<i>Fixed-point properties for predicate modal logics</i>

• IWATA Sohei

  Graduate School of System Informatics, Kobe University

• KURAHASHI Taishi

  Graduate School of System Informatics, Kobe University

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.

Journal

• Annals of the Japan Association for Philosophy of Science

  Annals of the Japan Association for Philosophy of Science 29 (0), 1-25, 2020

  Japan Association for Philosophy of Science

Keywords

• Predicate modal logic
• the logic of provability
• Fixed-point theorem.

Details

• CRID: 1391975276377929344
• NII Article ID: 130007940567
• DOI: 10.4288/jafpos.29.0_1
• ISSN: 18841228
• ISSN: 04530691
• HANDLE: 20.500.14094/90009481
• Web Site: https://www.jstage.jst.go.jp/article/jafpos/29/0/29_1/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed