Note on a Translation from First-Order Logic into the Calculus of Relations Preserving Validity and Finite Validity

TL;DR

This paper presents a linear-size translation from first-order logic to the calculus of relations that preserves validity and finite validity, also providing a reduction to the three-variable fragment.

Contribution

It introduces a new linear-size translation method that maintains validity and finite validity, and reduces first-order logic to the three-variable fragment efficiently.

Findings

Linear-size translation preserves validity.

Reduces first-order logic to three-variable fragment.

Efficient conservative reduction achieved.

Abstract

In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from formulas of first-order logic into formulas of the three-variable fragment of first-order logic.