Back to the future: revival of evidence theory and modal logic for robust and interpretable AI

Years ago, when AI research was still predominantly a theoretical endeavor due to the scarcity of data, we developed a multi-valued modal logic interpretation of evidence measures. This work attracted some interest within the research community at the time but was gradually forgotten, even by us. Only recently have we revisited this modal logic interpretation of evidence theory, with the aim of developing neuro-symbolic modelling workflows capable of handling imperfect real-world data. The purpose of this position paper is to highlight the largely unexploited potential of these formalisms and to encourage the research community to further develop them toward more reliable, genuinely reasoning, and interpretable AI models. We begin by providing a concise overview of the key concepts underlying multi-valued mappings, evidence theory, and modal logic, along with our proposed multi-valued modal logic interpretation of evidence measures. We then present recent results demonstrating how these interpretations can be used to learn class expressions in weakly supervised learning scenarios. In addition, we show how these class representations can support reasoning under uncertainty in real-world applications. Finally, we discuss the untapped potential of the evidence-based approach for analyzing and quantifying the complexity of learning tasks, and we outline promising directions for future research.