We address the problem of nding a tight representation of com plex logical constraints in a mixed integer programming model by de scribing a convex hull representation of cardinality rules A cardinality rule asserts that if at least k of the propositions A Am are true then at least l of the propositions B Bn are true As rule based systems and other types of logic modeling grow in popu larity lo...

In this paper we investigate certain aspects of infeasibility in convex integer programs. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining feasible region. We prove that for the considered class of convex functions, every infeasible system of inequality constraints in the convex integer pro...

The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for "valid" equalities which have the potential of strengthening the problem's formulation. Recently, Martello and Toth [13] included cardin...

Accurately estimating the cardinality of aggregate views is crucial for logical and physical design of data warehouses. While the warehouse is under development and data are not available yet, the approaches based on accessing data cannot be adopted. This paper proposes an approach to estimate the cardinality of views based on a-priori information derived from the application domain. We face th...

We propose a tree logic capable of expressing simple cardinality constraints on the number of nodes selected by an arbitrarily deep regular path with backward navigation. Specifically, a sublogic of the alternation-free μ−calculus with converse for finite trees is extended with a counting operator in order to reason on the cardinality of node sets. Also, we developed a bottom-up tableau-based s...

Describe in up to 200 words the nature of your proposed research in plain English for a general audience. This summary should be able to be used for publicity purposes if the proposal is offered funding. The eXtensible Markup Language (XML) has evolved to be the " lingua franca " for data integration and data exchange on the Internet and elsewhere. This development has led to a dramatic increas...

In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind problem is generally difficult to deal with, because it involves constraint that not continuous neither convex, but provides sparse solutions. Thereby reformulate MPCaC in suitable way, by modeling as mixed-integer and then addressing its counterpart, which will...

Given two classes of logic programs, we may be interested in modular translations from one class into the other that are sound wth respect to the answer set semantics. The main theorem of this paper characterizes the existence of such a translation in terms of strong equivalence. The theorem is used to study the expressiveness of several classes of programs, including the comparison of cardinal...