Topological Separation Principles And Logical Theories
Topological Separation Principles And Logical Theories
复制标题
拓扑分离原理和逻辑理论
作者：
C. Mortensen
本文献给牛顿·达科斯塔，在他的众多成就中，他是第一个致力于对偶直觉主义以产生次相容逻辑（C 系统）的人。本文同样将直觉主义对偶化为次相一致逻辑，但对偶是一种不同的逻辑，即封闭集合逻辑。我们研究拓扑空间的属性（特别是分离属性）与这些空间的逻辑理论之间的相互作用。本文首先从理论的不完备性和不一致的角度对拓扑与模态逻辑、直觉逻辑与次相干逻辑之间的关系进行了简要的考察，得出了T1性质与逻辑理论性质联系起来的充要条件。然后将结果扩展到豪斯多夫空间和正规空间。在最后一节中，这些方法用于改变身份的建模条件。
This paper is dedicated to Newton da Costa, who,among his many achievements, was the first toaim at dualising intuitionism in order to produce paraconsistent logics,the C-systems. This paper similarly dualises intuitionism to aparaconsistent logic, but the dual is a different logic, namely closed setlogic. We study the interaction between the properties of topologicalspaces, particularly separation properties, and logical theories on thosespaces. The paper begins with a brief survey of what is known about therelation between topology and modal logic, intuitionist logic and paraconsistentlogic in respect of the incompleteness and inconsistency of theories.Necessary and sufficient conditions which relate the T1-property to theproperties of logical theories, are obtained. The result is then extendedto Hausdorff and Normal spaces. In the final section these methods areused to vary the modelling conditions for identity.