Study, design, and implement the [Lyrics] symbolic knowledge injection algorithm

The integration of deep learning and symbolic reasoning is crucial for devel- oping intelligent agents capable of making complex decisions in dynamic envi- ronments. Despite the success of deep learning in numerous applications, the need for higher-level symbolic inference remains essential for achieving true in- telligent behaviour. This report explores the design and implementation of the [Lyrics][3] symbolic knowledge injection algorithm, a versatile interface layer for AI systems built within Pytorch. The [Lyrics] algorithm enables the def- inition and incorporation of First Order Logic (FOL) background knowledge into Pytorch computational graphs. By transforming FOL formulas into real- valued constraints, the algorithm allows for the optimization of learner weights while adhering to predefined knowledge constraints. This approach facilitates the seamless integration of diverse models and knowledge types, enhancing the robustness and generality of AI systems. The effectiveness of the [Lyrics] al- gorithm is demonstrated through various use cases, including model checking, supervised learning, and collective classification, underscoring its potential to advance the development of intelligent and adaptable AI.