Halldén Completeness for Relevant Modal Logics

Notre Dame Journal of Formal Logic 56 (2):333-350 (2015)
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Abstract

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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Citations of this work

Tracking reasons with extensions of relevant logics.Shawn Standefer - 2019 - Logic Journal of the IGPL 27 (4):543-569.
Neighbourhood Semantics for Modal Relevant Logics.Nicholas Ferenz & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (1):145-181.

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References found in this work

The semantics of entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
Classically complete modal relevant logics.Edwin D. Mares - 1993 - Mathematical Logic Quarterly 39 (1):165-177.
General Frames for Relevant Modal Logics.Takahiro Seki - 2003 - Notre Dame Journal of Formal Logic 44 (2):93-109.

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