Arithmetical completeness for some extensions of the pure logic of necessitation

2024/09/02 by Kogure, Haruka · 3 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2409.00938

Abstract

We investigate the arithmetical completeness theorems of some extensions of Fitting, Marek, and Truszczyński's pure logic of necessitation N. For m,n ∈ ω, let NA_m,n, which was introduced by Kurahashi and Sato, be the logic obtained from N by adding the axiom scheme \Boxⁿ A → \Box^m A. In this paper, among other things, we prove that for each m,n ≥ 1, the logic NA_m,n becomes a provability logic, that is, there exists a provability predicate Pr_T(x) of T whose T-verifiable modal principles are exactly the logic NA_m,n.

Cited by

• Provability interpretation of non-normal modal logics having neighborhood semantics
• Modal logical aspects of provability predicates and consistency statements
• Refinements of provability and consistency principles for the second incompleteness theorem

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