Theory and Practice of Logic Programming

Regular Papers

Preferred answer sets for ordered logic programs

a1 Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium (email:,

Article author query
van nieuwenborgh d   [Google Scholar] 
vermeir d   [Google Scholar] 


We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a “best” answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjunction and some other formalisms such as logic programs with ordered disjunction. The approach is shown to be useful in several application areas, e.g. repairing database, where minimal repairs correspond to preferred answer sets.

(Received November 27 2003)
(Revised June 6 2004)
(Accepted July 19 2004)

Key Words: nonmonotonic reasoning; knowledge representation; answer set programming; preference.


1 Supported by the FWO.

2 This work was partially funded by the Information Society Technologies programme of the European Commission, Future and Emerging Technologies under the IST-2001-37004 WASP project.