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Following a review of metric, ultrametric and generalized ultrametric, wereview their application in data analysis. We show how they allow us to exploreboth geometry and topology of information, starting with measured data. Somethemes are then developed based on the use of metric, ultrametric andgeneralized ultrametric in logic. In particular we study approximation chainsin an ultrametric or generalized ultrametric context. Our aim in this work isto extend the scope of data analysis by facilitating reasoning based on thedata analysis; and to show how quantitative and qualitative data analysis canbe incorporated into logic programming.

Ultrametric and Generalized Ultrametric in Computational Logic and in Data Analysis