On $k$-translations

On Various Negative Translations

Several proof translations of classical mathematics into intuitionistic mathematics have been proposed in the literature over the past century. These are normally referred to as negative translations or double-negation translations. Among those, the most commonly cited are translations due to Kolmogorov, Gödel, Gentzen, Kuroda and Krivine (in chronological order). In this paper we propose a fra...

q-Translations on quantum spaces

Attention is focused on quantum spaces of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. Each of these quantum spaces can be combined with its symmetry algebra to form a Hopf algebra. The Hopf structures on quantum space coordinates imply their translation. This article is devoted to t...

1 Translations on a Lattice

We have seen that symmetry groups may have different implications on the physics. The first we have seen is an “internal symmetry”, global, manifested by multiplets of states which form the space acted upon by a representation of the group. Quite different is a local symmetry, which, although it is a much larger group, being a product of groups at each space-time point, does not have a correspo...

Translations

Representing Translations on the Semantic Web

The increase of ontologies and data sets published in the Web in languages other than English raises some issues related to the representation of linguistic (multilingual) information in ontologies. Such linguistic descriptions can contribute to the establishment of links between ontologies and data sets described in multiple natural languages in the Linked Open Data cloud. For these reasons, s...