the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...

G. Plotkin and the author [13] have worked out the equivalence between state transformer semantics and predicate transformer semantics in a domain theoretical setting for programs combining nondeterminism and probability. Works of C. Morgan and co-authors [20], Keimel, Rosenbusch and Streicher [14, 15], already go in the same direction using only discrete state spaces. In fact, Keimel and Plotk...

Given a poset P , the set Γ(P ) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P ) ∼= Γ(Q) implies P ∼= Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not....

Given a poset P , the set, Γ(P), of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos d (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼ = Γ(Q) implies P ∼ = Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Pos d is ...

We show that a measurement μ on a continuous dcpo D extends to a measurement μ̄ on the convex powerdomain CD iff it is a Lebesgue measurement. In particular, kerμ must be metrizable in its relative Scott topology. Moreover, the space ker μ̄ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of kerμ, i.e., the space of nonempty compact subsets of kerμ in its Vietoris topolog...

Rios and Selinger have recently proposed a categorical model for the quantum programming language Proto-Quipper-M, which is an important fragment of the Quipper language. In this work, we describe an extension to their categorical model with the additional property that it is DCPOenriched, bringing us closer to modeling general recursion in the language. Similar to their model, our model exhibi...

As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily-sequential functionals is not ω-complete (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a potentially wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF = PCF + pif (parallel if). Here we will present ...

A model of a space X is simply a continuous dcpo D and a homeomorphism : X ! max D, where max D is given its inherited Scott topology. We show that a space has a coherent model ii it has a Scott domain model and investigate the topological structure of spaces which have G models.

Using the parallel between the preframe and the suplattice approach to locale theory it is shown that the patch construction, as an action on topologies, is the same thing as the process of recovering a discrete poset from its algebraic dcpo (ideal completion).

As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily sequential functionals is not ω-complete and therefore not continuous in the traditional terminology (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF ...