Interactive Theorem Provers: Applications in AI, Opportunities, and Challenges

Abstract

Interactive theorem provers (ITPs) are computer programs in which axioms and a conjecture are stated in a formal language, and a user provides the ITP with relatively high-level steps of a formal proof for the conjecture. Then, by invoking automated theorem provers, the ITP tries to generate low-level steps that fill the gaps between the steps provided by the user, thus forming a complete formal proof of the conjecture. The ITP also checks the entire formal proof against the axioms, thus confirming the soundness of all derivations in the formal proof. In this talk, I will discuss the existing opportunities and potential benefits to applying ITPs to reason about and verify AI concepts, algorithms, and software. I will also discuss the challenges we have to being able to apply ITPs in AI and reap those benefits. I will do so by discussing a number of my previous projects on the application of ITPs to different AI concepts, algorithms, and software systems. These projects span different areas of planning (classical planning, temporal planning, and planning under uncertainty) as well as algorithms with applications in algorithmic game theory, like general graph matching and online matching.