Three Modern Roles for Logic in AI

Abstract

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems. CCS CONCEPTS • Computing methodologies → Learning in probabilistic graphical models; Logical and relational learning; • Theory of computation → Automated reasoning; Complexity classes; Problems, reductions and completeness.

From Contrastive to Abductive Explanations and Back Again

“…Recent work [15,38,75,76] proposed to relate model-based explanations with prime implicants. All these approaches compute a set of feature values which, if unchanged, are sufficient for the prediction.…”

“…Past work on computing explanations has mostly addressed local (or instance-dependent) explanations [15,16,38,51,69,70,75,76]. Exceptions include for example approaches that distill ML models, e.g.…”

“…In contrast, local (or global) model-based explanations are referred to as rigorous, since these offer the strongest formal guarantees with respect to the underlying ML model. Concrete examples of such rigorous approaches include [15,16,35,[38][39][40][41]43,52,64,[75][76][77].…”

“…For rigorous approaches, the answer to a 'Why prediction π?' question has been referred to as PI-explanations [75,76], abductive explanations [38], but also as (minimal) sufficient reasons [15,16]. (Hereinafter, we use the term abductive explanation because of the other forms of explanations studied in the paper.…”

“…In this paper we focus on the relationship between local abductive and contrastive explanations 2 . One of our contributions is to show how recent approaches for computing rigorous abductive explanations [15,16,38,75,76] can also be exploited for computing contrastive explanations. To our knowledge, this is new.…”