In this paper we propose algorithms for generation of frequent itemsets by successive construction of the nodes of a lexicographic tree of itemsets. We discuss di erent strategies in generation and traversal of the lexicographic tree such as breadthrst search, depthrst search or a combination of the two. These techniques provide di erent trade-o s in terms of the I/O, memory and computational t...

Logical inconsistency may often occur throughout the development stage of a DL-based ontology. We apply the lexicographic inference to reason over inconsistent DL-based ontologies without repairing them first. We address the problem of checking consequences in a SHIQ ontology that are classically inferred from every consistent (or coherent) subontology having the highest lexicographic precedenc...

The design of most process control is essentially a dynamic multi-objective optimization problem (Meadowcroft et al., 1992), sometimes with nonlinear characters, and in which both economic benefit and social benefit should be considered. Commonly speaking, there are contradictory objectives such as quantity of products, quality of products, safety of manufacturing, cost of manufacturing, enviro...

We present a simple method to formally prove termination of recursive functions by searching for lexicographic combinations of size measures. Despite its simplicity, the method turns out to be powerful enough to solve a large majority of termination problems encountered in daily theorem proving practice.

We consider the nonlinear system of equations that results from the Van Leer flux vector-splitting discretization of the one dimensional Euler equations. This nonlinear system is linearized at the discrete solution. The main topic of this paper is a convergence analysis of blockGauss–Seidel methods applied to this linear system of equations. Both the lexicographic and the symmetric block-Gauss–...

A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in ...