We give a characterization of the non-empty binary relations  on a N∗-set A such that there exist two morphisms of N∗-sets u1, u2 : A → R+ verifying u1 ≤ u2 and x  y ⇔ u1(x) > u2(y). They are called homothetic interval orders. If  is a homothetic interval order, we also give a representation of  in terms of one morphism of N∗-sets u : A → R+ and a map σ : u(R+) × A → R+ such that x  y ⇔ σ(...

one mineral density measurements are useful for predicting the risk of fracture in an individual, for assessing the effect of a disease or drug on bone mass, and for monitoring the effect of therapy of osteoporosis. For the hip and spine, measurements made at the affected site discriminate better between fragility fractures and nonfracture cases than do measure ments made on other parts of the ...

With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability of current models to capture logical operations such as negation. As a solution we propose a tripartite formulation for a continuous vector space representat...

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