Effectively constructible fixed points in Sacchetti's modal logics of provability

2018/11/30 by Taishi Kurahashi, Kurahashi, Taishi, Yuya Okawa +1
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1811.12827

openalex publication_date 2018/11/30 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

We give a purely syntactical proof of the fixed point theorem for Sacchetti's modal logics \bf K + \Box(\Boxⁿ p → p) → \Box p (n ≥ 2) of provability. From our proof, an effective procedure for constructing fixed points in these logics is obtained. We also show the existence of simple fixed points for particular modal formulas.

Related

• Fixed-point properties for predicate modal logics
• Modal logical aspects of provability predicates and consistency statements
• Provability Interpretation of Propositional and Modal Logics
• Flat modal fixpoint logics with the converse modality
• Arithmetical completeness theorems for monotonic modal logics