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A Truth Maintenance System was presented by Doyle to support
nonmonotonic reasoning. Such a TMS has the ability to update
a knowledge base for which formulas can be inserted or
withdrawn. It uses "IN" and "OUT" to represent whether or not
an assertion is true in all models. But in the real world, not
all the things are crisp. There are some things which are
fuzzy, especially in the representation of human
knowledge. We can represent some kinds of fuzzy information by
using fuzzy logic. Vague logic is a kind of fuzzy logic
based on vague sets. A vague truth maintenance
methodology is developed in this thesis. This algorithm
is then rewritten as an anytime algorithm, where the
algorithm can be interrupted at anytime with an
approximate answer. The anytime version of the vague
TMS will give an approximation of the vague initial model of a
set of vague facts and axioms, where this approximation
can be guaranteed to be accurate within certain bounds. In
this thesis, we have presented two version of a vague TMS,
which can be used to maintain vague intervals in a
dynamic environment. By ordering the updated facts by truth
values, we will get a monotonic approach to computing the
vague initial model. With this property, when we are
oblidged to stop our computation before completion, we can
reply with an interval to bound the final result, and we can
guarantee that the algorithm, when run to completion, will give
the correct answers.
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