命题对象的空间逻辑运算模型

在现有逻辑系统中,各连接词的运算模型都可以归结为某些“代数算子”,其共同特征是仅考虑了命题所描述集合的代数测度大小,而没有考虑它们在几何空间中的位置关系。文章以“空间位置相关性”为中心,提出了“摸天花板问题”,分析了逻辑运算中存在的几何位置相关性。在“命题对象”、“真位向量”、“空间图像”等概念的基础上,提出了命题对象的空间逻辑运算模型,并结合格分维理论给出了在几何图像中的具体应用形式。本文工作拓展了泛逻辑学中广义相关性的含义,为连接词的运算形式提供了一种新的模型。

The Operation Model of Space Logics on Proposition Objects

In today's logic systems,the operation models of connectives belong to some "algebraic operators". The common characteristic is that they consider only the algebraic measures of sets without the space correlations in the geometrical space. The center idea of the paper is "space correlation". It raises "the problem to touch ceiling",and analyzes the geometrical correlation in logic operations. Based on the conceptions of "proposition object", "truth-value vector" and "space image",authors put forward the operation model of space logics on proposition objects, and give the embodiment of the model in the application of geometrical images under the grid dimension theory. The work en- larges the meanings of general correlation in universal logic,and offers a new kind of model on connective operations.