Bridging Theory and Practice in Implementing EL-MIATTs: Logic-Driven Algorithms for MIATTs Generation and Assessment

Based on the assumption that the true target for a given machine learning task is not assumed to exist as a well-defined object in the real world, the concept of Multiple Inaccurate True Targets (MIATTs) has been proposed to provide a data foundation for the paradigm of Evaluation and Learning with MIATTs (EL-MIATTs), particularly in scenarios where obtaining the true target is difficult, costly, or infeasible. Scientifically generating MIATTs and assessing their quality are pivotal steps in bridging theory and practice to realize the EL-MIATTs framework in real-world applications. In this paper, starting from first principles and leveraging the driving force of logic with necessarily provided resources, we propose two complementary algorithms: an abductive reasoning–driven algorithm for MIATTs generation and a Boolean algebra–driven algorithm for MIATTs assessment. The former enables the construction of MIATTs sets for individual instances by logically abducing plausible approximations of the underlying true target, while the latter provides a principled approach to quantitatively assessing the quality of MIATTs sets through Boolean operations on semantic facts. To further mitigate the multidisciplinary difficulties of implementing these logic-driven algorithms in practice, we also propose two simplified solutions for MIATTs generation and assessment that rely on retrievable real-world resources. Additionally, physical interpretations are presented for MIATTs and their assessment indicators. Together, these contributions to MIATTs generation and assessment strengthen the feasibility of EL-MIATTs in domains where the true target remains uncertain or inaccessible.