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キーワード:
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要旨:
The Lexicographic Path Order (LPO) and the Knuth-Bendix
Ordering (KBO) are two prominent term orders that are
utilised in automated theorem provers. The LPO features
some properties that allow it to be used in the context
of hierarchic signature extensions and in the presence
of term definitions, where special ordering criteria are
desired for the defined terms. The KBO, on the other
hand, can be computed more efficiently than the LPO and
it correlates better with the size of terms, but the KBO
cannot be used in the afore-mentioned situations, in
which a single term should supersede infinitely many
smaller terms of arbitrary sizes. In this diploma
thesis, we present two extensions of the KBO that
overcome these limitations. The first extension order is
suitable for hierarchic signature extensions and its
main characteristic is that it uses pairs of positive
real numbers as symbol weights, whereas the second
extension can handle the required ordering of term
definitions through the usage of ordinal numbers as
symbol weights.
