  In this article, we present a leap-forward expansion to the study of
explainability in neural networks by considering explanations as answers to
abstract reasoning-based questions. With $P$ as the prediction from a neural
network, these questions are `Why P?', `What if not P?', and `Why P, rather
than Q?' for a given contrast prediction $Q$. The answers to these questions
are observed correlations, observed counterfactuals, and observed contrastive
explanations respectively. Together, these explanations constitute the
abductive reasoning scheme. We term the three explanatory schemes as observed
explanatory paradigms. The term observed refers to the specific case of
post-hoc explainability, when an explanatory technique explains the decision
$P$ after a trained neural network has made the decision $P$. The primary
advantage of viewing explanations through the lens of abductive reasoning-based
questions is that explanations can be used as reasons while making decisions.
The post-hoc field of explainability, that previously only justified decisions,
becomes active by being involved in the decision making process and providing
limited, but relevant and contextual interventions. The contributions of this
article are: ($i$) realizing explanations as reasoning paradigms, ($ii$)
providing a probabilistic definition of observed explanations and their
completeness, ($iii$) creating a taxonomy for evaluation of explanations, and
($iv$) positioning gradient-based complete explanainability's replicability and
reproducibility across multiple applications and data modalities, ($v$) code
repositories, publicly available at
https://github.com/olivesgatech/Explanatory-Paradigms.
