TheoryGuru: A Mathematica Package to apply Quantifier Elimination

TL;DR

TheoryGuru is a Mathematica package that applies Quantifier Elimination to automate reasoning in economics, enabling proof verification and inconsistency detection of economic theorems.

Contribution

It introduces a user-friendly tool that adapts Quantifier Elimination technology for economists unfamiliar with advanced mathematical software.

Findings

Demonstrated QE's applicability to economic theorems

Showed how TheoryGuru automates proof and inconsistency checks

Lowered barriers for economists to use QE technology

Abstract

We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. There is a great body of work considering QE applications in science and engineering but we demonstrate here that it also has use in the social sciences. We explain how many suggested theorems in economics could either be proven, or even have their hypotheses shown to be inconsistent, automatically via QE. However, economists who this technology could benefit are usually unfamiliar with QE, and the use of mathematical software generally. This motivated the development of a Mathematica Package TheoryGuru, whose purpose is to lower the costs of applying QE to economics. We describe the package's functionality and give examples of its use.