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Neighbourhood Semantics for Modal Relevant Logics

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Abstract

In this paper, we investigate neighbourhood semantics for modal extensions of relevant logics. In particular, we combine the neighbourhood interpretation of the relevant implication (and related connectives) with a neighbourhood interpretation of modal operators. We prove completeness for a range of systems and investigate the relations between neighbourhood models and relational models, setting out a range of augmentation conditions for the various relations and operations.

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Authors and Affiliations

  1. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Nicholas Ferenz

  2. Department of Philosophy I, Ruhr University, Bochum, Germany

    Andrew Tedder

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  1. Nicholas Ferenz
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  2. Andrew Tedder
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Correspondence to Nicholas Ferenz.

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We thank Satoru Niki, Shawn Standefer, and two anonymous referees for comments on earlier versions. Ferenz gratefully acknowledges support by RVO 67985807 and by the Czech Science Foundation project GA22-01137S. Tedder gratefully acknowledges the Alexander von Humboldt foundation for fellowship funding.

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Ferenz, N., Tedder, A. Neighbourhood Semantics for Modal Relevant Logics. J Philos Logic 52, 145–181 (2023). https://doi.org/10.1007/s10992-022-09668-2

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