数学的基本特征之一,是逻辑推理的严格性以及它的结论的确定性。那末逻辑推理的确切涵义与根据是什么呢?本文试用逻辑代数的观点给以阐述。数学中推理的有效性数学中的命题,大都具有“如果…,那么…”的形式,或者,更简单些可以表为“若p则q”,其中p,q是命题。命题“若p则q”称为“条件命题”或“假言命题”,在逻辑代数中表为“p→q”,p称为前提(条件),q称为结论(终结)。命题p→q的真假由下表给出: One of the basic characteristics of mathematics is the rigor of logical reasoning and the certainty of its conclusion. So what is the exact meaning and basis of logical reasoning? This article tries to elaborate on the viewpoint of logical algebra. Validity of Inference in Mathematics Most of the propositions in mathematics are in the form of “if ..., then ...” or, more simply, in the form “if p then q” where p, q are propositions. The proposition “if p then q” is called a “conditional proposition” or a “hypothetical proposition”, the table in the logical algebra is “p → q”, p is called the premise (condition), and q is the conclusion. Proposition p → q true and false given by the following table: