174 research outputs found
Isotonies on ordered cones throught the concept of a decreasing scale
Using techniques based on decreasing scales, necessary and sufficient conditions are presented for the
existence of a continuous and homogeneous of degree one real-valued function representing a (not necessarily
complete) preorder defined on a cone of a real vector space. Applications to measure theory and expected
utility are given as consequences
The intuitionistic temporal logic of dynamical systems
A dynamical system is a pair , where is a topological space and
is continuous. Kremer observed that the language of
propositional linear temporal logic can be interpreted over the class of
dynamical systems, giving rise to a natural intuitionistic temporal logic. We
introduce a variant of Kremer's logic, which we denote , and show
that it is decidable. We also show that minimality and Poincar\'e recurrence
are both expressible in the language of , thus providing a
decidable logic expressive enough to reason about non-trivial asymptotic
behavior in dynamical systems
Conference Program
Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications
Real representations of preferences and applications.
In this thesis we first review some results concerning the real representation of preferences. Different kind of preferences are considered and a particular attention is devoted to the case of intransitivity of the associated indifference relation. Therefore, interval orders and semiorders appear as relevant types of binary relations for which indifference is not transitive. It is particulary interesting to guarantee the existence of continuous or at least upper semicontinuous representations. Homogeneity of the representations is studied in connection with the aforementioned continuity when the space of preferences is endowed with an algebraic structure
Stochastic order on metric spaces and the ordered Kantorovich monad
In earlier work, we had introduced the Kantorovich probability monad on
complete metric spaces, extending a construction due to van Breugel. Here we
extend the Kantorovich monad further to a certain class of ordered metric
spaces, by endowing the spaces of probability measures with the usual
stochastic order. It can be considered a metric analogue of the probabilistic
powerdomain.
The spaces we consider, which we call L-ordered, are spaces where the order
satisfies a mild compatibility condition with the metric itself, rather than
merely with the underlying topology. As we show, this is related to the theory
of Lawvere metric spaces, in which the partial order structure is induced by
the zero distances.
We show that the algebras of the ordered Kantorovich monad are the closed
convex subsets of Banach spaces equipped with a closed positive cone, with
algebra morphisms given by the short and monotone affine maps. Considering the
category of L-ordered metric spaces as a locally posetal 2-category, the lax
and oplax algebra morphisms are exactly the concave and convex short maps,
respectively.
In the unordered case, we had identified the Wasserstein space as the colimit
of the spaces of empirical distributions of finite sequences. We prove that
this extends to the ordered setting as well by showing that the stochastic
order arises by completing the order between the finite sequences, generalizing
a recent result of Lawson. The proof holds on any metric space equipped with a
closed partial order.Comment: 49 pages. Removed incorrect statement (Theorem 6.1.10 of previous
version
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