Weight constraint and aggregate programs are among the most widely used logic
programs with constraints. In this paper, we relate the semantics of these two
classes of programs, namely the stable model semantics for weight constraint
programs and the answer set semantics based on conditional satisfaction for
aggregate programs. Both classes of programs are instances of logic programs
with constraints, and in particular, the answer set semantics for aggregate
programs can be applied to weight constraint programs. We show that the two
semantics are closely related. First, we show that for a broad class of weight
constraint programs, called strongly satisfiable programs, the two semantics
coincide. When they disagree, a stable model admitted by the stable model
semantics may be circularly justified. We show that the gap between the two
semantics can be closed by transforming a weight constraint program to a
strongly satisfiable one, so that no circular models may be generated under the
current implementation of the stable model semantics. We further demonstrate
the close relationship between the two semantics by formulating a
transformation from weight constraint programs to logic programs with nested
expressions which preserves the answer set semantics. Our study on the
semantics leads to an investigation of a methodological issue, namely the
possibility of compact representation of aggregate programs by weight
constraint programs. We show that almost all standard aggregates can be encoded
by weight constraints compactly. This makes it possible to compute the answer
sets of aggregate programs using the ASP solvers for weight constraint
programs. This approach is compared experimentally with the ones where
aggregates are handled more explicitly, which show that the weight constraint
encoding of aggregates enables a competitive approach to answer set computation
for aggregate programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP), 2011.
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