K3, Ł3, LP, RM3, A3, FDE, M: How to Make Many-Valued Logics Work for You

Abstract

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 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 Fitch-style natural deduction system for our augmented FDE, and proofs of soundness and completeness. These rules and proofs are easily modifiable for all the logics we discuss.