KSL-92-29
## Order of Magnitude Reasoning Using Logarithms

**Reference: **
Nayak, P. P. Order of Magnitude Reasoning Using Logarithms. 1992.

**Abstract:** Converting complex equations into simpler, more tractable
equations usually involves approximation. Approximation is
usually done by identifying and removing insignificant terms,
while retaining significant ones. The significance of a term can
be determined by order of magnitude reasoning. In this paper we
describe NAPIER, an implemented order of magnitude reasoning
system. NAPIER defines the order of magnitude of a quantity on a
logarithmic scale, and uses a set of rules to propagate orders of
magnitudes through equations. A novel feature of NAPIER is the
way it handles non-linear simultaneous equations, using linear
programming in conjunction with backtracking. We show that order
of magnitude reasoning in NAPIER is, in general, intractable and
then discuss an approximate reasoning technique that allow it to
run fast in practice. Some of NAPIER's inference rules are
heuristic, and we estimate the error introduced by their use.

Full paper available as ps.

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