We extend the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general constraints expressed in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). In QFBAPA one can formulate Boolean combinations of inclusion constraints and numerical constraints on the cardinalities of sets. Our new formalism extends, on th...

We investigate the computational complexity of reasoning over temporal extensions of conceptual data models. The temporal conceptual models we analyse include the standard UML/EER ISA between entities and relationships, disjointness and covering, cardinality constraints and their refinements, multiplicity and key constraints; in the temporal dimension, we have timestamping, evolution and transi...

An algorithm is presented for solving nonlinear optimization problems with chance 5 constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at 6 least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained 7 nonlinear optimization problems that arise in sample average approximations of chance-constrained 8 ...

In the satisfiability domain, it is well-known that a SAT algorithm may solve a problem instance easily and another instance hardly, whilst these two instances are equivalent CNF encodings of the original problem. Moreover, different algorithms may disagree on which encoding makes the problem easier to solve. In this paper, we focus on the CNF encoding of cardinality constraints, which states t...

Aggregation functions are widely used in answer set programming (ASP) for representing and reasoning on knowledge involving sets of objects collectively. These sets may also depend recursively on the results of the aggregation functions, even if so far the support for such recursive aggregations was quite limited in ASP systems. In fact, recursion over aggregates was restricted to convex aggreg...

In this paper we consider the problem of minimizing a convex differentiable function subject to sparsity constraints. Such constraints are non-convex and the resulting optimization problem is known to be hard to solve. We propose a novel generalization of this problem and demonstrate that it is equivalent to the original sparsity-constrained problem if a certain weighting term is sufficiently l...

This work is concerned with approximating constraint satisfaction problems (CSPs) with an additional global cardinality constraints. For example, Max Cut is a boolean CSP where the input is a graph G = (V, E) and the goal is to find a cut S ∪ S̄ = V that maximizes the number of crossing edges, |E(S , S̄ )|. The Max Bisection problem is a variant of Max Cut with an additional global constraint tha...

In this paper, we propose a new encoding of the cardinality constraint ∑i=1 xi > b. It makes an original use of the general formulation of the Pigeon-Hole principle to derive a formula in conjunctive normal form (CNF). Our Pigeon-Hole based CNF encoding can be seen as a nice and simple way to express the semantic of the cardinality constraint, that can be defined as how to put b pigeons into n ...

We study the problem of encoding cardinality constraints (threshold functions) on Boolean variables into CNF. Specifically, we propose new encodings based on (perfect) hashing that are efficient in terms of the number of clauses, auxiliary variables, and propagation strength. We compare the properties of our encodings to known ones, and provide experimental results evaluating their practical ef...

We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such shari...