巴坎公式和自由逻辑

Barcan Formulas and Free Logic

在模态谓词逻辑语义学构建的过程中,巴坎公式扮演着重要的角色。以自由逻辑为基础的模态谓词逻辑是对经典模态谓词逻辑的改造。具有较好的柔韧性和宽容度,它可以容纳经典谓词逻辑。用自由逻辑系统解读巴坎公式,增加扩展公理和收缩公理,可以获得常域选择下的模态谓词逻辑。但这种逻辑仍有谜团需要我们去化解。

Barcan formulas play an important role in constructing semantics of quantified modal logic.Quantified modal logic based on free logic improves classic quantified modal logic.It can contain classic quantified modal logic and it is flexible and tolerated.If we interpret Barcan formulas with free logic and add expanding axiom and contract axiom to the free logic,we can obtain a quantified modal logic under the constant domain.But the logic still has problems to be solved by us.