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We achieve this by encoding each basic desire as a set of rules and by developing two sets of rules sat and pref .
Observe that for a desire with desire(n ) pref () we have that pref ().
These answer sets are used as inputs for the program pref , which is defined next.
We are now ready to define the set of rules pref (), which consists of the rules encoding and the rules encoding the computation of w .
The next theorem proves the correctness of pref ().
This is done as follows: (n ) = 0 if desire(n ) pref () (i. e., if is a desire); (n ) = 1 if preference(n ) pref () and = 1 2 .
To account for the structure of the preference, we associate an integer, denoted by (n ), to each constant n such that preference(n ) pref () or desire(n ) pref ().
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