Tautologies and contradictions are not pictures of reality.

重言式和矛盾式不是实在的图像。

Generalized tautologies theories of universal logic are studied for the first time.

本文首次对泛逻辑的广义重言式理论进行研究。

Propositions show what they say; tautologies and contradictions show that they say nothing.

命题显示它们所说的东西，重言式和矛盾式则显示它们什么也役有说。

Relationship between tautologies in fuzzy modal logic and valid formulas in basic modal logic is investigated.

研究了模糊模态逻辑中的永真式与基本模态逻辑中的有效公式之间的关系。

Proof in logic is merely a mechanical expedient to facilitate the recognition of tautologies in complicated cases.

逻辑中的证明只是一种使得在复杂的情况下易于辨识重言式的机械的便利方法。