Abstract: 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 problem of rigid assignment to variables. Finally, we proposed our method by analyzing the basic reasons behind the problem of rigid assignment to variables.

Key words: Propositional modal logic, Predicate modal logic, Possible world, Rigid assignment, Ontology