Similarity-Based Equational Inference in Physics
This addresses the problem of automating physics derivations for researchers, but it is incremental as it focuses on a specific task and dataset.
The paper tackles the challenge of automating the derivation of physics results by converting informal hand-written derivations into datasets and using a symbolic similarity-based heuristic search to solve an equation reconstruction task, achieving this as an early step towards multi-hop equational inference.
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 hand-written 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 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.