Similarity-Based Equational Inference in Physics

Derivation in physics, in the form of derivation reconstruction of published results, is expensive and difficult to automate, not least because the use of mathematics by physicists is less formal than that of mathematicians. Following demand for informal mathematical datasets, we describe a dataset creation method where we consider a derivation agent as a finite state machine which exists in equational states represented by strings, where transitions can occur through a combination of string operations that mimic mathematics, and defined computer algebra operations. We present the novel dataset PhysAI-DS1 generated by this method, which consists of a curated derivation of a contemporary condensed matter physics result reconstructed using a computer algebra system. We define an equation reconstruction task based on formulating derivation segments as basic units of non-trivial state sequences, with the goal of reconstructing an unknown intermediate state equivalent to one-hop inference, extensible to the multi-hop case. We present a symbolic similarity-based heuristic approach to solve an equation reconstruction task on the PhysAI-DS1 dataset, which employs a set of actions, a knowledge base of symbols and equations, and a computer algebra system, to reconstruct an unknown intermediate state within a sequence of three equational states, grouped together as a derivation unit. Informal derivation comprehension of contemporary results is an important step towards the comprehension and automation of modern physics reasoners.