Deriving Monotonic Function Envelopes from Observations*

Much work in qualitative physics involves constructing models of physical systems using functional descriptions such as "flow monotonically increases with pressure." Semiquantitative methods improve model precision by adding numerical envelopes to these monotonic functions . Ad hoc methods are normally used to determine these envelopes. This paper describes a systematic method for computing a bounding envelope of a multivariate monotonic function given a stream of data . The derived envelope is computed by determining a simultaneous confidence band for a special neural network which is guaranteed to produce only monotonic functions. By composing these envelopes, more complex systems can be simulated using semiquantitative methods.