A Powerdomain of Possibility Measures

✍ Scribed by Michael Huth

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 780 KB
• Volume: 6
• Category: Article
• ISSN: 1571-0661
• DOI: 10.1016/s1571-0661(05)80161-6

✦ Synopsis

We p r o vide a domain-theoretic framework for possibility theory by studying possibility measures on the lattice of opens O(X) of a topological space X . The powerspaces P 0 1] (X) and P 0 1] (X) o f a l l s u c h maps extend to functors in the natural way. We m a y think of possibility measures as continuous valuations by replacing +' with _' in their modular law. The functors above send continuous maps to sup-maps and continuous domains to completely distributive lattices in the latter case they are locally continuous. Finite suprema of scalar multiples of point v aluations form a basis of the powerdomains above if O(X) is the Scott-topology of a continuous domain. The notions of 0 1]-and 0 1]-modules corresponds to that of continuous cones if addition on the reals and on the module is replaced by suprema. The powerdomain P 0 1] (D) is the free 0 1]-module over a c o n tinuous domain D.