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Alternative Multilattice Logics: An Approach Based on Monosequent and Indexed Monosequent Calculi

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Abstract

Two new multilattice logics called submultilattice logic and indexed multilattice logic are introduced as a monosequent calculus and an indexed monosequent calculus, respectively. The submultilattice logic is regarded as a monosequent calculus version of Shramko’s original multilattice logic, which is also known as the logic of logical multilattices. The indexed multilattice logic is an extension of the submultilattice logic, and is regarded as the logic of multilattices. A completeness theorem with respect to a lattice-valued semantics is proved for the submultilattice logic, and a completeness theorem with respect to a multilattice-valued semantics is proved for the indexed multilattice logic.

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Acknowledgements

We would like to thank the anonymous referees for their valuable comments and suggestions. This research was supported by JSPS KAKENHI Grant Numbers JP18K11171 and JP16KK0007.

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Correspondence to Norihiro Kamide.

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Kamide, N. Alternative Multilattice Logics: An Approach Based on Monosequent and Indexed Monosequent Calculi. Stud Logica 109, 1241–1271 (2021). https://doi.org/10.1007/s11225-020-09939-6

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