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Displaying the Modal Logic of Consistency

Heinrich Wansing
The Journal of Symbolic Logic
Vol. 64, No. 4 (Dec., 1999), pp. 1573-1590
DOI: 10.2307/2586798
Stable URL: http://www.jstor.org/stable/2586798
Page Count: 18
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Displaying the Modal Logic of Consistency
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Abstract

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.

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