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Yves Moinard
General preferential entailments as circumscriptions
, ECSQARU 2001 (Symbolic and Quantitative Approaches to Reasoning and Uncertainty)
, Springer-Verlag, LNAI
, Vol. 2143
, 532--543
, sep
, 2001
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Abstract
A ``preferential entailment'' is defined by a binary
relation, or ``preference relation'', either among interpretations
(or models) or among ``states'' which are ``copies of interpretations''.
Only the models, or the states, minimal for this relation, are considered,
and this notion provides a natural formalization of aspects
of common sense reasoning such as rules with exceptions.
We study the best known modification of the vocabulary
which has been introduced in order to help the automatic computation of
all these ``preferential entailments''.
Firstly, we show how an extension of the vocabulary allows the
expression of any preferential entailment as a classical
preferential entailment (without state).
Then, we reexamine the role of this extension in the computation
of the best known classical preferential entailment: circumscription.
We provide various examples, all related to circumscriptions,
which is till now the
only preferential entailment for which efficient systems exist.
This study shows precisely how many kinds of preferential entailments
can be easily expressed in terms of circumscriptions.
In order to get a better understanding of the method,
we examine which fundamental properties of reasoning are
preserved by this modification of
the vocabulary, thus providing a powerful technical tool
allowing to determine whether the method can be applied or not.
For our purpose, we need to clarify the operations of extension or
reduction of the vocabulary, which may have applications in other domains,
as these modifications are very frequent, but have not been studied a lot
in recent works.
We provide constructive definitions, which are kept
as simple and natural as possible.
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