Selecting Implications in Fuzzy Abductive Problems

Abductive reasoning is an explanatory process in which potential causes of an observation are unearthed. We have concentrated on the formal definition of fuzzy abduction as an inversion of the Generalised Modus Ponens given by Mellouli and Bouchon-Meunier. While studying this formalism we noticed that some observations could not be explained properly. Observations, in abductive reasoning, are made within the conclusion space of the considered rule. Their potential shape is therefore highly constrained by the implication operator used. We claim that, given a feasible observation and a set of rules, we can categorise the set of implications to be used. Since a given observation will match only part of the conclusions in the rule-set, we offer a categorisation of a rule system coherent with observed data