From first order logic to Nd: a data driven reformulation

First order logic FOL ooers a natural way o f modeling domains such as chemistry: a molecule is most adequately described as a graph of atoms linked by simple or double bonds. To o vercome the speciic diiculties of dealing with FOL, this paper presents an automatic mapping from the initial problem domain onto the set of integer vectors IN d , where d is a user-supplied integer. This mapping onto a metric space induces a semi-distance on the problem domain. Within supervised learning, the quality of the reformulation can thus be estimated from the predictive accuracy of a k-nearest neighbor classiier based on this distance. The approach i s v alidated on a real-world problem pertaining to organic chemistry: toxicology prediction.