For a graph G = (V,E), a set D ⊆ V is called a disjunctive dominating set of G if for every vertex v ∈ V \D, v is either adjacent to a vertex of D or has at least two vertices in D at distance 2 from it. The cardinality of a minimum disjunctive dominating set of G is called the disjunctive domination number of graph G, and is denoted by γ 2 (G). The MINIMUM DISJUNCTIVE DOMINATION PROBLEM (MDDP)...

In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programs and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood and there exist several implementations of the best known semantics (well-founded semantics and stable semantics), the declarative and computational foundations of disjunctive p...

In the successful branch-and-cut approach to combinatorial optimization, linear inequalities are used as cutting planes within a branch-and-bound framework. Although researchers often prefer to use facet-inducing inequalities as cutting planes, good computational results have recently been obtained using disjunctive cuts, which are not guaranteed to be facet-inducing in general. A partial expla...

We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of th...

We investigate the derivation of disjunctive conic cuts for mixed integer second order cone optimization (MISOCO). These conic cuts characterize the convex hull of the intersection of a disjunctive set and the feasible set of a MISOCO problem. We present a full characterization of these inequalities when the disjunctive set considered is defined by parallel hyperplanes.

We study the problem of extending hybrid knowledge-based systems integrating rules and structured representation of information. Speciically, we deene disjunctive AL-log, a hybrid formalism which combines two very expressive knowledge representation languages: disjunctive datalog and the description logic ALC. First, by exploiting the use of nonmono-tonic features of disjunctive datalog, we sho...

DisLog is a system for reasoning in disjunctive deductive databases. It seeks to combine features of disjunctive logic programming, such as the support for incomplete information, with those of deductive databases, such as all{result inference capabilities. Several basic operators are provided for logical and non{monotonic reasoning: The logical consequence operator derives all logically implie...

An elementary, but fundamental, operation in disjunctive programming is a basic step, which is the intersection of two disjunctions to form a new disjunction. Basic steps bring a disjunctive set in regular form closer to its disjunctive normal form and, in turn, produce relaxations that are at least as tight. An open question is: What are guaranteed bounds on the improvement from a basic step? ...

This report constitutes the Doctoral Dissertation for Michael Perregaard and is a collection of results on the efficient generation of disjunctive cuts for mixed integer programs. Disjunctive cuts is a very broad class of cuts for mixed integer programming. In general, any cut that can be derived from a disjunctive argument can be considered a disjunctive cut. Here we consider specifically cuts...

We present a new framework for learning disjunctive logic programs from interpretation transitions, called LFDT. It is a nontrivial extension to Inoue, Ribeiro and Sakama’s LF1T learning framework, which learns normal logic programs from interpretation transitions. Two resolutions for disjunctive rules are also presented and used in LFDT to simplify learned disjunctive rules.