Open Access
2015 Halldén Completeness for Relevant Modal Logics
Takahiro Seki
Notre Dame J. Formal Logic 56(2): 333-350 (2015). DOI: 10.1215/00294527-2864334


Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.


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Takahiro Seki. "Halldén Completeness for Relevant Modal Logics." Notre Dame J. Formal Logic 56 (2) 333 - 350, 2015.


Published: 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1339.03020
MathSciNet: MR3337384
Digital Object Identifier: 10.1215/00294527-2864334

Primary: 03B45
Secondary: 03B47

Keywords: Halldén completeness , relevant modal logics , Routley–Meyer semantics , Sahlqvist formulas , van Benthem–Humberstone theorem

Rights: Copyright © 2015 University of Notre Dame

Vol.56 • No. 2 • 2015
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