Quantitative semantics, topology, and possibility measures
The authors present a new junction between the world of topological spaces and complete lattices. The main objective of this paper is to develop the notion of quantitative predicates in a topological setting that encompasses that of continuous domains, and to provide a dual view of such quantitative predicates as possibility measures on the lattice of opens. Since we may view any complete lattice \(L\) as a topological space in its Scott topology, we obtain another representation of the order dual of the function space \([L^{\text{op}}\to L^{\text{op}}]\); the lattice \(O(L^{\text{op}})\multimap L\). This should open up the possibility of proving new results in the theory of continuous lattices, especially in bi-continuous lattices.
scientific article; zbMATH DE number 1307930
scientific article