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

English (英語)

Studia Logica

Springer Nature

2024-11-04

2024-11-14

Published online: 04 November 2024

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.

Finite frame property

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