Following a review of metric, ultrametric and generalized ultrametric, we
review their application in data analysis. We show how they allow us to explore
both geometry and topology of information, starting with measured data. Some
themes are then developed based on the use of metric, ultrametric and
generalized ultrametric in logic. In particular we study approximation chains
in an ultrametric or generalized ultrametric context. Our aim in this work is
to extend the scope of data analysis by facilitating reasoning based on the
data analysis; and to show how quantitative and qualitative data analysis can
be incorporated into logic programming.Comment: 19 pp., 5 figures, 3 table
