Title：The Quotient-to-Symbol Principle of Human Reasoning

Speaker：Hanyu Li (PKU)

Time: 2024/11/26 15:10-18:00

Location: Room 206, Building of Geometry (地学楼), Peking University

Abstract：

At the heart of human reasoning lies the ability to encode infinite structures into finite symbolic representations, a process central to the development of proofs. In this talk, I further extend this idea with the quotient-to-symbol principle, which emphasizes that different encodings reflect distinct proof tactics and are key to human approaches to proof construction. This talk introduces experimental evidence for this principle from fields such as psychology, linguistics, and cognitive science and explores its transformative applications in theoretical computer science. Specifically, I will demonstrate how machines, guided by human intuition, can perform a range of proofs, including NP reductions and approximation analysis for algorithms for approximate Nash equilibria (ANE) and combinatorial optimization. These applications suggest a new paradigm of human-machine collaboration in algorithm design and analysis: humans focus on high-level creativity and tactics, while machines handle precise computations guided by these tactics.