谓词模态逻辑中变量的严格指派问题

Problem of Rigid Assignment to Variables in Predicate Modal Logic

目前,命题模态逻辑已成为人工智能以及计算机科学等其他领域的有效工具,但谓词模态逻辑却不是。关于谓词模态逻辑还存在着很多的争议和问题。表面上看,在命题模态逻辑中添加相应的量词而得到谓词模态逻辑似乎是一件很简单的事情,但是这些新添加的量词却带来了许多的问题和麻烦,例如,变量的严格指派问题、不变论域与可变论域问题、跨界相等问题等。主要研究谓词模态逻辑中变量的严格指派问题。首先,介绍什么是变量的严格指派问题;其次,讨论对于该问题现有的解决办法及所存在的不足;最后,分析造成该问题的深层次原因,并简要介绍该问题的解决办法。

Propositional modal logic is now an effective tool in artificial intelligence and other areas of computer science, but predicate modal logic is not. There exist many controversies and problems in predicate modal logic. It would seem to be a simple matter to obtain predicate modal logic by adding quantifiers to propositional modal logic. The addition of quantifiers, however, opens the door to a labyrinth full of twists and problems, such as the problem of rigid assignment to variables, the problem with constant domains versus varying domains, and the problem with transworld identity, etc. We mainly discussed the problem of rigid assignment to variables in predicate modal logic. First, we gave an introduction to the problem of rigid assignment to variables. Second,we discussed the shortcomings of existing methods for the pro- blem of rigid assignment to variables. Finally, we proposed our method by analyzing the basic reasons behind the problem of rigid assignment to variables.