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

IR (HANDLE) Open Access

Search this article

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.

Journal

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

Report a problem

Back to top