Set Constraints in Logic Programming

We investigate a generalization of weight-constraint programs with stable semantics, as implemented in the ASP solver smodels. Our programs admit atoms of the form \(\langle X,\mathcal{F} \rangle\) where X is a finite set of propositional atoms and \(\mathcal{F}\) is an arbitrary family of subsets of X. We call such atoms set constaints and show that the concept of stable model can be generalized to programs admitting set constraints both in the bodies and the heads of clauses. Natural tools to investigate the fixpoint semantics for such programs are nondeterministic operators in complete lattices. We prove two fixpoint theorems for such operators.

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