Towards a Formulation of Fuzzy Contrastive Explanations

Explaining a decision requires some properties that have been studied and established in cognitive sciences. An important one is the contrastive nature of explanations: an explanation should answer questions such as "why make decision P rather than Q?". This principle has been formalized recently by T. Miller in a logical framework exploiting knowledge represented as structural causal graphs, with variables taking crisp values. However this framework does not allow us to cope easily with imprecise knowledge or data, nor with imprecise formulations of explanations, that could be preferred in some situations. This paper discusses the principles of such fuzzy extensions of this model, exploring the various levels for integrating fuzzy semantics: it discusses successively (i) the input level, for imprecisely described data instances for which an explanation is required, (ii) the level of the structural causal graph itself, to model imprecise knowledge about the functional relations between the variables involved in the model, and (iii) the output level, to express the explanation, e.g. using fuzzy modalities. The combination of these levels is considered as well. Finally, the paper proposes a discussion about the definition of minimality in the fuzzy framework.