The Finite Frame Property of Some Extensions of the Pure Logic of Necessitation

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Description

We study the finite frame property of some extensions of Fitting, Marek, and Truszczyński's pure logic of necessitation N. For any natural numbers m,n, we introduce the logic N⁺Aₘ,ₙ by adding the single axiom scheme □ⁿφ→□ᵐφ and the rule ¬□φ/¬□□φ (Ros□) into N. We prove the finite frame property of N⁺Aₘ,ₙ with respect to Fitting, Marek, and Truszczyński's relational semantics. We also prove that for n≥2, the logic obtained by removing the rule Ros□ from N⁺A₀,ₙ is incomplete with respect to that semantics.

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Details 詳細情報について

  • CRID
    1050302237609524224
  • ISSN
    15728730
    00393215
  • HANDLE
    20.500.14094/0100492121
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • IRDB

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