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Yves Moinard
Forgetting literals with varying propositional symbols
, J. of Logic and Computation
, Oxford University Press
, Vol. 17
, No. 5
, 955--982
, oct
, 2007
, Document
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Abstract
Recently, the old logical notion of forgetting propositional symbols (or
reducing the logical vocabulary, called `elimination of middle terms` by Boole)
has been generalized to a new notion:
forgetting literals. The aim was to help the automatic computation of various
formalisms which are currently used in knowledge representation.
We extend here this notion, by allowing propositional symbols to vary
while forgetting literals.
We describe the new notion, on the syntactical and the semantical side
We provide various different syntactical characterizations,
in order to provide various methods for computing the notion introduced here.
This confirms that one of the main interests of the notion of
forgetting literals
(original, and new version)
is that it provides new kinds of methods of computation.
Then, we show how to apply it to the computation of circumscription.
This computation has been done before with standard literal forgetting,
but here
we show how introducing varying propositional symbols
simplifies significantly the computation.
We revisit a fifteen years old
result about computing circumscription, showing that it can be improved in the
same way.
We provide hints in order to apply this forgetting method also to other
logical formalisms.
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