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...

Results of Bunge and Funk and of Johnstone, providing constructively sound descriptions of the global points of the lower and upper powerlocales, are extended here to describe the generalized points and proved in a way that displays in a symmetric fashion two complementary treatments of frames: as suplattices and as preframes. We then also describe the points of the Vietoris powerlocale. In eac...

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...

We describe LOCALE, a system that allows cooperating information systems to share labels for photographs. Participating photographs are enhanced with a geographic location stamp – the latitude and longitude where the photograph was taken. For a photograph with no label, LOCALE can use the shared information to assign a label based on other photographs that were taken in the same area. LOCALE th...

These theories introduce a new command called statespace. It’s usage is similar to records. However, the command does not introduce a new type but an abstract specification based on the locale infrastructure. This leads to extra flexibility in composing state space components, in particular multiple inheritance and renaming of components. The state space infrastructure basically manages the fol...