三值自由模态逻辑FML

3-Valued Free Modal Logic FML

FML是以自由逻辑为基础构建起来的一个三值模态谓词逻辑表列系统。若一个词项无所指(空词项)则包含该词项的简单句子无所指(即无真值),FML的偏函数语义模型体现了这一思想。通过借鉴普利斯特的一度衍推系统和菲汀的抽象谓词思想,FML系统刻画了在内涵语境下关于空词项的推理规律。最后,用数模的方法证明了FML的强完全性。

FML is a tableau of modal predicate logic which is based on free logic. If one item has no reference,namely empty item,then the simple proposition including it has no truth value. In FML,the partial-functional semantic model can verify the idea above. Based on Priest's one-degree entailment system and Fitting's predicate abstraction,FML can characterize the inference rules of empty item in multi-value model context. Finally,it can be proved by means of digital analogy that FML is strongly complete.