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Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster

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Abstract

We generalize the incompleteness proof of the modal predicate logic Q-S4+ □⋄p ⊃ ⋄□p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.

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Authors and Affiliations

  1. Department of Mathematics College of Science and Technology, Nihon University, 1-8-14 Kanda Surugadai, Chiyoda-ku, Tokyo, 101-8308, Japan

    Tatsuya Shimura

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  1. Tatsuya Shimura
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Shimura, T. Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster. Studia Logica 65, 237–247 (2000). https://doi.org/10.1023/A:1005219831286

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