K Altn的另一族正规扩张

Bellissima证明KAltn的正规扩张都是典范的,并且给出了一族连续统多的无有穷模型性的逻辑,本文构造出了KAltn的另一族连续统多的正规扩张,并且证明它们与Bellissima给出的颇为不同,它们要小得多,并且都具有有穷模型性。

Another Normal Extensions of KAltn

The research of canonical problem is one of the important directions of theoretical studies on modal logic. One topic of this research is on the distribution of canonical logics in the lattice of modal logics. Bellissima proved that every normal extension of KAlt is canonical logic and he provided a continuum of logics without finite model property. In this paper, we construct another normal extensions of KAlt. We also show that they are much smaller and they all have finite model property, so they are different from the logics that had been given by Bellissima. The structure of the lattice of extensions of KAltn is more complex.