In this paper, we extend the progression semantics for firstorder disjunctive logic programs and show that it coincides with the stable model semantics. Based on it, we further show how disjunctive answer set programming is related to Satisfiability Modulo Theories.

If L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1, L2} is the least integer n, provided that it exists, such that for every 2-coloring of the set {1, 2, . . . , n} there exists a monochromatic solution to either L1 or L2. If such an integer n does not exist, then the disjunctive Rado number is infinite. In this paper, it is shown that for all integers a 1 and b ...

A thorough scrutiny of the literature dedicated to association rule mining highlights that a determined effort focused so far on mining the co-occurrence relations between items, i.e., conjunctive patterns. In this respect, disjunctive patterns presenting knowledge about complementary occurring items were neglected in the literature. Nevertheless, recently a growing number of works is shedding ...

We present a novel approach to fuzzy dl-programs under the answer set semantics, which is a tight integration of fuzzy disjunctive programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly integrated disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. We show that t...

Uninorms are a generalization of t-norms and tconorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In reallife applications, this kind of aggregation may be counter-intuitive. Atanassov’s i...

This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is pre...

In many situations, both in human and artificial societies, cooperating agents have different status with respect to the activity and it is not uncommon that certain actions are only allowed to coalitions that satisfy certain criteria, e.g., to sufficiently large coalitions or coalitions which involve players of sufficient seniority. Simmons (1988) formalized this idea in the context of secret ...

In this work, we present a Lagrangean relaxation of the hull-reformulation of discrete-continuous optimization problems formulated as linear generalized disjunctive programs (GDP). The proposed Lagrangean relaxation has three important properties. The first property is that it can be applied to any linear GDP. The second property is that the solution to its continuous relaxation always yields 0...

Aguilera et al. [DiscreteAppl.Math. 121 (2002) 1–13] give a generalization of a theorem of Lehman through an extension P̄j of the disjunctive procedure defined by Balas, Ceria and Cornuéjols. This generalization can be formulated as (A) For every clutter C, the disjunctive index of its set covering polyhedron Q(C) coincides with the disjunctive index of the set covering polyhedron of its blocker...

The paper proposes a new knowledge representation language, called DLP, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language providing a natural representation of default reasoning with exceptions. A declarative model-theoretic semantics of DLP is provided, which is shown to genera...