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- Ulrich Berger, Gerhard Gierz, +4 authors D. S. Scott
- Studia Logica
- 2007

In order to give the book under review the right appreciation it is necessary to first say a few words about its predecessor, the monograph A Compendium of Continuous Lattices which was published by the same six authors in 1980. The Compendium, as it is commonly called, contains a rather complete and very readable account of the theory of continuous… (More)

- Regina Tix, Klaus Keimel, Gordon D. Plotkin
- Electr. Notes Theor. Comput. Sci.
- 2005

We present domain-theoretic models that support both probabilistic and nondeterministic choice. In [36], Morgan and McIver developed an ad hoc semantics for a simple imperative language with both probabilistic and nondeterministic choice operators over a discrete state space, using domaintheoretic tools. We present a model also using domain theory in the… (More)

- Maurizio Alvarez-Manilla, Achim Jung, Klaus Keimel
- Theor. Comput. Sci.
- 2004

This paper reviews the one-to-one correspondence between stably compact spaces (a topological concept covering most classes of semantic domains) and compact ordered Hausdorff spaces. The correspondence is extended to certain classes of real-valued functions on these spaces. This is the basis for transferring methods and results from functional analysis to… (More)

We investigate laws for predicate transformers for the combination of nondeterministic choice and (extended) probabilistic choice, where predicates are taken to be functions to the extended nonnegative reals, or to closed intervals of such reals. These predicate transformers correspond to state transformers, which are functions to convex powerdomains, the… (More)

- Klaus Keimel
- Electr. Notes Theor. Comput. Sci.
- 2006

There are more and more papers dealing with situations where probabilistic features occur together with ordinary nondeterminism. Based on the PhD thesis by R. Tix [18], domain theoretical tools for combining probability with nondeterminism were developped in [19]. A motivating situation was the semantics of an imperative language with both probabilistic and… (More)

- Klaus Keimel, Jimmie D. Lawson
- Ann. Pure Appl. Logic
- 2009

In this article we study a type of directed completion for posets and T0-spaces introduced by O. Wyler [Wy81] that we call the D-completion. The category D of monotone convergence spaces is a full reflective subcategory of the category of topological spaces and continuous maps, and the D-completion gives the reflection of a topological space into D, and as… (More)

In his foundation of probability theory, Bruno de Finetti devised a betting scheme where a bookmaker offers bets on the outcome of events φ occurring in the future. He introduced a criterion for coherent bookmaking, and showed that coherent betting odds are given by some probability distribution. While de Finetti dealt with yes-no events and boolean… (More)

- Klaus Keimel
- 2005

The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces,… (More)

- Klaus Keimel, Jimmie D. Lawson
- Electr. Notes Theor. Comput. Sci.
- 2009

In this article we show how separately continuous algebraic operations on T0-spaces and the laws that they satisfy, both identities and inequalities, can be extended to the D-completion, that is, the universal monotone convergence space completion. Indeed we show that the operations can be extended to the lattice of closed sets, but in this case it is only… (More)

Already in his PhD Thesis on compact Abelian semigropups under the direction of Karl Heinrich Hofmann the author was lead to investigate locally compact cones [18]. This happened in the setting of Hausdorff topologies. The theme of topological cones has been reappearing in the author’s work in a non-Hausdorff setting motivated by the needs of mathematical… (More)