This paper takes a fresh look at the topic of trace semantics in the theory of coalgebras. The first development of coalgebraic trace semantics used final coalgebras in Kleisli categories, stemming from an initial algebra in the underlying category. This approach requires some non-trivial assumptions, like dcpo enrichment, which do not always hold, even in cases where one can reasonably speak o...

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

In this paper we show that three major classes of topological spaces are domain-representable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: T3 subcompact spaces, strongly α-favorable spaces with a Gδ-diagonal or with a base of countable order, and complete quasi-developable T3-spaces. It follows th...

In (Simpson 2003) A. Simpson introduced the category PreDom of topological predomains as a framework for denotational semantics containing also most classical spaces, namely all countably based T0 spaces. Countably based T0 spaces are isomorphic to subspaces of Pω where the latter is endowed with the Scott topology. A qcb space (as introduced in (Menni and Simpson 2002)) is a T0 space which app...

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, do form a directed complete partial ordering. This gives a full characterisation of for which types the partially ordered set of sequential functionals has this property. As a tool, we prove a normal form theorem for the finite sequential functionals of the type...

A construction of fully abstract typed models for PCF and PCF+ (i.e., PCF + “parallel conditional function”), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is...

15 evaluate the correction term for each triple in the left side of table 1, but for brevity of exposition we will evaluate this term only for a sample of each class (T 2 and T 4).

The double lepton pair decay modes of the KL meson are analyzed including all contributions of order p in Chiral Perturbation Theory. The experimentally established eeee mode and the recently observed eeμμ mode are discussed in detail. Typeset using REVTEX 0 In this note we reconsider the double lepton pair decays KL → llll that were studied many years ago by Miyazaki and Takasugi [1]. The two ...

In 1973 William Lawvere published a paper (reprinted as (Lawvere 2002)) where he explained that partial orders and metric spaces are examples of categories enriched in a closed category. Indeed, preorders are categories enriched over the two-element Boolean algebra 2, while (generalized) metric spaces are categories enriched over ([0,∞],+). Lawvere’s idea has been extremely influential in the f...