|
Moinard, Yves and Rolland, Raymond
Characterizations of preferential entailments
, INRIA, Research Report RR-3928, IRISA, Publication Interne 1326
, Rennes, France
, apr
, 2000
, Document
|
|
Abstract
A preferential entailment is defined by a binary
relation, or ``preference relation\'\'. This relation may be
among interpretations, or sets of interpretations, or
among ``states\'\' which are ``copies\'\' of interpretations
or of sets of interpretations.
This provides four kinds of preferential entailments.
The paper deals mainly with propositional logic, however
it describes also the situation in first order logic.
For instance, the third notion presented above can be seen as a way
to simulate the main aspects of the simplest first notion when it is
defined in the predicate calculus, while staying in the propositional calculus.
Indeed, the third notion allows as many copies of interpretations as we want
for a complete theory, even in the propositional calculus,
and this is precisely
what happens in the predicate calculus.
What we do here is to provide a characterization result for these four kinds
of preferential entailments. We choose properties as simple and natural as
possible, and sometimes we provide various characterizations for the same
notion.
It appears that the apparently most complicated
notion possesses by far the simplest
characterization result. A by-product of our results is that the fourth notion
is equivalent to the second notion: we may define directly the
relation among sets of interpretations, eliminating the need for ``states\'\'
in this case.
|
|