Transformation-based constraint-guided Generalised Modus Ponens
Michaël Blot, Marie‐Jeanne Lesot, Marcin Detyniecki · 2016
Generalised Modus Ponens (GMP) allows to perform logical inference in the case where an observation partially matches the premise of an implication, enriching the rule exploitation as compared to binary classical logic. This paper proposes to further enhance the rule exploitation, integrating additional constraints to guide the inference, both to reduce uncertainty in case of partial match and to perform inference in the case of an observation disjoint from the rule premise. These constraints are expressed as logical predicates derived from properties that characterise the observation, in an absolute way or relatively to the rule premise. An extension of GMP is proposed, to take into account the constraints, based on transformation operations applied to the fuzzy sets involved in the rule and the observation. An instantiation to a GMP preserving graduality and ambiguity is established and its validity is proven.