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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.
Journal
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- Studia Logica
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Studia Logica 2024-11-04
Springer Nature
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Details 詳細情報について
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- CRID
- 1050302237609524224
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- ISSN
- 15728730
- 00393215
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- HANDLE
- 20.500.14094/0100492121
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB