Abstraction Logic Is All You Need

Abstraction logic is a minimal yet maximally expressive logical system that serves both as a logic and a logical framework. While existing logics often trade simplicity for expressiveness, abstraction logic achieves both, making it an ideal foundation for machine-learning approaches to theorem proving. Its simplicity enables ML systems to manipulate and adapt it easily, while its expressiveness ensures no practical limitations. We present the core principles of abstraction logic and discuss its unique characteristics that make it well suited for AITP (artificial intelligence theorem proving). This is an extended abstract accepted for Theorem Proving and Machine Learning in the age of LLMs: State of the Art and Future Perspectives. There are also slides available.