Properties and Applications of Programs with Monotone and Convex Constraints

We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of off-the-shelf solvers of pseudo-boolean constraints, which is often much faster than the smodels system.

Fixpoint 3-valued semantics for autoepistemic logic

The paper presents a constructive fixpoint semantics for autoepistemic logic (AEL). This fixpoint characterizes a unique but possibly three-valued belief set of an autoepistemic theory. It may be three-valued in the sense that for a subclass of formulas F, the fixpoint may not specify whether F is believed or not. The paper presents a constructive 3-valued semantics for autoepistemic logic (AEL). We introduce a derivation operator and define the semantics as its least fixpoint. The semantics is 3-valued in the sense that, for some formulas, the least fixpoint does not specify whether they are believed or not. We show that complete fixpoints of the derivation operator correspond to Moore's stable expansions. In the case of modal representations of logic programs our least fixpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen semantics (depending on the embedding used). We show that, computationally, our semantics is simpler than the semantics proposed by Moore (assuming that the polynomial hierarchy does not collapse).