The Logics of Individual Medvedev Frames

2024/12/28 by Zhicheng Chen, Yi Ding, Chen, Zhicheng +1
Social Sciences · #Eastern European Communism and Reforms #FOS: Mathematics #Intelligence, Security, War Strategy #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2412.20178

openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n-Medvedev's logic ML_n be the intuitionistic logic of Medvedev frames based on the non-empty subsets of a set of size n, which we call n-Medvedev frames. While these are tabular logics, after characterizing n-Medvedev frames using the property of having at least n maximal points, we offer a uniform axiomatization of them through a Gabbay-style rule corresponding to this property. Further properties including compactness, disjunction property, and structural completeness of ML_n are explored and compared to those of Medvedev's logic ML.

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