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We investigate the notion of distance on domains. In particular, we show that measurement is a fundamental concept underlying partial metrics by proving that a domain in its Scott topology is partially metrizable only if it admits a measurement. Conversely, the natural notion of a distance associated with a measurement not only yields meaningful partial… (More)

This paper is about a generalization of Scott's domain theory in such a way that its definitions and theorems become meaningful in quasimetric spaces. The generalization is achieved by a change of logic: the fundamental concepts of original domain theory (order, way-below relation , Scott-open sets, continuous maps, etc.) are interpreted as predicates that… (More)

Our work is a fundamental study of the notion of approximation in Q-categories and in (U, Q)-categories, for a quantale Q and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of Q-and (U, Q)-categories. We fully characterize continuous Q-categories (resp. (U,… (More)

In this article, we characterise all continuous posets which are partially metrizable in their Scott topology. We present conditions for pmetrizability, which are both necessary and sufficient, in terms of measurements, domain-theoretic bases and, in a more general setting, in terms of radially convex metrics. These conditions, together with their… (More)

This paper presents an architecture for a Personal Travel Assistant (PTA) which can elaborate on a users travel request and evaluate travel offers. Information on user behaviour is stored in a case base in the form of a Case Retrieval Net. This lazy approach has the advantages that it is incremental, extendible and allows flexible reuse of the information.… (More)

We generalize the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann to obtain computational models for separated Q-categories. We fully describe (a) Yoneda complete and (b) continuous Yoneda complete Q-categories via their formal ball models. Our results yield solutions to two open problems in the theory of… (More)

We prove that the category of I-cocomplete separated Q-categories has bilimits of expanding sequences. This result generalises on various levels the well-known theorem of domain theory that guarantees existence of bilimits in the category of directed-complete posets and Scott-continuous maps. In 1973 William Lawvere published a paper (reprinted as (Lawvere… (More)

We provide a method for checking if a given auxiliary relation on a poset is the approximation relation on a domain. 1 Motivation If (P, ⊑) is a partial order, then the approximation (called also the way-below relation) is defined for x, y ∈ P as x ≪ y if and only of for any directed subset D of P , if y ⊑ ↑ D, then x ⊑ d for some d ∈ D (↑ D denotes the… (More)

In this paper we study the interplay between metric and order completeness of semantic domains equipped with generalised distances. We prove that for bounded complete posets directed-completeness and partial metric completeness are interdefinable. Moreover, we demonstrate that Lawson-compact, countably based domains are precisely the compact pmetric spaces… (More)

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