Studia Logica

, Volume 101, Issue 5, pp 1115-1141

First online:

Some Metacomplete Relevant Modal Logics

  • Takahiro SekiAffiliated withUniversity Evaluation Center, Headquarters for Strategy and Planning, Niigata University Email author 

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A logic is called metacomplete if formulas that are true in a certain preferred interpretation of that logic are theorems in its metalogic. In the area of relevant logics, metacompleteness is used to prove primeness, consistency, the admissibility of γ and so on. This paper discusses metacompleteness and its applications to a wider class of modal logics based on contractionless relevant logics and their neighbours using Slaney’s metavaluational technique.


Relevant modal logic Metacompleteness Primeness Consistency Admissibility of γ