Exterior Topology and Revision Spaces
John Pais · Journal of Logic and Computation · 1995
A mathematical model of knowledge base revision attempts to faithfully capture an intuitive notion of ‘closest’ new information relative to some given background information. An attempt to topologically characterize this notion of closest information leads naturally to an approach using non-monotonic exterior operators in contrast to standard monotonic interior or closure operators. This paper introduces exterior topology and uses it to create revision spaces. It is shown that a generalized AGM revision algebra may be characterized in terms of a suitable family of revision spaces and that symmetric revision spaces induced by a distance function provide a metric notion of theory change.