A probabilistic approximate logic for neuro-symbolic learning and reasoning

• Published in: Journal of logical and algebraic methods in programming 2022-01, Vol.124, p.100719, Article 100719
• Main Authors: Stehr, Mark-Oliver, Kim, Minyoung, Talcott, Carolyn L.
• Format: Article
• Language: English
• Subjects: First-order logic; Machine learning; Neural networks; Neuro-symbolic architecture; Probabilistic logic
• ISSN: 2352-2208
• DOI: 10.1016/j.jlamp.2021.100719

•Probabilistic semantic framework integrating logic and machine learning.•Systematic approach to incorporate domain knowledge (theories/hypotheses) into learning.•Wide range of learning settings and workflows supported (from supervised to unsupervised).•Leverages Maude (symbolic engine) and TensorFlow/Keras (deep learning framework).•Foundation to explore synergies of neuro-symbolic architectures (based on imagination). As witnessed by recent advances in deep learning technologies, neural network models of very high complexity have been successfully applied in many data-rich domains. Challenges remain, however, if the amount of training data is severely limited, which is often the case due to the cost of acquiring such data or due to interest in systems that are constantly evolving thereby imposing natural limits on how much data can be collected. The core hypothesis explored in this paper is that data (to some degree) can be substituted by domain knowledge, not only addressing the limited data problem but also offering potential improvements in data-rich settings. For the representation of suitable domain theories, we propose Probabilistic Approximate Logic (PALO) to deal with the natural uncertainty associated with such representations and also to serve as a foundation for a new class of neuro-symbolic architectures, in which both neural and symbolic computations can be peacefully and synergistically integrated. Utilizing TensorFlow and Maude as neural and symbolic frameworks, respectively, we discuss our prototypical implementation of PALO in what we call the Logical Imagination Engine (LIME). By means of a small toy example, we convey a glimpse of its capabilities, but we also briefly discuss some real-world applications and how it may serve as a prototypical framework to explore a broader range of neuro-symbolic strategies in the future.