Studia Logica

, Volume 101, Issue 5, pp 1115–1141

Some Metacomplete Relevant Modal Logics


DOI: 10.1007/s11225-012-9433-8

Cite this article as:
Seki, T. Stud Logica (2013) 101: 1115. doi:10.1007/s11225-012-9433-8


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 logicMetacompletenessPrimenessConsistencyAdmissibility of γ

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.University Evaluation Center, Headquarters for Strategy and PlanningNiigata UniversityNiigata CityJapan