Annals of the Japan Association for Philosophy of Science
Online ISSN : 1884-1228
Print ISSN : 0453-0691
ISSN-L : 0453-0691
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Fixed-point properties for predicate modal logics
Sohei IWATATaishi KURAHASHI
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2020 Volume 29 Pages 1-25

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Abstract

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 + ▢n+1 ⊥. 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.

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