Abstract
A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus \(\hbox {MML}_n\). Theorems for embedding \(\hbox {MML}_n\) into a Gentzen-type sequent calculus S4C (an extended S4-modal logic) and vice versa are proved. The cut-elimination theorem for \(\hbox {MML}_n\) is shown. A Kripke semantics for \(\hbox {MML}_n\) is introduced, and the completeness theorem with respect to this semantics is proved. Moreover, the duality principle is proved as a characteristic property of \(\hbox {MML}_n\).
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Norihiro Kamide was supported by JSPS KAKENHI Grant (C) JP26330263. Yaroslav Shramko’s work on this paper was a part of Marie Curie project PIRSES-GA-2012-318986 Generalizing Truth Functionality within the Seventh Framework Programme for Research funded by EU.
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Kamide, N., Shramko, Y. Modal Multilattice Logic. Log. Univers. 11, 317–343 (2017). https://doi.org/10.1007/s11787-017-0172-5
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DOI: https://doi.org/10.1007/s11787-017-0172-5