Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence (Watson et al., 2021), we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks

Inevitability of Phase-locking in a Charge Pump Phase Lock Loop using Deductive Verification

Phase-locking in a charge pump (CP) phase lock loop (PLL) is said to be inevitable if all possible states of the CP PLL eventually converge to the equilibrium, where the input and output phases are in lock and the node voltages vanish. We verify this property for a CP PLL using deductive verification. We split this complex property into two sub-properties defined in two disjoint subsets of the state space. We deductively verify the first property using multiple Lyapunov certificates for hybrid systems, and use the Escape certificate for the verification of the second property. Construction of deductive certificates involves positivity check of polynomial inequalities (which is an NP-Hard problem), so we use the sound but incomplete Sum of Squares (SOS) relaxation algorithm to provide a numerical solution

Local explanations via necessity and sufficiency: unifying theory and practice

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing explanatory factors with respect to a given context, and demonstrate its flexibility and competitive performance against state of the art alternatives on various tasks