K3, L3, LP, RM3, A3, FDE: How to Make Many-Valued Logics Work for You
This work addresses the utility of many-valued logics for logicians and researchers, but it appears incremental as it builds on existing systems with modifications.
The paper tackles the problem of making many-valued logics with 3 or 4 truth values practically useful by adding features to enhance their logical applicability, and it presents surprising results in the system FDE along with new examples of synonymous logics.
We investigate some well-known (and a few not-so-well-known) many-valued logics that have a small number (3 or 4) of truth values. For some of them we complain that they do not have any \emph{logical} use (despite their perhaps having some intuitive semantic interest) and we look at ways to add features so as to make them useful, while retaining their intuitive appeal. At the end, we show some surprising results in the system FDE, and its relationships with features of other logics. We close with some new examples of "synonymous logics." An Appendix contains a natural deduction system for our augmented FDE, and proofs of soundness and completeness.