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Multiset-Multiset Frames

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Abstract

This paper presents the notion of multiset-multiset frame (mm-frame for short), a frame equipped with a relation between (finite) multisets over the set of points which satisfies the condition called compositionality. This notion is an extension of Restall and Standefer’s multiset frame, a frame that relates a multiset to a single point. While multiset frames serve as frames for the positive fragments of relevant logics RW and R, mm-frames are for the full RW and R with negation. We show this by presenting a way of constructing an mm-frame from any GS-frame, a frame with two dual ternary relations in which the Routley star is definable.

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Acknowledgements

The author is grateful for the discussions and valuable feedback from the audience when an earlier version of this paper was presented at the online workshop “New Directions in Relevant Logic” (November 2022) and “Workshop on the occasion of the UNESCO World Logic Day” at Keio University, Tokyo. The author also thanks the members of “Unscripted” seminar group for their discussions and encouragement for this study. Finally, the author wishes to thank the anonymous reviewers, whose valuable comments have significantly improved this paper.

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  1. Graduate School of Letters, Kyoto University, Kyoto, Japan

    Takuro Onishi

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  1. Takuro Onishi
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Onishi, T. Multiset-Multiset Frames. J Philos Logic (2024). https://doi.org/10.1007/s10992-024-09764-5

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