For a Data-Driven Interpretation of Rules, wrt GMP Conclusions, in Abductive Problems

Abductive reasoning is an explanatory process in which potential causes of an observation are unearthed. In its classical { crisp { version it ofiers little lattitude for discovery of new knowledge. Placed in a fuzzy context, abduction can explain observations which did not, originally, exactly match the expected conclusions. Studying the efiects of slight modiflcations through the use of linguistic modiflers was, therefore, of interest in order to describe the extent to which observations can be modifled yet still explained and, possibly, create new knowledge. We will concentrate on the formal deflnition of fuzzy abduction given by Mellouli and Bouchon-Meunier. Our results will be shown to be incompatible with established theories. We will show where this incompatibility comes from and derive from it a selection of fuzzy implication, based on observable data. c