semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

We create an open multilingual wordnet with large wordnets for over 26 languages and smaller ones for 57 languages. It is made by combining wordnets with open licences, data from Wiktionary and the Unicode Common Locale Data Repository. Overall there are over 2 million senses for over 100 thousand concepts, linking over 1.4 million words in hundreds of languages.

In the context of constructive locale or frame theory (locale theory over a fixed base locale), we study some aspects of ’frame distributions’, meaning sup preserving maps from a frame to the base frame. We derive a relationship between results of Jibladze-Johnstone and Bunge-Funk, and also descriptions in distribution terms, as well as in double negation terms, of the ’interior of closure’ ope...

In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra A a topos T (A) of sheaves on a locale and a commutative C*-algebra A within that topos. The Gelfand spectrum of A is a locale Σ in this topos, which is equivalent to a bundle over the base locale. We further develop this external presentation of the locale Σ, by noting...

RÉSUMÉ. Nous présentons un algorithme heuristique pour déterminer une solution d’un problème de satisfaction de contraintes continu. Cet algorithme, appelé Recherche Locale Dichotomique ( ), combine la recherche locale, la bissection et la contraction d’intervalles avec la propagation de contraintes. Nous présentons des résultats expérimentaux et les comparons avec un algorithme de recherche lo...

1 Définir l’ontologie locale Une ontologie locale est définie l’ontologie du domaine, articulée à cette dernière par la relation de subsumption par : Spécialisation des sous-ensemble de classes de l’ontologie de domaine recouvrant les besoins du cahier de charges et par importation sélective des propriétés pertinentes. Enrichissement de l’ontologie locale pour répondre aux objectifs applicatifs...

This paper uses the locale theory approach to topology. Two descriptions are given of all locale limits, the first description using suplattice constructions and the second preframe constructions. The symmetries between these two approaches to locale theory are explored. Given an informal assumption that open locale maps are parallel to proper maps (an assumption hinted at by the underlying fin...

If X is a locale, then its double powerlocale PX is defined to be PU(PL(X)) where PU and PL are the upper and lower powerlocale constructions. We prove various results relating it to exponentiation of locales, including the following. First, if X is a locale for which the exponential S exists (where S is the Sierpinski locale), then PX is an exponential S X . Second, if in addition W is a local...

Locatedness is one of the fundamental notions in constructive mathematics. The existence of a positivity predicate on a locale, i.e. the locale being overt, or open, has proved to be fundamental in constructive locale theory. We show that the two notions are intimately connected. Bishop defines a metric space to be compact if it is complete and totally bounded. A subset of a totally bounded set...