basis with continuously changing data. An attractive approach to the problem is to match the current data set to a memory of script-like structures. Partial matching to scripts enables powerful understanding and prediction, but requires robust uncertainty mechanisms to overcome inherent ambiguity and error. Although powerful uncertainty techniques for dealing with time-relevant data have been developed, l i t t l e with regard to the implications of the real-time problem has been presented. This paper discusses some of the special requirements for a real-time script belief function, and presents a derivation of such a function. Finally, examples demonstrating the characteristics of the Script Belief function are provided.

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