Similarity-based equational inference in physics

Abstract

Automating the derivation of published results is a challenge, in part due to the informal use of mathematics by physicists compared to that of mathematicians. Following demand, we describe a method for converting informal handwritten derivations into datasets and present an example dataset crafted from a contemporary result in condensed matter. We define an equation reconstruction task completed by rederiving an unknown intermediate equation posed as a state, taken from three consecutive equational states within a derivation. Derivation automation is achieved via computer algebra system (CAS) by applying string-based CAS-reliant actions to states, which mimic mathematical operations and induce state transitions. We implement a symbolic similarity-based heuristic search to solve the equation reconstruction task as an early step towards multi-hop equational inference in physics.