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.

翻译：本文给出一种线性规模的翻译方法，将一阶逻辑公式转化为关系演算方程，并保持有效性和有限有效性。该翻译还提供了一阶逻辑公式到一阶逻辑三变量片段公式的线性规模保守归约。