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：本文给出了一种从一阶逻辑公式到关系演算方程的线性规模翻译，该翻译保持有效性与有限有效性。该翻译同时还提供了一种从一阶逻辑公式到一阶逻辑三变量片段公式的保守归约，且其规模亦为线性。