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次协调逻辑(Paraconsistent logic)这一术语的主要含义是指,在新逻辑中当矛盾律的有效性被削弱之后,仍要保持一种次于经典逻辑的新的协调性。一般来讲,一个次协调逻辑系统应具备两个条件:1、不协调性,即A和_(?)A部是系统的定理;2、不是过完备的(over—complete),即并非系统内的每一公式都是它的定理。由于次协调逻辑体系允许有意义、有价值的矛盾进入形式系统,并否认矛盾律的普遍性,因此它与数理逻辑和辩证逻辑都有密切的联系。自从1963年巴西逻辑学家达科斯塔创立这门学科以来,已吸引了大批逻辑学家、哲学家和数学家,最近几年又引起计算机科学和人工智能研究者的极大关注,现已成为国际逻辑学界一个新兴的研究领域,它的出现将使人们对逻辑科学产生新的理解。在我国,对次协调逻辑的研究还仅处于起步阶段。本文译自巴西逻辑学家阿鲁达(A.I.Arruda)的《次协调逻辑历史发展的若干问题》(‘Aspests of the historical development of paraconsistent logic’)一文的第二部分,它详细介绍了次协调逻辑发展的历史渊源,这对我们进一步理解这种新逻辑将有很大帮助。
The main meaning of the term paraconsistent logic is that after the validity of the contradictions has been weakened in the new logic, there is still to be maintained a new degree of coordination following the classical logic. In general, a sub-coordination logic system should have two conditions: 1. Inconsistency, that is, A and _ (?) A is the systematic theorem; 2. It is not over-complete, Each formula in it is its theorem. Since sub-coordination logic allows meaningful and valuable contradictions to enter the formal system and deny the universality of the law of contradictions, it is closely related to both mathematical logic and dialectical logic. Since the creation of this discipline by Brazilian logicist Da Costa in 1963, it has attracted a large number of logicians, philosophers and mathematicians. In recent years, researchers in computer science and artificial intelligence have drawn great attention and have now become In the emerging field of international logic, its emergence will lead to a new understanding of logic science. In our country, the research on the subordinate coordination logic is only in its infancy. This article is the second in a translation by Brazilian logician AIArruda entitled ’Aspests of the historical development of paraconsistent logic’, which details the logic of subordination The historical origins of development will be of great help in further understanding of this new logic.