Next: Representation of OMPs
Up: Dynamic Constraint Satisfaction with
Previous: Background: Activitybased dynamic preference
Orderofmagnitude preferences (OMPs)
Although an aDCSP can capture the hard constraints over decisions in a
given problem as well as their dynamically changing solution space (as
described by the activity constraints), the representation scheme it
employs does not take into account any preferences users may have over
possible alternative value assignments. Therefore, this work is
extended to allow preference information to be attached to
attributevalue assignments. The way in which this can be achieved
depends on the representation and reasoning mechanisms underlying the
preference calculus. In general, a preference calculus can be defined
as a tuple
where:

is the set of preferences,
 is a commutative, associative operator that is closed
in
, and

forms a partial order, that is, reflexive,
antisymmetric and transitive relation defined over
.
Because
is reflexive, antisymmetric and transitive,
comparing preferences with the
relation yields one of
four possible results:
 Two preferences
are equal to one another
(denoted ) iff
and
.
 A preference
is strictly greater than a
preference
(denoted
) iff
and
.
 A preference
is strictly smaller than a
preference
(denoted
) iff
and
.
 Two preferences
are incomparable with one
another (denoted ) iff
and
.
Thus, an activitybased dynamic preference constraint
satisfaction problem (aDPCSP) is a tuple
where

is
an aDCSP,

is a preference
calculus, and
 is a mapping
from the individual attributevalue
assignments to the preferences.
The preferences attached to attributevalue assignments express the
relative desirability of these assignments. The aim of the aDPCSP is
to find a solution with the highest combined preference. That is,
given an aDPCSP
,
any solution
of the
aDCSP
such
that no other solution
of
exists
with
is a solution
to the aDPCSP.
In this section, a preference calculus is introduced to extend an
aDCSP into an aDPCSP. The calculus will be illustrated with examples
from the compositional modelling domain.
Subsections
Next: Representation of OMPs
Up: Dynamic Constraint Satisfaction with
Previous: Background: Activitybased dynamic preference
Jeroen Keppens
20040301