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...

In this paper we consider multidimensional indexing with the additional constraint of lexicographical ordering. In order to deal with this problem we discuss two well-known tree data structures: R-Tree and B-Tree. We study the problem in the transactional environment with read committed isolation level. To evaluate these approaches we had implemented these structures (modified GiST ensures conc...

Motivation Outline Notation Lyndon words Smooth words Result Idea of the proof Case a) Case b) Case c) Case d) Open problems Motivation ◮ Lyndon words : class of words having lexicographical order properties. ◮ Smooth words : class of words, related to the Kolakoski word, that can be easily compressed. ◮ Some infinite smooth words are also Lyndon words.

The marriage of computers and the OED enhances end user access and simplifies basic publishing needs, but computerization can also result in more effective lexicography. Computerized lexicography has an important side benefit in the development of new information products. We briefly describe lexicographical activity as it was conducted on the Supplements for the OED and explore some possibilit...

In this paper, we prove that a Cayley digraph Γ = Cay(G, S) is a nontrivial lexicographical product if and only if there is a nontrivial subgroup H of G such that S \ H is a union of some double cosets of H in G.