Closed world assumptions are one of the major approaches for non{monotonic reasoning in artiicial intelligence. In 16] this formalism is applied to disjunctive logic programs, i.e. logic programs with positive disjunctive rule heads and positive atoms in the rule bodies. The disjunctive closure operator T S P allows for the derivation of the set MSP of all positive disjunctive clauses logically...

This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from others in a program. These semantics are based on lattice-structured multi-valued logics, and are characterized by a new xpoint semantics of extende...

While it is well-known how normal logic programs may be viewed as a form of abduction and argumentation, the problem of how disjunctive programs may be used for abductive reasoning is rarely discussed. In this paper we propose an abductive semantics for disjunctive logic programs with default negation and show that Eshghi and Kowal-ski's abductive proof procedure for normal programs can be adop...

Disjunctive logic programming under the stable model semantics [GL91] is a new methodology called answer set programming (ASP) for solving combinatorial search problems. This programming method uses answer set solvers, such as DLV [Lea05], GNT [Jea05], SMODELS [SS05], ASSAT [LZ02], CMODELS [Lie05a]. Systems DLV and GNT are more general as they work with the class of disjunctive logic programs, ...

Nonlinear disjunctive convex sets arise naturally in the formulation or solution methods of many discrete-continuous optimization problems. Often, a tight representation of the disjunctive convex set is sought, with the tightest such representation involving the characterization of the convex hull of the disjunctive convex set. In the most general case, this can be explicitly expressed through ...

Building on earlier work by Guo-Qiang Zhang on disjunctive information systems, and by Thomas Ehrhard, Pasquale Malacaria, and the first author on stable Stone duality, we develop a framework of disjunctive propositional logic in which theories correspond to algebraic L-domains. Disjunctions in the logic can be indexed by arbitrary sets (as in geometric logic) but must be provably disjoint. Thi...

Abductive logic programming (ALP) and disjunctive logic programming (DLP) are two different extensions of logic programming. This paper investigates the relationship between ALP and DLP from the program transformation viewpoint. It is shown that the belief set semantics of an abductive program is expressed by the answer set semantics and the possible model semantics of a disjunctive program. In...

Nowadays, many real problems can be modelled as Constraint Satisfaction Problems (CSPs). Some CSPs are considered nonbinary disjunctive CSPs. Many researchers study the problems of deciding consistency for Disjunctive Linear Relations (DLRs). In this paper, we propose a new class of constraints called Extended DLRs consisting of disjunctions of linear inequalities, linear disequations and non-l...

In this paper we relate antiblocker duality between polyhedra, graph theory and the disjunctive procedure. In particular, we analyze the behavior of the disjunctive procedure over the clique relaxation, K(G), of the stable set polytope in a graph G and the one associated to its complementary graph, K(Ḡ). We obtain a generalization of the Perfect Graph Theorem proving that the disjunctive indice...

We define the inverse operation for disjunctive completion, introducing the notion of least disjunctive basis for an abstract domain D: this is the most abstract domain inducing the same disjunctive completion as D. We show that the least disjunctive basis exists in most cases, and study its properties in relation with reduced product of abstract interpretations. The resulting framework is powe...