Toward learning and reasoning in first-order justification logic

In his seminal 1980 paper, Reiter introduced default logic to formalize reasoning with incomplete information. During the 1990s, researchers explored default logic as a qualitative counterpart to inductive-statistical reasoning. A key limitation of Reiter’s original framework is its inability to eliminate unintended extensions, where defeated conclusions, such as Tweety the bird flying despite being a penguin, cannot be retracted. We propose first-order default justification logic as a novel formal system to qualitatively represent uncertainty resulting from learning and generalization. We demonstrate how to encode default reasoning schemas in this system, avoiding the pitfall of unintended extensions. Using (quantifier-free) first-order justification logic, we efficiently formalize rules with exceptions directly in the object language, rendering extra-logical solutions, such as rule prioritization, unnecessary. We establish that the basic system is well-behaved and argue that it offers an intuitive logical foundation for integrating learning and reasoning in artificial intelligence.