The Research Of Non-contingent Logic

In the history of logic, non-contingency modal operator has not been fully researched, the related literature is quite scarce, and the domestic research on this field is totally blank. By inferring Humberstone’s construction of non-contingency logic NCK which uses non-contingency as its sole modal operator, we can get much theorem and valid frames. Based on these, we prove the soundness and completeness of NCK, which shows the non-contingency logic NCK is minimal. And then, starting from the semantic definition of non-contingency, we get the semantic definition of disagreement and build the belief-disagreement logical system and analyze its soundness and completeness.The whole thesis can be divided into five parts:In the introduction part, we briefly introduce the research status and significance of non-contingency. The targets are also mentioned in this part.Chapter one talks about the logical properties of non-contingency. On the one hand, by teasing the logical meaning of contingency, we get to know the logical meaning of non-contingency; On the other hand, we study the question whether non-contingency operator owns an syntactic interactive definition with necessity operator. Based on above conclusion, chapter two focuses on the logical system which talks about non-contingent operator LpvL-p. By inferring Humberstone’s construction, we rebuild the non-contingency logic NCK and prove its soundness and completeness, arguing that NCK is minimal.Chapter three, starting from the semantic definition of non-contingency operator, we get the semantic definition of disagreement operator. By applying this definition, we build belief-disagreement logical system BD and analyze its soundness and completeness.The final part briefly reviews the former conclusions, points out the existing problems in the whole research process and gives a description of possible directions for further research.