2019/06/30 by Iwata, Sohei, Kurahashi, Taishi
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1907.00306
It is well known that the propositional modal logic GL of provability satisfies the de Jongh-Sambin fixed-point property. On the other hand, Montagna showed that the predicate modal system QGL, which is the natural variant of GL, loses the fixed-point property. In this paper, we discuss some versions of the fixed-point property for predicate modal logics. First, we prove that several extensions of QGL including NQGL do not have the fixed-point property. Secondly, we prove the fixed-point theorem for the logic QK + \Boxn+1 \bot. As a consequence, we obtain that the class FH of Kripke frames which are transitive and finite height satisfies the fixed-point property locally. We also show the failure of the Craig interpolation property for NQGL. Finally, we give a sufficient condition for formulas to have a fixed-point in QGL.