It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.
@article{1183745939,
author = {Wansing, Heinrich},
title = {Displaying the Modal Logic of Consistency},
journal = {J. Symbolic Logic},
volume = {64},
number = {1},
year = {1999},
pages = { 1573-1590},
language = {en},
url = {http://dml.mathdoc.fr/item/1183745939}
}
Wansing, Heinrich. Displaying the Modal Logic of Consistency. J. Symbolic Logic, Tome 64 (1999) no. 1, pp. 1573-1590. http://gdmltest.u-ga.fr/item/1183745939/