Cambridge Journals Online

Technical Note

A Constructive semantic characterization of aggregates in answer set programming

TRAN CAO SONa1 and ENRICO PONTELLIa1 a1 Department of Computer Science, New Mexico State University, NM, USA (e-mail: tson@cs.nmsu.edu, epontell@cs.nmsu.edu)

Article author query son tc  pontelli e

Abstract

This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator Φ^aggr_P for aggregate programs, independently proposed in Pelov (2004) and Pelov et al. (2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.

(Received June 17 2005)

(Revised October 27 2005)

(Accepted February 08 2006)

Key Words: aggregates; answer set programming; semantics