Publication Date



Technical Report: UTEP-CS-11-22a

To appear in Journal of Uncertain Systems, 2012, Vol. 6, No. 2.


In this paper, we describe how checking whether a givenproperty F is true for a product A1 X A2 of partiallyordered spaces can be reduced to checking several relatedproperties of the original spaces Ai.

This result can be useful in the analysis of propertiesof intervals [a,b] = {x: a <= x <= b}over general partially ordered spaces -- such as the spaceof all vectors with component-wise order or the set of allfunctions with component-wise ordering f <= g <-->for all x (f(x) <= g(x)). When we consider sets of pairs ofsuch objects A1 X A2, it is natural to define the orderon this set in terms of orders in A1 and A2 -- this is, e.g.,how ordering and intervals are defined on the set R2 of all2-D vectors.

This result can also be useful in the analysis of orderedspaces describing different degrees of certainty in expert knowledge.

tr11-22.pdf (87 kB)
Original file: CS-UTEP-11-22